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<h2> <a href="maths.html"> ⇦ Back to the Maths chapter list</a></h2>
<section class="sv-section">
<h1>Finance, growth and decay</h1>
<section class="sv-section">
<h2>1. Revision</h2>
<hr><section class="sv-section sv-question sv-table"><br><div class="id312-9001">ID is: 312 Seed is: 9001<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/7d0c3007-0e0d-5f51-b370-3210d312622f" method="POST">
<span class="worked_example"><h3 class="sv-heading">Inflation: finding an original price</h3>
</span><div class="problem">
<p>
A box of nuttfluffs costs <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-1-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace" /><mtext>18</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1" style="width: 2.286em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.876em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.82em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-2"><span class="mtext" id="MathJax-Span-3" style="font-family: STIXGeneral;">R</span><span class="mspace" id="MathJax-Span-4" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mtext" id="MathJax-Span-5" style="font-family: STIXGeneral;">18</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace"></mspace><mtext>18</mtext></math></span></span><script type="math/tex" id="MathJax-Element-1">\text{R}\,\text{18}</script></span> today.
</p>
<p>
How much did it cost <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-2-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>6</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-6" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-7"><span class="mtext" id="MathJax-Span-8" style="font-family: STIXGeneral;">6</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>6</mtext></math></span></span><script type="math/tex" id="MathJax-Element-2">\text{6}</script></span> years ago if the average rate of inflation was <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-3-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>5</mtext><mi mathvariant="normal">&#x0025;</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-9" style="width: 1.525em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.232em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.17em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-10"><span class="mtext" id="MathJax-Span-11" style="font-family: STIXGeneral;">5</span><span class="mi" id="MathJax-Span-12" style="font-family: STIXGeneral;">%</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>5</mtext><mi mathvariant="normal">%</mi></math></span></span><script type="math/tex" id="MathJax-Element-3">\text{5}\%</script></span> p.a.? <br>
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
Round your answer to two decimal places.
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
The cost <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-4-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>6</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-13" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-14"><span class="mtext" id="MathJax-Span-15" style="font-family: STIXGeneral;">6</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>6</mtext></math></span></span><script type="math/tex" id="MathJax-Element-4">\text{6}</script></span> years ago was R <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="13,43" size="10">.
<div class="response-type">numeric</div></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:06:49.879151"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><section class="sv-section sv-question sv-table"><br><div class="id312-945">ID is: 312 Seed is: 945<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/7d0c3007-0e0d-5f51-b370-3210d312622f" method="POST">
<span class="worked_example"><h3 class="sv-heading">Inflation: finding an original price</h3>
</span><div class="problem">
<p>
A box of yum-yums costs <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-5-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace" /><mtext>22</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-16" style="width: 2.286em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.876em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.88em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-17"><span class="mtext" id="MathJax-Span-18" style="font-family: STIXGeneral;">R</span><span class="mspace" id="MathJax-Span-19" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mtext" id="MathJax-Span-20" style="font-family: STIXGeneral;">22</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace"></mspace><mtext>22</mtext></math></span></span><script type="math/tex" id="MathJax-Element-5">\text{R}\,\text{22}</script></span> today.
</p>
<p>
How much did it cost <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-6-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>7</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-21" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-22"><span class="mtext" id="MathJax-Span-23" style="font-family: STIXGeneral;">7</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>7</mtext></math></span></span><script type="math/tex" id="MathJax-Element-6">\text{7}</script></span> years ago if the average rate of inflation was <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-7-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>8</mtext><mi mathvariant="normal">&#x0025;</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-24" style="width: 1.525em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.232em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.17em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-25"><span class="mtext" id="MathJax-Span-26" style="font-family: STIXGeneral;">8</span><span class="mi" id="MathJax-Span-27" style="font-family: STIXGeneral;">%</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>8</mtext><mi mathvariant="normal">%</mi></math></span></span><script type="math/tex" id="MathJax-Element-7">\text{8}\%</script></span> p.a.? <br>
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
Round your answer to two decimal places.
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
The cost <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-8-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>7</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-28" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-29"><span class="mtext" id="MathJax-Span-30" style="font-family: STIXGeneral;">7</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>7</mtext></math></span></span><script type="math/tex" id="MathJax-Element-8">\text{7}</script></span> years ago was R <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="12,84" size="10">.
<div class="response-type">numeric</div></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:06:49.896199"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id317-2220">ID is: 317 Seed is: 2220<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/7d0c3007-0e0d-5f51-b370-3210d312622f" method="POST">
<span class="worked_example"><h3 class="sv-heading">Inflation </h3>
</span><div class="problem">
<p>
The price of a bag of potatoes is <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-9-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace" /><mtext>16</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-31" style="width: 2.286em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.876em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.82em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-32"><span class="mtext" id="MathJax-Span-33" style="font-family: STIXGeneral;">R</span><span class="mspace" id="MathJax-Span-34" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mtext" id="MathJax-Span-35" style="font-family: STIXGeneral;">16</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace"></mspace><mtext>16</mtext></math></span></span><script type="math/tex" id="MathJax-Element-9">\text{R}\,\text{16}</script></span>. How much will it cost in <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-10-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>6</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-36" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-37"><span class="mtext" id="MathJax-Span-38" style="font-family: STIXGeneral;">6</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>6</mtext></math></span></span><script type="math/tex" id="MathJax-Element-10">\text{6}</script></span> years time if the inflation rate is <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-11-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>5</mtext><mi mathvariant="normal">&#x0025;</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-39" style="width: 1.525em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.232em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.17em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-40"><span class="mtext" id="MathJax-Span-41" style="font-family: STIXGeneral;">5</span><span class="mi" id="MathJax-Span-42" style="font-family: STIXGeneral;">%</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>5</mtext><mi mathvariant="normal">%</mi></math></span></span><script type="math/tex" id="MathJax-Element-11">\text{5}\%</script></span> p.a.?
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
Write your answer in rands and cents (it should have the form <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-12-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>0,00</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-43" style="width: 2.169em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.759em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.76em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-44"><span class="mtext" id="MathJax-Span-45" style="font-family: STIXGeneral;">0,00</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>0,00</mtext></math></span></span><script type="math/tex" id="MathJax-Element-12">\text{0,00}</script></span>).
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
The price will be <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-13-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-46" style="width: 0.823em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.647em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1000.65em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-47"><span class="mtext" id="MathJax-Span-48" style="font-family: STIXGeneral;">R</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext></math></span></span><script type="math/tex" id="MathJax-Element-13">\text{R}</script></span> <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="21,44" size="10">.
<div class="response-type">numeric</div></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:06:49.914237"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><section class="sv-section sv-question sv-table"><br><div class="id317-5097">ID is: 317 Seed is: 5097<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/7d0c3007-0e0d-5f51-b370-3210d312622f" method="POST">
<span class="worked_example"><h3 class="sv-heading">Inflation </h3>
</span><div class="problem">
<p>
The price of 2 litres of milk is <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-14-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace" /><mtext>16</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-49" style="width: 2.286em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.876em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.82em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-50"><span class="mtext" id="MathJax-Span-51" style="font-family: STIXGeneral;">R</span><span class="mspace" id="MathJax-Span-52" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mtext" id="MathJax-Span-53" style="font-family: STIXGeneral;">16</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace"></mspace><mtext>16</mtext></math></span></span><script type="math/tex" id="MathJax-Element-14">\text{R}\,\text{16}</script></span>. How much will it cost in <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-15-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>3</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-54" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-55"><span class="mtext" id="MathJax-Span-56" style="font-family: STIXGeneral;">3</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>3</mtext></math></span></span><script type="math/tex" id="MathJax-Element-15">\text{3}</script></span> years time if the inflation rate is <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-16-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>4</mtext><mi mathvariant="normal">&#x0025;</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-57" style="width: 1.525em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.232em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.17em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-58"><span class="mtext" id="MathJax-Span-59" style="font-family: STIXGeneral;">4</span><span class="mi" id="MathJax-Span-60" style="font-family: STIXGeneral;">%</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>4</mtext><mi mathvariant="normal">%</mi></math></span></span><script type="math/tex" id="MathJax-Element-16">\text{4}\%</script></span> p.a.?
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
Write your answer in rands and cents (it should have the form <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-17-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>0,00</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-61" style="width: 2.169em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.759em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.76em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-62"><span class="mtext" id="MathJax-Span-63" style="font-family: STIXGeneral;">0,00</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>0,00</mtext></math></span></span><script type="math/tex" id="MathJax-Element-17">\text{0,00}</script></span>).
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
The price will be <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-18-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-64" style="width: 0.823em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.647em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1000.65em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-65"><span class="mtext" id="MathJax-Span-66" style="font-family: STIXGeneral;">R</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext></math></span></span><script type="math/tex" id="MathJax-Element-18">\text{R}</script></span> <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="18" size="10">.
<div class="response-type">numeric</div></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:06:49.931058"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id318-3172">ID is: 318 Seed is: 3172<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/7d0c3007-0e0d-5f51-b370-3210d312622f" method="POST">
<span class="worked_example"><h3 class="sv-heading">Compound interest investment</h3>
</span><div class="problem">
<p>
Kelly wants to invest some money at a compound interest rate of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-19-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>13,3</mtext><mi mathvariant="normal">&#x0025;</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-67" style="width: 3.106em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.52em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.46em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-68"><span class="mtext" id="MathJax-Span-69" style="font-family: STIXGeneral;">13,3</span><span class="mi" id="MathJax-Span-70" style="font-family: STIXGeneral;">%</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>13,3</mtext><mi mathvariant="normal">%</mi></math></span></span><script type="math/tex" id="MathJax-Element-19">\text{13,3}\%</script></span> p.a.
</p>
<p>
How much money should be invested if she wants to reach a sum of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-20-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace" /><mtext>54&#xA0;300</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-71" style="width: 4.394em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.574em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1003.57em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-72"><span class="mtext" id="MathJax-Span-73" style="font-family: STIXGeneral;">R</span><span class="mspace" id="MathJax-Span-74" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mtext" id="MathJax-Span-75" style="font-family: STIXGeneral;">54 300</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace"></mspace><mtext>54 300</mtext></math></span></span><script type="math/tex" id="MathJax-Element-20">\text{R}\,\text{54 300}</script></span> in <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-21-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>5</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-76" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-77"><span class="mtext" id="MathJax-Span-78" style="font-family: STIXGeneral;">5</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>5</mtext></math></span></span><script type="math/tex" id="MathJax-Element-21">\text{5}</script></span> years' time?
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
Round <strong>up</strong> your answer to the nearest rand.
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
Kelly must invest R <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="29 084" size="10">.
<div class="response-type">numeric</div></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:06:49.950206"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><section class="sv-section sv-question sv-table"><br><div class="id318-721">ID is: 318 Seed is: 721<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/7d0c3007-0e0d-5f51-b370-3210d312622f" method="POST">
<span class="worked_example"><h3 class="sv-heading">Compound interest investment</h3>
</span><div class="problem">
<p>
Mathe wants to invest some money at a compound interest rate of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-22-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>9,3</mtext><mi mathvariant="normal">&#x0025;</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-79" style="width: 2.462em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.994em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.93em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-80"><span class="mtext" id="MathJax-Span-81" style="font-family: STIXGeneral;">9,3</span><span class="mi" id="MathJax-Span-82" style="font-family: STIXGeneral;">%</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>9,3</mtext><mi mathvariant="normal">%</mi></math></span></span><script type="math/tex" id="MathJax-Element-22">\text{9,3}\%</script></span> p.a.
</p>
<p>
How much money should be invested if she wants to reach a sum of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-23-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace" /><mtext>19&#xA0;200</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-83" style="width: 4.394em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.574em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1003.57em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-84"><span class="mtext" id="MathJax-Span-85" style="font-family: STIXGeneral;">R</span><span class="mspace" id="MathJax-Span-86" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mtext" id="MathJax-Span-87" style="font-family: STIXGeneral;">19 200</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace"></mspace><mtext>19 200</mtext></math></span></span><script type="math/tex" id="MathJax-Element-23">\text{R}\,\text{19 200}</script></span> in <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-24-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>7</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-88" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-89"><span class="mtext" id="MathJax-Span-90" style="font-family: STIXGeneral;">7</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>7</mtext></math></span></span><script type="math/tex" id="MathJax-Element-24">\text{7}</script></span> years' time?
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
Round <strong>up</strong> your answer to the nearest rand.
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
Mathe must invest R <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="10 303" size="10">.
<div class="response-type">numeric</div></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:06:49.968003"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id310-3300">ID is: 310 Seed is: 3300<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/7d0c3007-0e0d-5f51-b370-3210d312622f" method="POST">
<span class="worked_example"><h3 class="sv-heading">Compound interest investment</h3>
</span><div class="problem">
<p>
An amount of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-25-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace" /><mtext>3&#xA0;840</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-91" style="width: 3.809em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.106em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1003.11em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-92"><span class="mtext" id="MathJax-Span-93" style="font-family: STIXGeneral;">R</span><span class="mspace" id="MathJax-Span-94" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mtext" id="MathJax-Span-95" style="font-family: STIXGeneral;">3 840</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace"></mspace><mtext>3 840</mtext></math></span></span><script type="math/tex" id="MathJax-Element-25">\text{R}\,\text{3 840}</script></span> is invested in a savings account which pays a compound interest rate of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-26-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>11,8</mtext><mi mathvariant="normal">&#x0025;</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-96" style="width: 3.106em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.52em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.46em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-97"><span class="mtext" id="MathJax-Span-98" style="font-family: STIXGeneral;">11,8</span><span class="mi" id="MathJax-Span-99" style="font-family: STIXGeneral;">%</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>11,8</mtext><mi mathvariant="normal">%</mi></math></span></span><script type="math/tex" id="MathJax-Element-26">\text{11,8}\%</script></span> p.a.
</p>
<p>
Calculate the balance accumulated by the end of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-27-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>8</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-100" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-101"><span class="mtext" id="MathJax-Span-102" style="font-family: STIXGeneral;">8</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>8</mtext></math></span></span><script type="math/tex" id="MathJax-Element-27">\text{8}</script></span> years. As usual with financial calculations, round your answer to two decimal places, but do not round off until you have reached the solution.
</p>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
The final balance is R <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="9 372,72" size="10">.
<div class="response-type">numeric</div></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:06:49.996233"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><section class="sv-section sv-question sv-table"><br><div class="id310-2714">ID is: 310 Seed is: 2714<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/7d0c3007-0e0d-5f51-b370-3210d312622f" method="POST">
<span class="worked_example"><h3 class="sv-heading">Compound interest investment</h3>
</span><div class="problem">
<p>
An amount of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-28-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace" /><mtext>3&#xA0;660</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-103" style="width: 3.809em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.106em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1003.11em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-104"><span class="mtext" id="MathJax-Span-105" style="font-family: STIXGeneral;">R</span><span class="mspace" id="MathJax-Span-106" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mtext" id="MathJax-Span-107" style="font-family: STIXGeneral;">3 660</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace"></mspace><mtext>3 660</mtext></math></span></span><script type="math/tex" id="MathJax-Element-28">\text{R}\,\text{3 660}</script></span> is invested in a savings account which pays a compound interest rate of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-29-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>11,3</mtext><mi mathvariant="normal">&#x0025;</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-108" style="width: 3.106em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.52em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.46em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-109"><span class="mtext" id="MathJax-Span-110" style="font-family: STIXGeneral;">11,3</span><span class="mi" id="MathJax-Span-111" style="font-family: STIXGeneral;">%</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>11,3</mtext><mi mathvariant="normal">%</mi></math></span></span><script type="math/tex" id="MathJax-Element-29">\text{11,3}\%</script></span> p.a.
</p>
<p>
Calculate the balance accumulated by the end of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-30-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>2</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-112" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.53em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-113"><span class="mtext" id="MathJax-Span-114" style="font-family: STIXGeneral;">2</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>2</mtext></math></span></span><script type="math/tex" id="MathJax-Element-30">\text{2}</script></span> years. As usual with financial calculations, round your answer to two decimal places, but do not round off until you have reached the solution.
</p>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
The final balance is R <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="4 533,89" size="10">.
<div class="response-type">numeric</div></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:06:50.019322"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id1306-9260">ID is: 1306 Seed is: 9260<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/7d0c3007-0e0d-5f51-b370-3210d312622f" method="POST">
<span class="worked_example"><h3 class="sv-heading">Applications of exponentials: population growth</h3>
</span><div class="problem">
<p>
A type of bacteria has a very high exponential growth rate of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-31-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>30%</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-115" style="width: 2.169em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.759em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.7em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-116"><span class="mtext" id="MathJax-Span-117" style="font-family: STIXGeneral;">30%</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>30%</mtext></math></span></span><script type="math/tex" id="MathJax-Element-31">\text{30%}</script></span> every hour. If there are initially <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-32-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>22</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-118" style="width: 1.232em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.998em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-119"><span class="mtext" id="MathJax-Span-120" style="font-family: STIXGeneral;">22</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>22</mtext></math></span></span><script type="math/tex" id="MathJax-Element-32">\text{22}</script></span> individual bacteria cells in the population, determine how many there will be in <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-33-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>12</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-121" style="width: 1.232em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.998em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-122"><span class="mtext" id="MathJax-Span-123" style="font-family: STIXGeneral;">12</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>12</mtext></math></span></span><script type="math/tex" id="MathJax-Element-33">\text{12}</script></span> hours. Use the formula here to answer the question.
</p>
<p class="centre">
<span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-34-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle mathsize="0.85em"><mtext>Population</mtext><mo>=</mo><mspace width="thinmathspace" /></mstyle></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-124" style="width: 6.385em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.214em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.584em, 1005.21em, 2.813em, -999.997em); top: -2.398em; left: 0em;"><span class="mrow" id="MathJax-Span-125"><span class="mstyle" id="MathJax-Span-126"><span class="mrow" id="MathJax-Span-127"><span class="mtext" id="MathJax-Span-128" style="font-size: 95.6%; font-family: STIXGeneral;">Population</span><span class="mo" id="MathJax-Span-129" style="font-size: 95.6%; font-family: STIXGeneral; padding-left: 0.296em;">=</span><span class="mspace" id="MathJax-Span-130" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.403em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.354em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle mathsize="0.85em"><mtext>Population</mtext><mo>=</mo><mspace width="thinmathspace"></mspace></mstyle></math></span></span><script type="math/tex" id="MathJax-Element-34">\small\text{Population} =\,</script></span> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-35-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle mathsize="0.85em"><mtext>Initial population</mtext><mstyle mathsize="1em" /></mstyle></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-131" style="width: 8.083em; display: inline-block;"><span style="display: inline-block; position: relative; width: 6.619em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.584em, 1006.62em, 2.813em, -999.997em); top: -2.398em; left: 0em;"><span class="mrow" id="MathJax-Span-132"><span class="mstyle" id="MathJax-Span-133"><span class="mrow" id="MathJax-Span-134"><span class="mtext" id="MathJax-Span-135" style="font-size: 95.6%; font-family: STIXGeneral;">Initial population</span><span class="mstyle" id="MathJax-Span-136"><span class="mrow" id="MathJax-Span-137"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.403em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.354em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle mathsize="0.85em"><mtext>Initial population</mtext><mstyle mathsize="1em"></mstyle></mstyle></math></span></span><script type="math/tex" id="MathJax-Element-35">\small\text{Initial population}\normalsize </script></span> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-36-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x00D7;</mo><mspace width="thinmathspace" /><msup><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mstyle mathsize="0.85em"><mtext>growth rate</mtext><mstyle mathsize="1em" /></mstyle><mo>)</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mstyle mathsize="0.85em"><mtext>time in hours</mtext></mstyle></mrow></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-138" style="width: 13.645em; display: inline-block;"><span style="display: inline-block; position: relative; width: 11.186em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.467em, 1011.19em, 2.93em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-139"><span class="mo" id="MathJax-Span-140" style="font-family: STIXGeneral;">×</span><span class="mspace" id="MathJax-Span-141" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="msubsup" id="MathJax-Span-142"><span style="display: inline-block; position: relative; width: 10.366em; height: 0px;"><span style="position: absolute; clip: rect(3.106em, 1006.68em, 4.394em, -999.997em); top: -3.978em; left: 0em;"><span class="mrow" id="MathJax-Span-143"><span class="mo" id="MathJax-Span-144" style="vertical-align: 0em;"><span style="font-family: STIXGeneral;">(</span></span><span class="mn" id="MathJax-Span-145" style="font-family: STIXGeneral;">1</span><span class="mo" id="MathJax-Span-146" style="font-family: STIXGeneral; padding-left: 0.237em;">+</span><span class="mstyle" id="MathJax-Span-147" style="padding-left: 0.237em;"><span class="mrow" id="MathJax-Span-148"><span class="mtext" id="MathJax-Span-149" style="font-size: 95.6%; font-family: STIXGeneral;">growth rate</span><span class="mstyle" id="MathJax-Span-150"><span class="mrow" id="MathJax-Span-151"></span></span></span></span><span class="mo" id="MathJax-Span-152" style="vertical-align: 0em;"><span style="font-family: STIXGeneral;">)</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.388em; left: 6.736em;"><span class="texatom" id="MathJax-Span-153"><span class="mrow" id="MathJax-Span-154"><span class="mstyle" id="MathJax-Span-155"><span class="mrow" id="MathJax-Span-156"><span class="mtext" id="MathJax-Span-157" style="font-size: 67.6%; font-family: STIXGeneral;">time in hours</span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.354em; border-left: 0px solid; width: 0px; height: 1.432em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>×</mo><mspace width="thinmathspace"></mspace><msup><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mstyle mathsize="0.85em"><mtext>growth rate</mtext><mstyle mathsize="1em"></mstyle></mstyle><mo>)</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mstyle mathsize="0.85em"><mtext>time in hours</mtext></mstyle></mrow></msup></math></span></span><script type="math/tex" id="MathJax-Element-36">\times \, \left(1 + \small\text{growth rate}\normalsize\right)^{\small\text{time in hours}}</script></span>
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
Round your answer to the <strong>nearest whole number</strong>.
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
There will be <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="513" size="10"> bacteria cells (rounded to the nearest whole number). <br>
<div class="response-type">numeric</div></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:06:50.048331"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><section class="sv-section sv-question sv-table"><br><div class="id1306-2110">ID is: 1306 Seed is: 2110<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/7d0c3007-0e0d-5f51-b370-3210d312622f" method="POST">
<span class="worked_example"><h3 class="sv-heading">Applications of exponentials: population growth</h3>
</span><div class="problem">
<p>
A type of bacteria has a very high exponential growth rate of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-37-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>40%</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-158" style="width: 2.169em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.759em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.7em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-159"><span class="mtext" id="MathJax-Span-160" style="font-family: STIXGeneral;">40%</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>40%</mtext></math></span></span><script type="math/tex" id="MathJax-Element-37">\text{40%}</script></span> every hour. If there are initially <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-38-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>31</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-161" style="width: 1.232em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.998em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.88em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-162"><span class="mtext" id="MathJax-Span-163" style="font-family: STIXGeneral;">31</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>31</mtext></math></span></span><script type="math/tex" id="MathJax-Element-38">\text{31}</script></span> individual bacteria cells in the population, determine how many there will be in <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-39-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>6</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-164" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-165"><span class="mtext" id="MathJax-Span-166" style="font-family: STIXGeneral;">6</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>6</mtext></math></span></span><script type="math/tex" id="MathJax-Element-39">\text{6}</script></span> hours. Use the formula here to answer the question.
</p>
<p class="centre">
<span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-40-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle mathsize="0.85em"><mtext>Population</mtext><mo>=</mo><mspace width="thinmathspace" /></mstyle></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-167" style="width: 6.385em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.214em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.584em, 1005.21em, 2.813em, -999.997em); top: -2.398em; left: 0em;"><span class="mrow" id="MathJax-Span-168"><span class="mstyle" id="MathJax-Span-169"><span class="mrow" id="MathJax-Span-170"><span class="mtext" id="MathJax-Span-171" style="font-size: 95.6%; font-family: STIXGeneral;">Population</span><span class="mo" id="MathJax-Span-172" style="font-size: 95.6%; font-family: STIXGeneral; padding-left: 0.296em;">=</span><span class="mspace" id="MathJax-Span-173" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.403em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.354em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle mathsize="0.85em"><mtext>Population</mtext><mo>=</mo><mspace width="thinmathspace"></mspace></mstyle></math></span></span><script type="math/tex" id="MathJax-Element-40">\small\text{Population} =\,</script></span> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-41-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle mathsize="0.85em"><mtext>Initial population</mtext><mstyle mathsize="1em" /></mstyle></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-174" style="width: 8.083em; display: inline-block;"><span style="display: inline-block; position: relative; width: 6.619em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.584em, 1006.62em, 2.813em, -999.997em); top: -2.398em; left: 0em;"><span class="mrow" id="MathJax-Span-175"><span class="mstyle" id="MathJax-Span-176"><span class="mrow" id="MathJax-Span-177"><span class="mtext" id="MathJax-Span-178" style="font-size: 95.6%; font-family: STIXGeneral;">Initial population</span><span class="mstyle" id="MathJax-Span-179"><span class="mrow" id="MathJax-Span-180"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.403em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.354em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle mathsize="0.85em"><mtext>Initial population</mtext><mstyle mathsize="1em"></mstyle></mstyle></math></span></span><script type="math/tex" id="MathJax-Element-41">\small\text{Initial population}\normalsize </script></span> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-42-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x00D7;</mo><mspace width="thinmathspace" /><msup><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mstyle mathsize="0.85em"><mtext>growth rate</mtext><mstyle mathsize="1em" /></mstyle><mo>)</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mstyle mathsize="0.85em"><mtext>time in hours</mtext></mstyle></mrow></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-181" style="width: 13.645em; display: inline-block;"><span style="display: inline-block; position: relative; width: 11.186em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.467em, 1011.19em, 2.93em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-182"><span class="mo" id="MathJax-Span-183" style="font-family: STIXGeneral;">×</span><span class="mspace" id="MathJax-Span-184" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="msubsup" id="MathJax-Span-185"><span style="display: inline-block; position: relative; width: 10.366em; height: 0px;"><span style="position: absolute; clip: rect(3.106em, 1006.68em, 4.394em, -999.997em); top: -3.978em; left: 0em;"><span class="mrow" id="MathJax-Span-186"><span class="mo" id="MathJax-Span-187" style="vertical-align: 0em;"><span style="font-family: STIXGeneral;">(</span></span><span class="mn" id="MathJax-Span-188" style="font-family: STIXGeneral;">1</span><span class="mo" id="MathJax-Span-189" style="font-family: STIXGeneral; padding-left: 0.237em;">+</span><span class="mstyle" id="MathJax-Span-190" style="padding-left: 0.237em;"><span class="mrow" id="MathJax-Span-191"><span class="mtext" id="MathJax-Span-192" style="font-size: 95.6%; font-family: STIXGeneral;">growth rate</span><span class="mstyle" id="MathJax-Span-193"><span class="mrow" id="MathJax-Span-194"></span></span></span></span><span class="mo" id="MathJax-Span-195" style="vertical-align: 0em;"><span style="font-family: STIXGeneral;">)</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.388em; left: 6.736em;"><span class="texatom" id="MathJax-Span-196"><span class="mrow" id="MathJax-Span-197"><span class="mstyle" id="MathJax-Span-198"><span class="mrow" id="MathJax-Span-199"><span class="mtext" id="MathJax-Span-200" style="font-size: 67.6%; font-family: STIXGeneral;">time in hours</span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.354em; border-left: 0px solid; width: 0px; height: 1.432em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>×</mo><mspace width="thinmathspace"></mspace><msup><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mstyle mathsize="0.85em"><mtext>growth rate</mtext><mstyle mathsize="1em"></mstyle></mstyle><mo>)</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mstyle mathsize="0.85em"><mtext>time in hours</mtext></mstyle></mrow></msup></math></span></span><script type="math/tex" id="MathJax-Element-42">\times \, \left(1 + \small\text{growth rate}\normalsize\right)^{\small\text{time in hours}}</script></span>
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
Round your answer to the <strong>nearest whole number</strong>.
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
There will be <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="233" size="10"> bacteria cells (rounded to the nearest whole number). <br>
<div class="response-type">numeric</div></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:06:50.072861"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id1307-9867">ID is: 1307 Seed is: 9867<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/7d0c3007-0e0d-5f51-b370-3210d312622f" method="POST">
<span class="worked_example"><h3 class="sv-heading">Applications of exponentials: populations of rare species</h3>
</span><div class="problem">
<p>
A species of extremely rare shark has a very long lifespan and seldom has children. If there are a total of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-43-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>208</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-201" style="width: 1.876em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.525em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-202"><span class="mtext" id="MathJax-Span-203" style="font-family: STIXGeneral;">208</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>208</mtext></math></span></span><script type="math/tex" id="MathJax-Element-43">\text{208}</script></span> of this type of shark and the population's growth rate is <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-44-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>11%</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-204" style="width: 2.169em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.759em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.7em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-205"><span class="mtext" id="MathJax-Span-206" style="font-family: STIXGeneral;">11%</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>11%</mtext></math></span></span><script type="math/tex" id="MathJax-Element-44">\text{11%}</script></span> each year, determine how many sharks there will be in <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-45-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>10</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-207" style="width: 1.232em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.998em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-208"><span class="mtext" id="MathJax-Span-209" style="font-family: STIXGeneral;">10</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>10</mtext></math></span></span><script type="math/tex" id="MathJax-Element-45">\text{10}</script></span> years.
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
Round your answer to the <strong>nearest whole number</strong>.
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
There will be <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="591" size="10"> sharks (rounded to the nearest whole number)<br>
<div class="response-type">numeric</div></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:06:50.098786"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><section class="sv-section sv-question sv-table"><br><div class="id1307-1165">ID is: 1307 Seed is: 1165<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/7d0c3007-0e0d-5f51-b370-3210d312622f" method="POST">
<span class="worked_example"><h3 class="sv-heading">Applications of exponentials: populations of rare species</h3>
</span><div class="problem">
<p>
A species of extremely rare crocodile has a very long lifespan and seldom has children. If there are a total of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-46-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>336</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-210" style="width: 1.876em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.525em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-211"><span class="mtext" id="MathJax-Span-212" style="font-family: STIXGeneral;">336</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>336</mtext></math></span></span><script type="math/tex" id="MathJax-Element-46">\text{336}</script></span> of this type of crocodile and the population's growth rate is <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-47-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>3%</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-213" style="width: 1.525em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.232em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.17em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-214"><span class="mtext" id="MathJax-Span-215" style="font-family: STIXGeneral;">3%</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>3%</mtext></math></span></span><script type="math/tex" id="MathJax-Element-47">\text{3%}</script></span> each year, determine how many crocodiles there will be in <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-48-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>4</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-216" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.53em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-217"><span class="mtext" id="MathJax-Span-218" style="font-family: STIXGeneral;">4</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>4</mtext></math></span></span><script type="math/tex" id="MathJax-Element-48">\text{4}</script></span> years.
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
Round your answer to the <strong>nearest whole number</strong>.
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
There will be <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="378" size="10"> crocodiles (rounded to the nearest whole number)<br>
<div class="response-type">numeric</div></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:06:50.123620"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id311-3344">ID is: 311 Seed is: 3344<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/7d0c3007-0e0d-5f51-b370-3210d312622f" method="POST">
<span class="worked_example"><h3 class="sv-heading">Compound interest rate</h3>
</span><div class="problem">
<p>
Adebankole invests <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-49-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace" /><mtext>4&#xA0;750</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-219" style="width: 3.809em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.106em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1003.11em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-220"><span class="mtext" id="MathJax-Span-221" style="font-family: STIXGeneral;">R</span><span class="mspace" id="MathJax-Span-222" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mtext" id="MathJax-Span-223" style="font-family: STIXGeneral;">4 750</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace"></mspace><mtext>4 750</mtext></math></span></span><script type="math/tex" id="MathJax-Element-49">\text{R}\,\text{4 750}</script></span> into an account which pays out a lump sum at the end of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-50-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>12</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-224" style="width: 1.232em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.998em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-225"><span class="mtext" id="MathJax-Span-226" style="font-family: STIXGeneral;">12</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>12</mtext></math></span></span><script type="math/tex" id="MathJax-Element-50">\text{12}</script></span> years.
</p>
<p>
If he gets <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-51-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace" /><mtext>8&#xA0;455,00</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-227" style="width: 5.331em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.335em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1004.34em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-228"><span class="mtext" id="MathJax-Span-229" style="font-family: STIXGeneral;">R</span><span class="mspace" id="MathJax-Span-230" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mtext" id="MathJax-Span-231" style="font-family: STIXGeneral;">8 455,00</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace"></mspace><mtext>8 455,00</mtext></math></span></span><script type="math/tex" id="MathJax-Element-51">\text{R}\,\text{8 455,00}</script></span> at the end of the period, what annual compound interest rate did the bank offer him?
</p>
<div class="note instructions"><span class="note-header">INSTRUCTIONS:</span>
Give the answer correct to one decimal place.
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
The interest rate is <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="4,9" size="10">% per annum.
<div class="response-type">numeric</div></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:06:50.140944"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><section class="sv-section sv-question sv-table"><br><div class="id311-6724">ID is: 311 Seed is: 6724<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/7d0c3007-0e0d-5f51-b370-3210d312622f" method="POST">
<span class="worked_example"><h3 class="sv-heading">Compound interest rate</h3>
</span><div class="problem">
<p>
Joshua invests <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-52-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace" /><mtext>6&#xA0;220</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-232" style="width: 3.809em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.106em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1003.11em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-233"><span class="mtext" id="MathJax-Span-234" style="font-family: STIXGeneral;">R</span><span class="mspace" id="MathJax-Span-235" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mtext" id="MathJax-Span-236" style="font-family: STIXGeneral;">6 220</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace"></mspace><mtext>6 220</mtext></math></span></span><script type="math/tex" id="MathJax-Element-52">\text{R}\,\text{6 220}</script></span> into an account which pays out a lump sum at the end of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-53-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>11</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-237" style="width: 1.232em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.998em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.88em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-238"><span class="mtext" id="MathJax-Span-239" style="font-family: STIXGeneral;">11</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>11</mtext></math></span></span><script type="math/tex" id="MathJax-Element-53">\text{11}</script></span> years.
</p>
<p>
If he gets <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-54-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace" /><mtext>9&#xA0;641,00</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-240" style="width: 5.331em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.335em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1004.34em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-241"><span class="mtext" id="MathJax-Span-242" style="font-family: STIXGeneral;">R</span><span class="mspace" id="MathJax-Span-243" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mtext" id="MathJax-Span-244" style="font-family: STIXGeneral;">9 641,00</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace"></mspace><mtext>9 641,00</mtext></math></span></span><script type="math/tex" id="MathJax-Element-54">\text{R}\,\text{9 641,00}</script></span> at the end of the period, what annual compound interest rate did the bank offer him?
</p>
<div class="note instructions"><span class="note-header">INSTRUCTIONS:</span>
Give the answer correct to one decimal place.
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
The interest rate is <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="4,1" size="10">% per annum.
<div class="response-type">numeric</div></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:06:50.159782"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id4348-3516">ID is: 4348 Seed is: 3516<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/7d0c3007-0e0d-5f51-b370-3210d312622f" method="POST">
<span class="worked_example"><h3 class="sv-heading">Cost of an item after a period of inflation</h3>
</span><div class="problem">
<p>
<span class="colored" style="color:gray"><em>Adapted from DBE Nov 2015 Grade 11, P1, Q8</em></span><br>
<a url="/info/maths-formulae" href="https://www.emas.com/info/maths-formulae">Maths formulas</a>
</p>
<p>
A school buys tablets at a total cost of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-55-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace" /><mtext>180&#xA0;000</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-245" style="width: 5.038em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.101em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1004.1em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-246"><span class="mtext" id="MathJax-Span-247" style="font-family: STIXGeneral;">R</span><span class="mspace" id="MathJax-Span-248" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mtext" id="MathJax-Span-249" style="font-family: STIXGeneral;">180 000</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace"></mspace><mtext>180 000</mtext></math></span></span><script type="math/tex" id="MathJax-Element-55">\text{R}\,\text{180 000}</script></span>. If the average rate of inflation is <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-56-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>6,8</mtext><mi mathvariant="normal">&#x0025;</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-250" style="width: 2.462em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.994em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.93em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-251"><span class="mtext" id="MathJax-Span-252" style="font-family: STIXGeneral;">6,8</span><span class="mi" id="MathJax-Span-253" style="font-family: STIXGeneral;">%</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>6,8</mtext><mi mathvariant="normal">%</mi></math></span></span><script type="math/tex" id="MathJax-Element-56">\text{6,8}\%</script></span> per annum over the next <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-57-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>6</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-254" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-255"><span class="mtext" id="MathJax-Span-256" style="font-family: STIXGeneral;">6</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>6</mtext></math></span></span><script type="math/tex" id="MathJax-Element-57">\text{6}</script></span> years, determine the cost of buying a new set of tablets (to replace the old ones) in <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-58-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>6</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-257" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-258"><span class="mtext" id="MathJax-Span-259" style="font-family: STIXGeneral;">6</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>6</mtext></math></span></span><script type="math/tex" id="MathJax-Element-58">\text{6}</script></span> years' time.
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
Round your answer to two decimal places.
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<p>
Cost of new tablets is <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-59-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-260" style="width: 0.823em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.647em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1000.65em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-261"><span class="mtext" id="MathJax-Span-262" style="font-family: STIXGeneral;">R</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext></math></span></span><script type="math/tex" id="MathJax-Element-59">\text{R}</script></span> <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="267 116,07" size="10">.
</p>
<div class="response-type">one-of<div class="response-subtype">type(numeric.abserror(0.01))</div></div></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:06:50.185581"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><section class="sv-section sv-question sv-table"><br><div class="id4348-3757">ID is: 4348 Seed is: 3757<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/7d0c3007-0e0d-5f51-b370-3210d312622f" method="POST">
<span class="worked_example"><h3 class="sv-heading">Cost of an item after a period of inflation</h3>
</span><div class="problem">
<p>
<span class="colored" style="color:gray"><em>Adapted from DBE Nov 2015 Grade 11, P1, Q8</em></span><br>
<a url="/info/maths-formulae" href="https://www.emas.com/info/maths-formulae">Maths formulas</a>
</p>
<p>
A business buys tablets at a total cost of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-60-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace" /><mtext>200&#xA0;000</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-263" style="width: 5.038em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.101em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1004.1em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-264"><span class="mtext" id="MathJax-Span-265" style="font-family: STIXGeneral;">R</span><span class="mspace" id="MathJax-Span-266" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mtext" id="MathJax-Span-267" style="font-family: STIXGeneral;">200 000</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace"></mspace><mtext>200 000</mtext></math></span></span><script type="math/tex" id="MathJax-Element-60">\text{R}\,\text{200 000}</script></span>. If the average rate of inflation is <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-61-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>5,4</mtext><mi mathvariant="normal">&#x0025;</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-268" style="width: 2.462em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.994em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.93em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-269"><span class="mtext" id="MathJax-Span-270" style="font-family: STIXGeneral;">5,4</span><span class="mi" id="MathJax-Span-271" style="font-family: STIXGeneral;">%</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>5,4</mtext><mi mathvariant="normal">%</mi></math></span></span><script type="math/tex" id="MathJax-Element-61">\text{5,4}\%</script></span> per annum over the next <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-62-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>5</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-272" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-273"><span class="mtext" id="MathJax-Span-274" style="font-family: STIXGeneral;">5</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>5</mtext></math></span></span><script type="math/tex" id="MathJax-Element-62">\text{5}</script></span> years, determine the cost of buying a new set of tablets (to replace the old ones) in <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-63-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>5</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-275" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-276"><span class="mtext" id="MathJax-Span-277" style="font-family: STIXGeneral;">5</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>5</mtext></math></span></span><script type="math/tex" id="MathJax-Element-63">\text{5}</script></span> years' time.
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
Round your answer to two decimal places.
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<p>
Cost of new tablets is <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-64-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-278" style="width: 0.823em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.647em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1000.65em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-279"><span class="mtext" id="MathJax-Span-280" style="font-family: STIXGeneral;">R</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext></math></span></span><script type="math/tex" id="MathJax-Element-64">\text{R}</script></span> <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="260 155,52" size="10">.
</p>
<div class="response-type">one-of<div class="response-subtype">type(numeric.abserror(0.01))</div></div></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:06:50.210819"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id2975-2900">ID is: 2975 Seed is: 2900<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/7d0c3007-0e0d-5f51-b370-3210d312622f" method="POST">
<span class="worked_example"><h3 class="sv-heading">A diminishing elephant population in Zimbabwe</h3>
</span><div class="problem">
<p>
The elephant population in Zimbabwe starts to decrease at a rate of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-65-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>8</mtext><mi mathvariant="normal">&#x0025;</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-281" style="width: 1.525em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.232em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.17em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-282"><span class="mtext" id="MathJax-Span-283" style="font-family: STIXGeneral;">8</span><span class="mi" id="MathJax-Span-284" style="font-family: STIXGeneral;">%</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>8</mtext><mi mathvariant="normal">%</mi></math></span></span><script type="math/tex" id="MathJax-Element-65">\text{8}\%</script></span> per annum. Determine how long it will take for the population to be <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-66-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>4</mn></mfrac></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-285" style="width: 0.881em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.706em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.057em, 1000.71em, 2.755em, -999.997em); top: -2.163em; left: 0em;"><span class="mrow" id="MathJax-Span-286"><span class="mfrac" id="MathJax-Span-287"><span style="display: inline-block; position: relative; width: 0.471em; height: 0px; margin-right: 0.12em; margin-left: 0.12em;"><span style="position: absolute; clip: rect(3.34em, 1000.3em, 4.16em, -999.997em); top: -4.388em; left: 50%; margin-left: -0.173em;"><span class="mn" id="MathJax-Span-288" style="font-size: 70.7%; font-family: STIXGeneral;">3</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; clip: rect(3.34em, 1000.35em, 4.16em, -999.997em); top: -3.569em; left: 50%; margin-left: -0.173em;"><span class="mn" id="MathJax-Span-289" style="font-size: 70.7%; font-family: STIXGeneral;">4</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; clip: rect(0.823em, 1000.47em, 1.232em, -999.997em); top: -1.285em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.471em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.057em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.169em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.568em; border-left: 0px solid; width: 0px; height: 1.718em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>4</mn></mfrac></math></span></span><script type="math/tex" id="MathJax-Element-66">\frac{3}{4}</script></span> of the current population size.
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
Round your answer to the nearest integer.
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<p>It will take approximately <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="3" size="10"> years.</p>
<div class="response-type">one-of<div class="response-subtype">type(numeric.abserror(1.0))</div></div></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:06:50.243554"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><section class="sv-section sv-question sv-table"><br><div class="id2975-688">ID is: 2975 Seed is: 688<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/7d0c3007-0e0d-5f51-b370-3210d312622f" method="POST">
<span class="worked_example"><h3 class="sv-heading">A diminishing lion population in Zimbabwe</h3>
</span><div class="problem">
<p>
Determine how long it will take for the lion population in Zimbabwe to be <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-67-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>5</mn></mfrac></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-290" style="width: 0.881em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.706em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.057em, 1000.71em, 2.755em, -999.997em); top: -2.163em; left: 0em;"><span class="mrow" id="MathJax-Span-291"><span class="mfrac" id="MathJax-Span-292"><span style="display: inline-block; position: relative; width: 0.471em; height: 0px; margin-right: 0.12em; margin-left: 0.12em;"><span style="position: absolute; clip: rect(3.34em, 1000.3em, 4.16em, -999.997em); top: -4.388em; left: 50%; margin-left: -0.173em;"><span class="mn" id="MathJax-Span-293" style="font-size: 70.7%; font-family: STIXGeneral;">3</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; clip: rect(3.34em, 1000.3em, 4.16em, -999.997em); top: -3.569em; left: 50%; margin-left: -0.173em;"><span class="mn" id="MathJax-Span-294" style="font-size: 70.7%; font-family: STIXGeneral;">5</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; clip: rect(0.823em, 1000.47em, 1.232em, -999.997em); top: -1.285em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.471em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.057em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.169em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.568em; border-left: 0px solid; width: 0px; height: 1.789em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>5</mn></mfrac></math></span></span><script type="math/tex" id="MathJax-Element-67">\frac{3}{5}</script></span> of the current population size, if it is given that the lion population starts to decrease at a rate of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-68-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>5</mtext><mi mathvariant="normal">&#x0025;</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-295" style="width: 1.525em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.232em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.17em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-296"><span class="mtext" id="MathJax-Span-297" style="font-family: STIXGeneral;">5</span><span class="mi" id="MathJax-Span-298" style="font-family: STIXGeneral;">%</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>5</mtext><mi mathvariant="normal">%</mi></math></span></span><script type="math/tex" id="MathJax-Element-68">\text{5}\%</script></span> per annum.
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
Round your answer to the nearest integer.
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<p>It will take approximately <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="10" size="10"> years.</p>
<div class="response-type">one-of<div class="response-subtype">type(numeric.abserror(1.0))</div></div></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:06:50.278176"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id4106-1341">ID is: 4106 Seed is: 1341<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/7d0c3007-0e0d-5f51-b370-3210d312622f" method="POST">
<span class="worked_example"><h3 class="sv-heading">Compound growth on property</h3>
</span><div class="problem">
<p>
<span class="colored" style="color:gray"><em>Adapted from DBE Nov 2016 Grade 11, P1, Q8.3</em></span> <br>
<a url="/info/maths-formulas" href="https://www.emas.com/info/maths-formulas">Maths formulas</a>
</p>
<p>
The value of a block of offices increased from <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-69-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace" /><mtext>2&#xA0;300&#xA0;000</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-299" style="width: 5.975em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.862em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1004.86em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-300"><span class="mtext" id="MathJax-Span-301" style="font-family: STIXGeneral;">R</span><span class="mspace" id="MathJax-Span-302" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mtext" id="MathJax-Span-303" style="font-family: STIXGeneral;">2 300 000</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace"></mspace><mtext>2 300 000</mtext></math></span></span><script type="math/tex" id="MathJax-Element-69">\text{R}\,\text{2 300 000}</script></span> to <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-70-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace" /><mtext>4&#xA0;633&#xA0;343,19</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-304" style="width: 7.439em; display: inline-block;"><span style="display: inline-block; position: relative; width: 6.092em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1006.03em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-305"><span class="mtext" id="MathJax-Span-306" style="font-family: STIXGeneral;">R</span><span class="mspace" id="MathJax-Span-307" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mtext" id="MathJax-Span-308" style="font-family: STIXGeneral;">4 633 343,19</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace"></mspace><mtext>4 633 343,19</mtext></math></span></span><script type="math/tex" id="MathJax-Element-70">\text{R}\,\text{4 633 343,19}</script></span> over <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-71-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>11</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-309" style="width: 1.232em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.998em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.88em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-310"><span class="mtext" id="MathJax-Span-311" style="font-family: STIXGeneral;">11</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>11</mtext></math></span></span><script type="math/tex" id="MathJax-Element-71">\text{11}</script></span> years. Calculate the average annual rate of increase in the value of the block of offices over <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-72-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>11</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-312" style="width: 1.232em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.998em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.88em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-313"><span class="mtext" id="MathJax-Span-314" style="font-family: STIXGeneral;">11</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>11</mtext></math></span></span><script type="math/tex" id="MathJax-Element-72">\text{11}</script></span> years.
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
Round your answer to two decimal places.
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-73-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-315" style="width: 1.759em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.408em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.876em, 1001.35em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-316"><span class="mi" id="MathJax-Span-317" style="font-family: STIXGeneral; font-style: italic;">𝑟</span><span class="mo" id="MathJax-Span-318" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo></math></span></span><script type="math/tex" id="MathJax-Element-73">r = </script></span> <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="6,57" size="10"> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-74-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">&#x0025;</mi><mtext>&#xA0;p.a.</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-319" style="width: 3.047em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.462em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.4em, 2.93em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-320"><span class="mi" id="MathJax-Span-321" style="font-family: STIXGeneral;">%</span><span class="mtext" id="MathJax-Span-322" style="font-family: STIXGeneral;"> p.a.</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.354em; border-left: 0px solid; width: 0px; height: 1.289em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">%</mi><mtext> p.a.</mtext></math></span></span><script type="math/tex" id="MathJax-Element-74">\% \text{ p.a.}</script></span>
<div class="response-type">one-of<div class="response-subtype">type(numeric.abserror(0.01))</div></div></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:06:50.308705"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><section class="sv-section sv-question sv-table"><br><div class="id4106-9294">ID is: 4106 Seed is: 9294<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/7d0c3007-0e0d-5f51-b370-3210d312622f" method="POST">
<span class="worked_example"><h3 class="sv-heading">Compound growth on property</h3>
</span><div class="problem">
<p>
<span class="colored" style="color:gray"><em>Adapted from DBE Nov 2016 Grade 11, P1, Q8.3</em></span> <br>
<a url="/info/maths-formulas" href="https://www.emas.com/info/maths-formulas">Maths formulas</a>
</p>
<p>
The value of a block of offices increased from <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-75-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace" /><mtext>2&#xA0;750&#xA0;000</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-323" style="width: 5.975em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.862em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1004.86em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-324"><span class="mtext" id="MathJax-Span-325" style="font-family: STIXGeneral;">R</span><span class="mspace" id="MathJax-Span-326" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mtext" id="MathJax-Span-327" style="font-family: STIXGeneral;">2 750 000</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace"></mspace><mtext>2 750 000</mtext></math></span></span><script type="math/tex" id="MathJax-Element-75">\text{R}\,\text{2 750 000}</script></span> to <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-76-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace" /><mtext>6&#xA0;117&#xA0;118,77</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-328" style="width: 7.439em; display: inline-block;"><span style="display: inline-block; position: relative; width: 6.092em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1006.03em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-329"><span class="mtext" id="MathJax-Span-330" style="font-family: STIXGeneral;">R</span><span class="mspace" id="MathJax-Span-331" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mtext" id="MathJax-Span-332" style="font-family: STIXGeneral;">6 117 118,77</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace"></mspace><mtext>6 117 118,77</mtext></math></span></span><script type="math/tex" id="MathJax-Element-76">\text{R}\,\text{6 117 118,77}</script></span> over <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-77-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>10</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-333" style="width: 1.232em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.998em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-334"><span class="mtext" id="MathJax-Span-335" style="font-family: STIXGeneral;">10</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>10</mtext></math></span></span><script type="math/tex" id="MathJax-Element-77">\text{10}</script></span> years. Calculate the average annual rate of increase in the value of the block of offices over <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-78-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>10</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-336" style="width: 1.232em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.998em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-337"><span class="mtext" id="MathJax-Span-338" style="font-family: STIXGeneral;">10</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>10</mtext></math></span></span><script type="math/tex" id="MathJax-Element-78">\text{10}</script></span> years.
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
Round your answer to two decimal places.
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-79-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-339" style="width: 1.759em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.408em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.876em, 1001.35em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-340"><span class="mi" id="MathJax-Span-341" style="font-family: STIXGeneral; font-style: italic;">𝑟</span><span class="mo" id="MathJax-Span-342" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo></math></span></span><script type="math/tex" id="MathJax-Element-79">r = </script></span> <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="8,32" size="10"> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-80-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">&#x0025;</mi><mtext>&#xA0;p.a.</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-343" style="width: 3.047em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.462em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.4em, 2.93em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-344"><span class="mi" id="MathJax-Span-345" style="font-family: STIXGeneral;">%</span><span class="mtext" id="MathJax-Span-346" style="font-family: STIXGeneral;"> p.a.</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.354em; border-left: 0px solid; width: 0px; height: 1.289em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">%</mi><mtext> p.a.</mtext></math></span></span><script type="math/tex" id="MathJax-Element-80">\% \text{ p.a.}</script></span>
<div class="response-type">one-of<div class="response-subtype">type(numeric.abserror(0.01))</div></div></div></div></div>
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</div></section></section> <section class="sv-section">
<h2>2. Simple and compound depreciation</h2>
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<span class="worked_example"><h3 class="sv-heading">Compound interest: finding <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-81-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-347" style="width: 0.392em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.314em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.797em, 1000.27em, 2.656em, -999.998em); top: -2.535em; left: 0em;"><span class="mrow" id="MathJax-Span-348"><span class="mi" id="MathJax-Span-349" style="font-family: STIXGeneral; font-style: italic;">𝑖</span></span><span style="display: inline-block; width: 0px; height: 2.539em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.045em; border-left: 0px solid; width: 0px; height: 0.86em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></span></span><script type="math/tex" id="MathJax-Element-81"> i </script></span> </h3>
</span><div class="problem">
<p>
Joanna deposits <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-82-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace" /><mtext>7&#xA0;500</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-350" style="width: 3.809em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.106em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1003.11em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-351"><span class="mtext" id="MathJax-Span-352" style="font-family: STIXGeneral;">R</span><span class="mspace" id="MathJax-Span-353" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mtext" id="MathJax-Span-354" style="font-family: STIXGeneral;">7 500</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace"></mspace><mtext>7 500</mtext></math></span></span><script type="math/tex" id="MathJax-Element-82">\text{R}\,\text{7 500}</script></span> into a savings account which gets compound interest. The account grows to a value of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-83-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace" /><mtext>16&#xA0;950,54</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-355" style="width: 5.975em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.862em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1004.86em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-356"><span class="mtext" id="MathJax-Span-357" style="font-family: STIXGeneral;">R</span><span class="mspace" id="MathJax-Span-358" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mtext" id="MathJax-Span-359" style="font-family: STIXGeneral;">16 950,54</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace"></mspace><mtext>16 950,54</mtext></math></span></span><script type="math/tex" id="MathJax-Element-83">\text{R}\,\text{16 950,54}</script></span> in <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-84-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>8</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-360" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-361"><span class="mtext" id="MathJax-Span-362" style="font-family: STIXGeneral;">8</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>8</mtext></math></span></span><script type="math/tex" id="MathJax-Element-84">\text{8}</script></span> years. Determine the interest rate the account earns.
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
Give your answer as a percentage rounded to two decimal places.
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="10,73" size="10">% per annum.
<div class="response-type">numeric</div></div></div></div>
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</div></section><section class="sv-section sv-question sv-table"><br><div class="id1524-4790">ID is: 1524 Seed is: 4790<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/7d0c3007-0e0d-5f51-b370-3210d312622f" method="POST">
<span class="worked_example"><h3 class="sv-heading">Compound interest: finding <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-85-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-363" style="width: 0.392em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.314em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.797em, 1000.27em, 2.656em, -999.998em); top: -2.535em; left: 0em;"><span class="mrow" id="MathJax-Span-364"><span class="mi" id="MathJax-Span-365" style="font-family: STIXGeneral; font-style: italic;">𝑖</span></span><span style="display: inline-block; width: 0px; height: 2.539em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.045em; border-left: 0px solid; width: 0px; height: 0.86em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></span></span><script type="math/tex" id="MathJax-Element-85"> i </script></span> </h3>
</span><div class="problem">
<p>
Carina deposits <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-86-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace" /><mtext>7&#xA0;000</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-366" style="width: 3.809em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.106em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1003.11em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-367"><span class="mtext" id="MathJax-Span-368" style="font-family: STIXGeneral;">R</span><span class="mspace" id="MathJax-Span-369" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mtext" id="MathJax-Span-370" style="font-family: STIXGeneral;">7 000</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace"></mspace><mtext>7 000</mtext></math></span></span><script type="math/tex" id="MathJax-Element-86">\text{R}\,\text{7 000}</script></span> into a savings account which gets compound interest. The account grows to a value of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-87-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace" /><mtext>11&#xA0;273,57</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-371" style="width: 5.975em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.862em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1004.8em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-372"><span class="mtext" id="MathJax-Span-373" style="font-family: STIXGeneral;">R</span><span class="mspace" id="MathJax-Span-374" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mtext" id="MathJax-Span-375" style="font-family: STIXGeneral;">11 273,57</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace"></mspace><mtext>11 273,57</mtext></math></span></span><script type="math/tex" id="MathJax-Element-87">\text{R}\,\text{11 273,57}</script></span> in <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-88-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>5</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-376" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-377"><span class="mtext" id="MathJax-Span-378" style="font-family: STIXGeneral;">5</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>5</mtext></math></span></span><script type="math/tex" id="MathJax-Element-88">\text{5}</script></span> years. What is the interest rate for this account?
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
Give your answer as a percentage rounded to two decimal places.
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="10" size="10">% per annum.
<div class="response-type">numeric</div></div></div></div>
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</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id1528-2902">ID is: 1528 Seed is: 2902<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/7d0c3007-0e0d-5f51-b370-3210d312622f" method="POST">
<span class="worked_example"><h3 class="sv-heading">Simple depreciation: when an asset goes to zero value!</h3>
</span><div class="problem">
<p>
A small business buys a computer for <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-89-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace" /><mtext>9&#xA0;000</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-379" style="width: 3.809em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.106em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1003.11em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-380"><span class="mtext" id="MathJax-Span-381" style="font-family: STIXGeneral;">R</span><span class="mspace" id="MathJax-Span-382" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mtext" id="MathJax-Span-383" style="font-family: STIXGeneral;">9 000</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace"></mspace><mtext>9 000</mtext></math></span></span><script type="math/tex" id="MathJax-Element-89">\text{R}\,\text{9 000}</script></span>.
For the tax return, the owner depreciates this asset over <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-90-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>9</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-384" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-385"><span class="mtext" id="MathJax-Span-386" style="font-family: STIXGeneral;">9</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>9</mtext></math></span></span><script type="math/tex" id="MathJax-Element-90">\text{9}</script></span> years
using a straight-line depreciation method. Each year the company's owner must fill in the value of the
computer on this tax form. What amount will he put on his tax form after
<span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-91-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>2</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-387" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.53em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-388"><span class="mtext" id="MathJax-Span-389" style="font-family: STIXGeneral;">2</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>2</mtext></math></span></span><script type="math/tex" id="MathJax-Element-91">\text{2}</script></span> year(s)?
</p>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-92-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-390" style="width: 0.94em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.764em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1000.76em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-391"><span class="mi" id="MathJax-Span-392" style="font-family: STIXGeneral; font-style: italic;">𝑅</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math></span></span><script type="math/tex" id="MathJax-Element-92">R</script></span> <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="7 000" size="10"><div class="response-type">numeric</div></div></div></div>
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</div></section><section class="sv-section sv-question sv-table"><br><div class="id1528-9469">ID is: 1528 Seed is: 9469<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/7d0c3007-0e0d-5f51-b370-3210d312622f" method="POST">
<span class="worked_example"><h3 class="sv-heading">Simple depreciation: when an asset goes to zero value!</h3>
</span><div class="problem">
<p>
A small business buys a fridge for <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-93-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace" /><mtext>14&#xA0;000</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-393" style="width: 4.394em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.574em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1003.57em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-394"><span class="mtext" id="MathJax-Span-395" style="font-family: STIXGeneral;">R</span><span class="mspace" id="MathJax-Span-396" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mtext" id="MathJax-Span-397" style="font-family: STIXGeneral;">14 000</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace"></mspace><mtext>14 000</mtext></math></span></span><script type="math/tex" id="MathJax-Element-93">\text{R}\,\text{14 000}</script></span>.
For the tax return, the owner depreciates this asset over <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-94-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>8</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-398" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-399"><span class="mtext" id="MathJax-Span-400" style="font-family: STIXGeneral;">8</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>8</mtext></math></span></span><script type="math/tex" id="MathJax-Element-94">\text{8}</script></span> years
on a straight-line basis. Each year the company's owner must fill in the value of the
fridge on this tax form. What amount will he put on his tax form after
<span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-95-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>4</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-401" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.53em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-402"><span class="mtext" id="MathJax-Span-403" style="font-family: STIXGeneral;">4</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>4</mtext></math></span></span><script type="math/tex" id="MathJax-Element-95">\text{4}</script></span> year(s)?
</p>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-96-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-404" style="width: 0.94em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.764em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1000.76em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-405"><span class="mi" id="MathJax-Span-406" style="font-family: STIXGeneral; font-style: italic;">𝑅</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math></span></span><script type="math/tex" id="MathJax-Element-96">R</script></span> <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="7 000" size="10"><div class="response-type">numeric</div></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:06:48.795040"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id1536-4595">ID is: 1536 Seed is: 4595<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/7d0c3007-0e0d-5f51-b370-3210d312622f" method="POST">
<span class="worked_example"><h3 class="sv-heading">Compound depreciation</h3>
</span><div class="problem">
<p>
Farmer Mike buys a tractor for <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-97-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace" /><mtext>149&#xA0;000</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-407" style="width: 5.038em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.101em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1004.1em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-408"><span class="mtext" id="MathJax-Span-409" style="font-family: STIXGeneral;">R</span><span class="mspace" id="MathJax-Span-410" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mtext" id="MathJax-Span-411" style="font-family: STIXGeneral;">149 000</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace"></mspace><mtext>149 000</mtext></math></span></span><script type="math/tex" id="MathJax-Element-97">\text{R}\,\text{149 000}</script></span>. The tractor depreciates by <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-98-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>12</mtext><mi mathvariant="normal">&#x0025;</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-412" style="width: 2.169em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.759em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.7em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-413"><span class="mtext" id="MathJax-Span-414" style="font-family: STIXGeneral;">12</span><span class="mi" id="MathJax-Span-415" style="font-family: STIXGeneral;">%</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>12</mtext><mi mathvariant="normal">%</mi></math></span></span><script type="math/tex" id="MathJax-Element-98">\text{12}\%</script></span> per year following the compound depreciation method. What is the depreciated value of the tractor after <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-99-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>12</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-416" style="width: 1.232em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.998em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-417"><span class="mtext" id="MathJax-Span-418" style="font-family: STIXGeneral;">12</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>12</mtext></math></span></span><script type="math/tex" id="MathJax-Element-99">\text{12}</script></span> years?
</p>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<p>
The depreciated value of the tractor is <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-100-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-419" style="width: 0.823em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.647em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1000.65em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-420"><span class="mtext" id="MathJax-Span-421" style="font-family: STIXGeneral;">R</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext></math></span></span><script type="math/tex" id="MathJax-Element-100">\text{R}</script></span> <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="32 135" size="10">.
</p>
<div class="response-type">numeric</div></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:06:48.815312"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><section class="sv-section sv-question sv-table"><br><div class="id1536-2908">ID is: 1536 Seed is: 2908<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/7d0c3007-0e0d-5f51-b370-3210d312622f" method="POST">
<span class="worked_example"><h3 class="sv-heading">Compound depreciation</h3>
</span><div class="problem">
<p>
Farmer Andrew buys a tractor for <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-101-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace" /><mtext>227&#xA0;000</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-422" style="width: 5.038em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.101em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1004.1em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-423"><span class="mtext" id="MathJax-Span-424" style="font-family: STIXGeneral;">R</span><span class="mspace" id="MathJax-Span-425" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mtext" id="MathJax-Span-426" style="font-family: STIXGeneral;">227 000</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace"></mspace><mtext>227 000</mtext></math></span></span><script type="math/tex" id="MathJax-Element-101">\text{R}\,\text{227 000}</script></span>. The tractor depreciates by <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-102-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>25</mtext><mi mathvariant="normal">&#x0025;</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-427" style="width: 2.169em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.759em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.7em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-428"><span class="mtext" id="MathJax-Span-429" style="font-family: STIXGeneral;">25</span><span class="mi" id="MathJax-Span-430" style="font-family: STIXGeneral;">%</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>25</mtext><mi mathvariant="normal">%</mi></math></span></span><script type="math/tex" id="MathJax-Element-102">\text{25}\%</script></span> per year where the depreciation happens at a compound rate. What is the depreciated value of the tractor after <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-103-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>6</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-431" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-432"><span class="mtext" id="MathJax-Span-433" style="font-family: STIXGeneral;">6</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>6</mtext></math></span></span><script type="math/tex" id="MathJax-Element-103">\text{6}</script></span> years?
</p>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<p>
The depreciated value of the tractor is <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-104-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-434" style="width: 0.823em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.647em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1000.65em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-435"><span class="mtext" id="MathJax-Span-436" style="font-family: STIXGeneral;">R</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext></math></span></span><script type="math/tex" id="MathJax-Element-104">\text{R}</script></span> <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="40 401,12" size="10">.
</p>
<div class="response-type">numeric</div></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:06:48.832458"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id1522-3416">ID is: 1522 Seed is: 3416<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/7d0c3007-0e0d-5f51-b370-3210d312622f" method="POST">
<span class="worked_example"><h3 class="sv-heading">Compound depreciation: population loss</h3>
</span><div class="problem">
<p>
The number of pelicans at the Bloukrans river mouth is decreasing at a compound rate of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-105-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>12</mtext><mi mathvariant="normal">&#x0025;</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-437" style="width: 2.169em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.759em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.7em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-438"><span class="mtext" id="MathJax-Span-439" style="font-family: STIXGeneral;">12</span><span class="mi" id="MathJax-Span-440" style="font-family: STIXGeneral;">%</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>12</mtext><mi mathvariant="normal">%</mi></math></span></span><script type="math/tex" id="MathJax-Element-105">\text{12}\%</script></span> p.a. If there are now <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-106-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>10&#xA0;000</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-441" style="width: 3.399em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.755em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.75em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-442"><span class="mtext" id="MathJax-Span-443" style="font-family: STIXGeneral;">10 000</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>10 000</mtext></math></span></span><script type="math/tex" id="MathJax-Element-106">\text{10 000}</script></span> pelicans, how many will there be in <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-107-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>13</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-444" style="width: 1.232em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.998em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.94em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-445"><span class="mtext" id="MathJax-Span-446" style="font-family: STIXGeneral;">13</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>13</mtext></math></span></span><script type="math/tex" id="MathJax-Element-107">\text{13}</script></span> years' time?
</p>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
There will be <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="1 898" size="10"> pelicans.
<div class="response-type">numeric</div></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:06:48.849638"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><section class="sv-section sv-question sv-table"><br><div class="id1522-2038">ID is: 1522 Seed is: 2038<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/7d0c3007-0e0d-5f51-b370-3210d312622f" method="POST">
<span class="worked_example"><h3 class="sv-heading">Compound depreciation: population loss</h3>
</span><div class="problem">
<p>
The number of flamingos at the Sundays river mouth is decreasing at a compound rate of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-108-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>15</mtext><mi mathvariant="normal">&#x0025;</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-447" style="width: 2.169em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.759em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.7em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-448"><span class="mtext" id="MathJax-Span-449" style="font-family: STIXGeneral;">15</span><span class="mi" id="MathJax-Span-450" style="font-family: STIXGeneral;">%</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>15</mtext><mi mathvariant="normal">%</mi></math></span></span><script type="math/tex" id="MathJax-Element-108">\text{15}\%</script></span> p.a. If there are now <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-109-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>3&#xA0;000</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-451" style="width: 2.755em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.228em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.23em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-452"><span class="mtext" id="MathJax-Span-453" style="font-family: STIXGeneral;">3 000</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>3 000</mtext></math></span></span><script type="math/tex" id="MathJax-Element-109">\text{3 000}</script></span> flamingos, how many will there be in <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-110-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>15</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-454" style="width: 1.232em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.998em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.94em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-455"><span class="mtext" id="MathJax-Span-456" style="font-family: STIXGeneral;">15</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>15</mtext></math></span></span><script type="math/tex" id="MathJax-Element-110">\text{15}</script></span> years' time?
</p>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
There will be <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="262" size="10"> flamingos.
<div class="response-type">numeric</div></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:06:48.865786"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id1535-5787">ID is: 1535 Seed is: 5787<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/7d0c3007-0e0d-5f51-b370-3210d312622f" method="POST">
<span class="worked_example"><h3 class="sv-heading">Simple depreciation</h3>
</span><div class="problem">
<p>
A delivery van is worth <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-111-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace" /><mtext>33&#xA0;000</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-457" style="width: 4.394em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.574em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1003.57em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-458"><span class="mtext" id="MathJax-Span-459" style="font-family: STIXGeneral;">R</span><span class="mspace" id="MathJax-Span-460" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mtext" id="MathJax-Span-461" style="font-family: STIXGeneral;">33 000</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace"></mspace><mtext>33 000</mtext></math></span></span><script type="math/tex" id="MathJax-Element-111">\text{R}\,\text{33 000}</script></span> now. It depreciates at a rate of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-112-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>16</mtext><mi mathvariant="normal">&#x0025;</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-462" style="width: 2.169em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.759em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.7em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-463"><span class="mtext" id="MathJax-Span-464" style="font-family: STIXGeneral;">16</span><span class="mi" id="MathJax-Span-465" style="font-family: STIXGeneral;">%</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>16</mtext><mi mathvariant="normal">%</mi></math></span></span><script type="math/tex" id="MathJax-Element-112">\text{16}\%</script></span> p.a. on a straight-line basis. What is the delivery van worth in <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-113-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>4</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-466" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.53em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-467"><span class="mtext" id="MathJax-Span-468" style="font-family: STIXGeneral;">4</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>4</mtext></math></span></span><script type="math/tex" id="MathJax-Element-113">\text{4}</script></span> years' time?
</p>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
The delivery van will be worth <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-114-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-469" style="width: 0.823em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.647em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1000.65em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-470"><span class="mtext" id="MathJax-Span-471" style="font-family: STIXGeneral;">R</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext></math></span></span><script type="math/tex" id="MathJax-Element-114">\text{R}</script></span> <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="11 880" size="10">.
<div class="response-type">numeric</div></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:06:48.883790"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><section class="sv-section sv-question sv-table"><br><div class="id1535-5677">ID is: 1535 Seed is: 5677<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/7d0c3007-0e0d-5f51-b370-3210d312622f" method="POST">
<span class="worked_example"><h3 class="sv-heading">Simple depreciation</h3>
</span><div class="problem">
<p>
A bakkie is worth <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-115-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace" /><mtext>18&#xA0;000</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-472" style="width: 4.394em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.574em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1003.57em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-473"><span class="mtext" id="MathJax-Span-474" style="font-family: STIXGeneral;">R</span><span class="mspace" id="MathJax-Span-475" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mtext" id="MathJax-Span-476" style="font-family: STIXGeneral;">18 000</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace"></mspace><mtext>18 000</mtext></math></span></span><script type="math/tex" id="MathJax-Element-115">\text{R}\,\text{18 000}</script></span> now. It depreciates at a rate of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-116-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>15</mtext><mi mathvariant="normal">&#x0025;</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-477" style="width: 2.169em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.759em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.7em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-478"><span class="mtext" id="MathJax-Span-479" style="font-family: STIXGeneral;">15</span><span class="mi" id="MathJax-Span-480" style="font-family: STIXGeneral;">%</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>15</mtext><mi mathvariant="normal">%</mi></math></span></span><script type="math/tex" id="MathJax-Element-116">\text{15}\%</script></span> p.a. following the straight-line depreciation method. What is the bakkie worth in <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-117-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>4</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-481" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.53em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-482"><span class="mtext" id="MathJax-Span-483" style="font-family: STIXGeneral;">4</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>4</mtext></math></span></span><script type="math/tex" id="MathJax-Element-117">\text{4}</script></span> years' time?
</p>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
The bakkie will be worth <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-118-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-484" style="width: 0.823em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.647em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1000.65em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-485"><span class="mtext" id="MathJax-Span-486" style="font-family: STIXGeneral;">R</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext></math></span></span><script type="math/tex" id="MathJax-Element-118">\text{R}</script></span> <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="7 200" size="10">.
<div class="response-type">numeric</div></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:06:48.900556"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id4104-4564">ID is: 4104 Seed is: 4564<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/7d0c3007-0e0d-5f51-b370-3210d312622f" method="POST">
<span class="worked_example"><h3 class="sv-heading">Depreciation and book value</h3>
</span><div class="problem">
<p>
<span class="colored" style="color:gray"><em>Adapted from DBE Nov 2016 Grade 11, P1, Q8.1</em></span> <br>
<a url="/info/maths-formulas" href="https://www.emas.com/info/maths-formulas">Maths formulas</a>
</p>
<p>
A machine costs <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-119-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace" /><mtext>27&#xA0;000</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-487" style="width: 4.394em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.574em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1003.57em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-488"><span class="mtext" id="MathJax-Span-489" style="font-family: STIXGeneral;">R</span><span class="mspace" id="MathJax-Span-490" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mtext" id="MathJax-Span-491" style="font-family: STIXGeneral;">27 000</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace"></mspace><mtext>27 000</mtext></math></span></span><script type="math/tex" id="MathJax-Element-119">\text{R}\,\text{27 000}</script></span> in 2016. If the machine depreciates at <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-120-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>11,5</mtext><mi mathvariant="normal">&#x0025;</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-492" style="width: 3.106em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.52em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.46em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-493"><span class="mtext" id="MathJax-Span-494" style="font-family: STIXGeneral;">11,5</span><span class="mi" id="MathJax-Span-495" style="font-family: STIXGeneral;">%</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>11,5</mtext><mi mathvariant="normal">%</mi></math></span></span><script type="math/tex" id="MathJax-Element-120">\text{11,5}\%</script></span> per annum (p.a.) compound depreciation, calculate the book value of the machine after <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-121-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>8</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-496" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-497"><span class="mtext" id="MathJax-Span-498" style="font-family: STIXGeneral;">8</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>8</mtext></math></span></span><script type="math/tex" id="MathJax-Element-121">\text{8}</script></span> years.
</p>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-122-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-499" style="width: 2.111em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.701em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1001.64em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-500"><span class="mi" id="MathJax-Span-501" style="font-family: STIXGeneral; font-style: italic;">𝐴</span><span class="mo" id="MathJax-Span-502" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo></math></span></span><script type="math/tex" id="MathJax-Element-122">A = </script></span> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-123-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-503" style="width: 0.823em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.647em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1000.65em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-504"><span class="mtext" id="MathJax-Span-505" style="font-family: STIXGeneral;">R</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext></math></span></span><script type="math/tex" id="MathJax-Element-123">\text{R}</script></span> <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="10 160,38" size="10">
<div class="response-type">numeric</div></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:06:48.919085"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><section class="sv-section sv-question sv-table"><br><div class="id4104-6412">ID is: 4104 Seed is: 6412<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/7d0c3007-0e0d-5f51-b370-3210d312622f" method="POST">
<span class="worked_example"><h3 class="sv-heading">Depreciation and book value</h3>
</span><div class="problem">
<p>
<span class="colored" style="color:gray"><em>Adapted from DBE Nov 2016 Grade 11, P1, Q8.1</em></span> <br>
<a url="/info/maths-formulas" href="https://www.emas.com/info/maths-formulas">Maths formulas</a>
</p>
<p>
Rebecca bought a delivery vehicle for <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-124-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace" /><mtext>30&#xA0;500</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-506" style="width: 4.394em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.574em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1003.57em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-507"><span class="mtext" id="MathJax-Span-508" style="font-family: STIXGeneral;">R</span><span class="mspace" id="MathJax-Span-509" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mtext" id="MathJax-Span-510" style="font-family: STIXGeneral;">30 500</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace"></mspace><mtext>30 500</mtext></math></span></span><script type="math/tex" id="MathJax-Element-124">\text{R}\,\text{30 500}</script></span> in 2016. If the delivery vehicle depreciates at <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-125-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>6,9</mtext><mi mathvariant="normal">&#x0025;</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-511" style="width: 2.462em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.994em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.93em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-512"><span class="mtext" id="MathJax-Span-513" style="font-family: STIXGeneral;">6,9</span><span class="mi" id="MathJax-Span-514" style="font-family: STIXGeneral;">%</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>6,9</mtext><mi mathvariant="normal">%</mi></math></span></span><script type="math/tex" id="MathJax-Element-125">\text{6,9}\%</script></span> per annum (p.a.) compound depreciation, calculate the book value of the machine after <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-126-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>3</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-515" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-516"><span class="mtext" id="MathJax-Span-517" style="font-family: STIXGeneral;">3</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>3</mtext></math></span></span><script type="math/tex" id="MathJax-Element-126">\text{3}</script></span> years.
</p>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-127-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-518" style="width: 2.111em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.701em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1001.64em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-519"><span class="mi" id="MathJax-Span-520" style="font-family: STIXGeneral; font-style: italic;">𝐴</span><span class="mo" id="MathJax-Span-521" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo></math></span></span><script type="math/tex" id="MathJax-Element-127">A = </script></span> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-128-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-522" style="width: 0.823em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.647em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1000.65em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-523"><span class="mtext" id="MathJax-Span-524" style="font-family: STIXGeneral;">R</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext></math></span></span><script type="math/tex" id="MathJax-Element-128">\text{R}</script></span> <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="24 612,11" size="10">
<div class="response-type">numeric</div></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:06:48.938210"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id1525-4778">ID is: 1525 Seed is: 4778<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/7d0c3007-0e0d-5f51-b370-3210d312622f" method="POST">
<span class="worked_example"><h3 class="sv-heading">Simple interest: finding <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-129-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-525" style="width: 0.392em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.314em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.797em, 1000.27em, 2.656em, -999.998em); top: -2.535em; left: 0em;"><span class="mrow" id="MathJax-Span-526"><span class="mi" id="MathJax-Span-527" style="font-family: STIXGeneral; font-style: italic;">𝑖</span></span><span style="display: inline-block; width: 0px; height: 2.539em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.045em; border-left: 0px solid; width: 0px; height: 0.86em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></span></span><script type="math/tex" id="MathJax-Element-129"> i </script></span> </h3>
</span><div class="problem">
<p>
Langalibalele deposits <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-130-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace" /><mtext>3&#xA0;500</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-528" style="width: 3.809em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.106em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1003.11em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-529"><span class="mtext" id="MathJax-Span-530" style="font-family: STIXGeneral;">R</span><span class="mspace" id="MathJax-Span-531" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mtext" id="MathJax-Span-532" style="font-family: STIXGeneral;">3 500</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace"></mspace><mtext>3 500</mtext></math></span></span><script type="math/tex" id="MathJax-Element-130">\text{R}\,\text{3 500}</script></span> into a savings account which earns simple interest. The account grows to a value of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-131-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace" /><mtext>7&#xA0;042,00</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-533" style="width: 5.331em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.335em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1004.34em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-534"><span class="mtext" id="MathJax-Span-535" style="font-family: STIXGeneral;">R</span><span class="mspace" id="MathJax-Span-536" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mtext" id="MathJax-Span-537" style="font-family: STIXGeneral;">7 042,00</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace"></mspace><mtext>7 042,00</mtext></math></span></span><script type="math/tex" id="MathJax-Element-131">\text{R}\,\text{7 042,00}</script></span> in <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-132-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>11</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-538" style="width: 1.232em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.998em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.88em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-539"><span class="mtext" id="MathJax-Span-540" style="font-family: STIXGeneral;">11</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>11</mtext></math></span></span><script type="math/tex" id="MathJax-Element-132">\text{11}</script></span> years. What is the interest rate for this account?
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
Give your answer as a percentage rounded to one decimal place.
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="9,2" size="10">% per annum.
<div class="response-type">numeric</div></div></div></div>
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</div></section><section class="sv-section sv-question sv-table"><br><div class="id1525-226">ID is: 1525 Seed is: 226<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/7d0c3007-0e0d-5f51-b370-3210d312622f" method="POST">
<span class="worked_example"><h3 class="sv-heading">Simple interest: finding <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-133-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-541" style="width: 0.392em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.314em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.797em, 1000.27em, 2.656em, -999.998em); top: -2.535em; left: 0em;"><span class="mrow" id="MathJax-Span-542"><span class="mi" id="MathJax-Span-543" style="font-family: STIXGeneral; font-style: italic;">𝑖</span></span><span style="display: inline-block; width: 0px; height: 2.539em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.045em; border-left: 0px solid; width: 0px; height: 0.86em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></span></span><script type="math/tex" id="MathJax-Element-133"> i </script></span> </h3>
</span><div class="problem">
<p>
Chukwuma deposits <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-134-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace" /><mtext>5&#xA0;000</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-544" style="width: 3.809em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.106em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1003.11em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-545"><span class="mtext" id="MathJax-Span-546" style="font-family: STIXGeneral;">R</span><span class="mspace" id="MathJax-Span-547" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mtext" id="MathJax-Span-548" style="font-family: STIXGeneral;">5 000</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace"></mspace><mtext>5 000</mtext></math></span></span><script type="math/tex" id="MathJax-Element-134">\text{R}\,\text{5 000}</script></span> into a savings account which pays simple interest. The account grows to a value of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-135-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace" /><mtext>9&#xA0;730,00</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-549" style="width: 5.331em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.335em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1004.34em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-550"><span class="mtext" id="MathJax-Span-551" style="font-family: STIXGeneral;">R</span><span class="mspace" id="MathJax-Span-552" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mtext" id="MathJax-Span-553" style="font-family: STIXGeneral;">9 730,00</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace"></mspace><mtext>9 730,00</mtext></math></span></span><script type="math/tex" id="MathJax-Element-135">\text{R}\,\text{9 730,00}</script></span> in <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-136-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>11</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-554" style="width: 1.232em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.998em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.88em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-555"><span class="mtext" id="MathJax-Span-556" style="font-family: STIXGeneral;">11</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>11</mtext></math></span></span><script type="math/tex" id="MathJax-Element-136">\text{11}</script></span> years. Determine the interest rate the account earns.
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
Give your answer as a percentage rounded to one decimal place.
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="8,6" size="10">% per annum.
<div class="response-type">numeric</div></div></div></div>
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</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id4349-5182">ID is: 4349 Seed is: 5182<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/7d0c3007-0e0d-5f51-b370-3210d312622f" method="POST">
<span class="worked_example"><h3 class="sv-heading">Calculate the compound rate of depreciation</h3>
</span><div class="problem">
<p>
<span class="colored" style="color:gray"><em>Adapted from DBE Nov 2015 Grade 11, P1, Q8</em></span><br>
<a url="/info/maths-formulae" href="https://www.emas.com/info/maths-formulae">Maths formulas</a>
</p>
<p>
A car costing <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-137-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace" /><mtext>210&#xA0;000</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-557" style="width: 5.038em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.101em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1004.1em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-558"><span class="mtext" id="MathJax-Span-559" style="font-family: STIXGeneral;">R</span><span class="mspace" id="MathJax-Span-560" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mtext" id="MathJax-Span-561" style="font-family: STIXGeneral;">210 000</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace"></mspace><mtext>210 000</mtext></math></span></span><script type="math/tex" id="MathJax-Element-137">\text{R}\,\text{210 000}</script></span> has a book value of
<span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-138-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace" /><mtext>34&#xA0;629,44</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-562" style="width: 5.975em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.862em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1004.86em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-563"><span class="mtext" id="MathJax-Span-564" style="font-family: STIXGeneral;">R</span><span class="mspace" id="MathJax-Span-565" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mtext" id="MathJax-Span-566" style="font-family: STIXGeneral;">34 629,44</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace"></mspace><mtext>34 629,44</mtext></math></span></span><script type="math/tex" id="MathJax-Element-138">\text{R}\,\text{34 629,44}</script></span> after <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-139-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>7</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-567" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-568"><span class="mtext" id="MathJax-Span-569" style="font-family: STIXGeneral;">7</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>7</mtext></math></span></span><script type="math/tex" id="MathJax-Element-139">\text{7}</script></span> years.
If the value of the car depreciates at <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-140-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mspace width="thinmathspace" /><mi mathvariant="normal">&#x0025;</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-570" style="width: 1.642em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.35em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.29em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-571"><span class="mi" id="MathJax-Span-572" style="font-family: STIXGeneral; font-style: italic;">𝑟</span><span class="mspace" id="MathJax-Span-573" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-574" style="font-family: STIXGeneral;">%</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mspace width="thinmathspace"></mspace><mi mathvariant="normal">%</mi></math></span></span><script type="math/tex" id="MathJax-Element-140">r \,\%</script></span> p.a. on a reducing
balance, calculate <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-141-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-575" style="width: 0.53em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.413em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.876em, 1000.41em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-576"><span class="mi" id="MathJax-Span-577" style="font-family: STIXGeneral; font-style: italic;">𝑟</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></span></span><script type="math/tex" id="MathJax-Element-141">r</script></span>.</span>
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
Give your answer as a percentage, rounded to two decimal places. <strong>Do not</strong> type the percent symbol (<span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-142-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">&#x0025;</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-578" style="width: 0.94em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.764em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.71em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-579"><span class="mi" id="MathJax-Span-580" style="font-family: STIXGeneral;">%</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">%</mi></math></span></span><script type="math/tex" id="MathJax-Element-142">\%</script></span>): it has already been written for you.
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-143-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-581" style="width: 1.759em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.408em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.876em, 1001.35em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-582"><span class="mi" id="MathJax-Span-583" style="font-family: STIXGeneral; font-style: italic;">𝑟</span><span class="mo" id="MathJax-Span-584" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo></math></span></span><script type="math/tex" id="MathJax-Element-143">r = </script></span> <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="22,7" size="10"> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-144-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">&#x0025;</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-585" style="width: 0.94em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.764em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.71em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-586"><span class="mi" id="MathJax-Span-587" style="font-family: STIXGeneral;">%</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">%</mi></math></span></span><script type="math/tex" id="MathJax-Element-144">\%</script></span>
<div class="response-type">one-of<div class="response-subtype">type(numeric.abserror(0.01))</div></div></div></div></div>
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</div></section><section class="sv-section sv-question sv-table"><br><div class="id4349-4076">ID is: 4349 Seed is: 4076<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/7d0c3007-0e0d-5f51-b370-3210d312622f" method="POST">
<span class="worked_example"><h3 class="sv-heading">Calculate the compound rate of depreciation</h3>
</span><div class="problem">
<p>
<span class="colored" style="color:gray"><em>Adapted from DBE Nov 2015 Grade 11, P1, Q8</em></span><br>
<a url="/info/maths-formulae" href="https://www.emas.com/info/maths-formulae">Maths formulas</a>
</p>
<p>
Classroom furniture has a book value of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-145-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace" /><mtext>202&#xA0;725,79</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-588" style="width: 6.502em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.331em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1005.27em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-589"><span class="mtext" id="MathJax-Span-590" style="font-family: STIXGeneral;">R</span><span class="mspace" id="MathJax-Span-591" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mtext" id="MathJax-Span-592" style="font-family: STIXGeneral;">202 725,79</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace"></mspace><mtext>202 725,79</mtext></math></span></span><script type="math/tex" id="MathJax-Element-145">\text{R}\,\text{202 725,79}</script></span>. The school bought the furniture <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-146-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>8</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-593" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-594"><span class="mtext" id="MathJax-Span-595" style="font-family: STIXGeneral;">8</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>8</mtext></math></span></span><script type="math/tex" id="MathJax-Element-146">\text{8}</script></span>
years ago for <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-147-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace" /><mtext>432&#xA0;000</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-596" style="width: 5.038em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.101em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1004.1em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-597"><span class="mtext" id="MathJax-Span-598" style="font-family: STIXGeneral;">R</span><span class="mspace" id="MathJax-Span-599" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mtext" id="MathJax-Span-600" style="font-family: STIXGeneral;">432 000</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace"></mspace><mtext>432 000</mtext></math></span></span><script type="math/tex" id="MathJax-Element-147">\text{R}\,\text{432 000}</script></span>. If the value of the classroom furniture
depreciates at <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-148-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mspace width="thinmathspace" /><mi mathvariant="normal">&#x0025;</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-601" style="width: 1.642em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.35em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.29em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-602"><span class="mi" id="MathJax-Span-603" style="font-family: STIXGeneral; font-style: italic;">𝑟</span><span class="mspace" id="MathJax-Span-604" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-605" style="font-family: STIXGeneral;">%</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mspace width="thinmathspace"></mspace><mi mathvariant="normal">%</mi></math></span></span><script type="math/tex" id="MathJax-Element-148">r\, \%</script></span> p.a. on a reducing balance, calculate <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-149-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-606" style="width: 0.53em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.413em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.876em, 1000.41em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-607"><span class="mi" id="MathJax-Span-608" style="font-family: STIXGeneral; font-style: italic;">𝑟</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></span></span><script type="math/tex" id="MathJax-Element-149">r</script></span>.</span>
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
Give your answer as a percentage, rounded to two decimal places. <strong>Do not</strong> type the percent symbol (<span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-150-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">&#x0025;</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-609" style="width: 0.94em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.764em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.71em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-610"><span class="mi" id="MathJax-Span-611" style="font-family: STIXGeneral;">%</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">%</mi></math></span></span><script type="math/tex" id="MathJax-Element-150">\%</script></span>): it has already been written for you.
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-151-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-612" style="width: 1.759em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.408em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.876em, 1001.35em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-613"><span class="mi" id="MathJax-Span-614" style="font-family: STIXGeneral; font-style: italic;">𝑟</span><span class="mo" id="MathJax-Span-615" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo></math></span></span><script type="math/tex" id="MathJax-Element-151">r = </script></span> <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="9,02" size="10"> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-152-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">&#x0025;</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-616" style="width: 0.94em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.764em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.71em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-617"><span class="mi" id="MathJax-Span-618" style="font-family: STIXGeneral;">%</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">%</mi></math></span></span><script type="math/tex" id="MathJax-Element-152">\%</script></span>
<div class="response-type">one-of<div class="response-subtype">type(numeric.abserror(0.01))</div></div></div></div></div>
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</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id1534-2819">ID is: 1534 Seed is: 2819<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/7d0c3007-0e0d-5f51-b370-3210d312622f" method="POST">
<span class="worked_example"><h3 class="sv-heading">Increasing values: finding i</h3>
</span><div class="problem">
<p>
After <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-153-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>5</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-619" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-620"><span class="mtext" id="MathJax-Span-621" style="font-family: STIXGeneral;">5</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>5</mtext></math></span></span><script type="math/tex" id="MathJax-Element-153">\text{5}</script></span> years an investment doubles in value. At what annual percentage rate was interest compounded? Give your answer correct to two decimal places.
</p>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span> <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="14,87" size="10">% per annum.<div class="response-type">numeric</div></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:06:49.075660"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><section class="sv-section sv-question sv-table"><br><div class="id1534-7281">ID is: 1534 Seed is: 7281<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/7d0c3007-0e0d-5f51-b370-3210d312622f" method="POST">
<span class="worked_example"><h3 class="sv-heading">Increasing values: finding i</h3>
</span><div class="problem">
<p>
After <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-154-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>9</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-622" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-623"><span class="mtext" id="MathJax-Span-624" style="font-family: STIXGeneral;">9</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>9</mtext></math></span></span><script type="math/tex" id="MathJax-Element-154">\text{9}</script></span> years an investment triples (gets 3 times bigger) in value. At what annual percentage rate was interest compounded? Give your answer correct to two decimal places.
</p>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span> <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="12,98" size="10">% per annum.<div class="response-type">numeric</div></div></div></div>
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</div></section></section> <section class="sv-section">
<h2>3. Timelines</h2>
<hr><section class="sv-section sv-question sv-table"><br><div class="id1549-813">ID is: 1549 Seed is: 813<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/7d0c3007-0e0d-5f51-b370-3210d312622f" method="POST">
<span class="worked_example"><h3 class="sv-heading">Timeline questions: making a timeline diagram</h3>
</span><div class="problem">
<p>One of your classmates is making a timeline diagram for the situation described here:</p>
<ul>
<li>Make Some Money Bank offers a savings account which gets <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-155-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>10,9</mtext><mi mathvariant="normal">&#x0025;</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-625" style="width: 3.106em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.52em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.46em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-626"><span class="mtext" id="MathJax-Span-627" style="font-family: STIXGeneral;">10,9</span><span class="mi" id="MathJax-Span-628" style="font-family: STIXGeneral;">%</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>10,9</mtext><mi mathvariant="normal">%</mi></math></span></span><script type="math/tex" id="MathJax-Element-155">\text{10,9}\%</script></span> interest p.a. compounded semi-annually. Khethang decides to open an account, and deposits <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-156-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace" /><mtext>6&#xA0;750,00</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-629" style="width: 5.331em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.335em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1004.34em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-630"><span class="mtext" id="MathJax-Span-631" style="font-family: STIXGeneral;">R</span><span class="mspace" id="MathJax-Span-632" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mtext" id="MathJax-Span-633" style="font-family: STIXGeneral;">6 750,00</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace"></mspace><mtext>6 750,00</mtext></math></span></span><script type="math/tex" id="MathJax-Element-156">\text{R}\,\text{6 750,00}</script></span>. His account accrues interest for <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-157-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>5</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-634" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-635"><span class="mtext" id="MathJax-Span-636" style="font-family: STIXGeneral;">5</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>5</mtext></math></span></span><script type="math/tex" id="MathJax-Element-157">\text{5}</script></span> years until he puts <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-158-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace" /><mtext>2&#xA0;500</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-637" style="width: 3.809em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.106em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1003.11em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-638"><span class="mtext" id="MathJax-Span-639" style="font-family: STIXGeneral;">R</span><span class="mspace" id="MathJax-Span-640" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mtext" id="MathJax-Span-641" style="font-family: STIXGeneral;">2 500</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace"></mspace><mtext>2 500</mtext></math></span></span><script type="math/tex" id="MathJax-Element-158">\text{R}\,\text{2 500}</script></span> more into the account. After that, Khethang leaves the money in the account until <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-159-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>12</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-642" style="width: 1.232em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.998em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-643"><span class="mtext" id="MathJax-Span-644" style="font-family: STIXGeneral;">12</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>12</mtext></math></span></span><script type="math/tex" id="MathJax-Element-159">\text{12}</script></span> years after his original deposit. </li>
</ul>
<p> Here is the diagram he started; however, he is not finished yet.</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/1549/813/0"><img src="./CAPS-Maths-Grade-11-9-Finance-growth-and-decay_files/0" width="450" height="250"></a></div>
<p>He needs help with this information: </p>
<ul>
<li><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-160-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace" /><mtext>2&#xA0;500</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-645" style="width: 3.809em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.106em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1003.11em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-646"><span class="mtext" id="MathJax-Span-647" style="font-family: STIXGeneral;">R</span><span class="mspace" id="MathJax-Span-648" style="height: 0em; vertical-align: 0em; width: 0.179em; display: inline-block; overflow: hidden;"></span><span class="mtext" id="MathJax-Span-649" style="font-family: STIXGeneral;">2 500</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mspace width="thinmathspace"></mspace><mtext>2 500</mtext></math></span></span><script type="math/tex" id="MathJax-Element-160">\text{R}\,\text{2 500}</script></span></li>
<li><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-161-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>,</mo><mn>9</mn><mi mathvariant="normal">&#x0025;</mi><mrow class="MJX-TeXAtom-ORD"><mtext>&#xA0;compounded semi-annually</mtext></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-650" style="width: 17.099em; display: inline-block;"><span style="display: inline-block; position: relative; width: 13.996em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1014em, 2.93em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-651"><span class="mn" id="MathJax-Span-652" style="font-family: STIXGeneral;">10</span><span class="mo" id="MathJax-Span-653" style="font-family: STIXGeneral;">,</span><span class="mn" id="MathJax-Span-654" style="font-family: STIXGeneral; padding-left: 0.179em;">9</span><span class="mi" id="MathJax-Span-655" style="font-family: STIXGeneral;">%</span><span class="texatom" id="MathJax-Span-656"><span class="mrow" id="MathJax-Span-657"><span class="mtext" id="MathJax-Span-658" style="font-family: STIXGeneral;"> compounded semi-annually</span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.354em; border-left: 0px solid; width: 0px; height: 1.289em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>,</mo><mn>9</mn><mi mathvariant="normal">%</mi><mrow class="MJX-TeXAtom-ORD"><mtext> compounded semi-annually</mtext></mrow></math></span></span><script type="math/tex" id="MathJax-Element-161">10,9\% \textrm{ compounded semi-annually}</script></span></li>