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style="width: 100px; height: 100px; float: left;">This chapter explores the financial application of geometric sequences in the form of compound interest calculations. It then goes on to look at loans and annuities where payments at regular intervals make for some complex algorithms. The finance app on your GDC is a huge help here and this chapter will talk you through using all of that.</div> <div class="panel panel-has-colored-body panel-turquoise"> <div class="panel-heading"><a class="expander pull-right" href="#"><span class="fa fa-plus"></span></a> <div> <p>Key Concepts</p> </div> </div> <div class="panel-body"> <p>In this chapter you will learn about and practice,</p> <ul> <li>The concept of compound interest as repeated percentage increase and depreciation as repeated percentage decrease.</li> <li>working with different compounding periods</li> <li>Solving problems in involving loans and annuities</li> <li>Learning how to use your GDC in different ways and, in particular the finance app to solve problems in involving all of the above</li> </ul> </div> <div class="panel-footer"> <div> <p>text</p> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander pull-right" href="#"><span class="fa fa-plus"></span></a> <div> <p>Essentials</p> </div> </div> <div class="panel-body"> <h4>Compound Interest Slides</h4> <p>The following slides outline the key points to know and understand about compound interest and include lots of worked examples. See the video section below for explanations.</p> <div id="carousel-279" class="dynamic-gallery carousel slide" data-id="279"><div class="carousel-inner" role="listbox"><div class="item active"><a class="fancy" href="../../../std-galleries/15-279/compound-interest-etc001.jpeg" data-fancybox="gallery-279" title="" data-caption=""><img alt="" src="../../../std-galleries/15-279/compound-interest-etc001.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-279/compound-interest-etc002.jpeg" data-fancybox="gallery-279" title="" data-caption=""><img alt="" src="../../../std-galleries/15-279/compound-interest-etc002.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-279/compound-interest-etc003.jpeg" data-fancybox="gallery-279" title="" data-caption=""><img alt="" src="../../../std-galleries/15-279/compound-interest-etc003.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-279/compound-interest-etc004.jpeg" data-fancybox="gallery-279" title="" data-caption=""><img alt="" src="../../../std-galleries/15-279/compound-interest-etc004.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-279/compound-interest-etc006.jpeg" data-fancybox="gallery-279" title="" data-caption=""><img alt="" src="../../../std-galleries/15-279/compound-interest-etc006.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-279/compound-interest-etc007.jpeg" data-fancybox="gallery-279" title="" data-caption=""><img alt="" src="../../../std-galleries/15-279/compound-interest-etc007.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-279/compound-interest-etc008.jpeg" data-fancybox="gallery-279" title="" data-caption=""><img alt="" src="../../../std-galleries/15-279/compound-interest-etc008.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-279/compound-interest-etc009.jpeg" data-fancybox="gallery-279" title="" data-caption=""><img alt="" src="../../../std-galleries/15-279/compound-interest-etc009.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-279/compound-interest-etc011.jpeg" data-fancybox="gallery-279" title="" data-caption=""><img alt="" src="../../../std-galleries/15-279/compound-interest-etc011.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-279/compound-interest-etc012.jpeg" data-fancybox="gallery-279" title="" data-caption=""><img alt="" src="../../../std-galleries/15-279/compound-interest-etc012.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-279/compound-interest-etc014.jpeg" data-fancybox="gallery-279" title="" data-caption=""><img alt="" src="../../../std-galleries/15-279/compound-interest-etc014.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-279/compound-interest-etc015.jpeg" data-fancybox="gallery-279" title="" data-caption=""><img alt="" src="../../../std-galleries/15-279/compound-interest-etc015.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-279/compound-interest-etc016.jpeg" data-fancybox="gallery-279" title="" data-caption=""><img alt="" src="../../../std-galleries/15-279/compound-interest-etc016.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-279/compound-interest-etc018.jpeg" data-fancybox="gallery-279" title="" data-caption=""><img alt="" src="../../../std-galleries/15-279/compound-interest-etc018.jpeg"></a></div></div><a class="left carousel-control" href="#carousel-279" role="button" data-slide="prev"><i class="fa fa-fw fa-chevron-left"></i></a><a class="right carousel-control" href="#carousel-279" role="button" data-slide="next"><i class="fa fa-fw fa-chevron-right"></i></a></div><ol class="std-carousel-indicators"><li data-index="0"><img title="Click to view" src="../../../std-galleries/15-279/compound-interest-etc001-thumb128.jpg"><li><li data-index="1"><img title="Click to view" src="../../../std-galleries/15-279/compound-interest-etc002-thumb128.jpg"><li><li data-index="2"><img title="Click to view" src="../../../std-galleries/15-279/compound-interest-etc003-thumb128.jpg"><li><li data-index="3"><img title="Click to view" src="../../../std-galleries/15-279/compound-interest-etc004-thumb128.jpg"><li><li data-index="4"><img title="Click to view" src="../../../std-galleries/15-279/compound-interest-etc006-thumb128.jpg"><li><li data-index="5"><img title="Click to view" src="../../../std-galleries/15-279/compound-interest-etc007-thumb128.jpg"><li><li data-index="6"><img title="Click to view" src="../../../std-galleries/15-279/compound-interest-etc008-thumb128.jpg"><li><li data-index="7"><img title="Click to view" src="../../../std-galleries/15-279/compound-interest-etc009-thumb128.jpg"><li><li data-index="8"><img title="Click to view" src="../../../std-galleries/15-279/compound-interest-etc011-thumb128.jpg"><li><li data-index="9"><img title="Click to view" src="../../../std-galleries/15-279/compound-interest-etc012-thumb128.jpg"><li><li data-index="10"><img title="Click to view" src="../../../std-galleries/15-279/compound-interest-etc014-thumb128.jpg"><li><li data-index="11"><img title="Click to view" src="../../../std-galleries/15-279/compound-interest-etc015-thumb128.jpg"><li><li data-index="12"><img title="Click to view" src="../../../std-galleries/15-279/compound-interest-etc016-thumb128.jpg"><li><li data-index="13"><img title="Click to view" src="../../../std-galleries/15-279/compound-interest-etc018-thumb128.jpg"><li></li></ol> <h4>Compound Interest Videos</h4> <p>The following series of videos explain all the key points and go through worked examples</p> <div class="panel panel-has-colored-body panel-orange"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>1. Compound Interest Concept</p> </div> </div> <div class="panel-body"> <p>Here we look at understanding and carrying out compound interest calculations, how it works and what it means.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/703262125"></iframe></div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-expandable panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>2. Different Compounding periods</p> </div> </div> <div class="panel-body"> <p>In this video we look at how to deal with different compounding periods, when interest is calculate more often than once a year.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/703280356"></iframe></div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-expandable panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>3. The Compound Interest Formula</p> </div> </div> <div class="panel-body"> <p>Here we look at the compound interest formula that you have in your formula booklets and show how it fits with what was done in the first two videos.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/703290713"></iframe></div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-expandable panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>4. The finance app for Compound Interest calculations</p> </div> </div> <div class="panel-body"> <p>Here we look at how to use your finance app to do compound interest calculations and, in particular, for problems where you need to solve for time and interest rate.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/703312048"></iframe></div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-expandable panel-yellow"> <div class="panel-heading"> <div> <p>5. Depreciation</p> </div> </div> <div class="panel-body"> <p>This video shows how the same principles used above apply to work with depreciation.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/703315316"></iframe></div> </div> <div class="panel-footer"> <div> </div> </div> </div> <h4>Loans & Annuities Slides</h4> <p>The following slides outline the key points to know and understand about loans and annuities and include lots of worked examples. See the video section below for explanations.</p> <div id="carousel-280" class="dynamic-gallery carousel slide" data-id="280"><div class="carousel-inner" role="listbox"><div class="item active"><a class="fancy" href="../../../std-galleries/15-280/compound-interest-etc019.jpeg" data-fancybox="gallery-280" title="" data-caption=""><img alt="" src="../../../std-galleries/15-280/compound-interest-etc019.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-280/compound-interest-etc020.jpeg" data-fancybox="gallery-280" title="" data-caption=""><img alt="" src="../../../std-galleries/15-280/compound-interest-etc020.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-280/compound-interest-etc021.jpeg" data-fancybox="gallery-280" title="" data-caption=""><img alt="" src="../../../std-galleries/15-280/compound-interest-etc021.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-280/compound-interest-etc022.jpeg" data-fancybox="gallery-280" title="" data-caption=""><img alt="" src="../../../std-galleries/15-280/compound-interest-etc022.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-280/compound-interest-etc023.jpeg" data-fancybox="gallery-280" title="" data-caption=""><img alt="" src="../../../std-galleries/15-280/compound-interest-etc023.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-280/compound-interest-etc024.jpeg" data-fancybox="gallery-280" title="" data-caption=""><img alt="" src="../../../std-galleries/15-280/compound-interest-etc024.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-280/compound-interest-etc027.jpeg" data-fancybox="gallery-280" title="" data-caption=""><img alt="" src="../../../std-galleries/15-280/compound-interest-etc027.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-280/compound-interest-etc028.jpeg" data-fancybox="gallery-280" title="" data-caption=""><img alt="" src="../../../std-galleries/15-280/compound-interest-etc028.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-280/compound-interest-etc031.jpeg" data-fancybox="gallery-280" title="" data-caption=""><img alt="" src="../../../std-galleries/15-280/compound-interest-etc031.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-280/compound-interest-etc032.jpeg" data-fancybox="gallery-280" title="" data-caption=""><img alt="" src="../../../std-galleries/15-280/compound-interest-etc032.jpeg"></a></div></div><a class="left carousel-control" href="#carousel-280" role="button" data-slide="prev"><i class="fa fa-fw fa-chevron-left"></i></a><a class="right carousel-control" href="#carousel-280" role="button" data-slide="next"><i class="fa fa-fw fa-chevron-right"></i></a></div><ol class="std-carousel-indicators"><li data-index="0"><img title="Click to view" src="../../../std-galleries/15-280/compound-interest-etc019-thumb128.jpg"><li><li data-index="1"><img title="Click to view" src="../../../std-galleries/15-280/compound-interest-etc020-thumb128.jpg"><li><li data-index="2"><img title="Click to view" src="../../../std-galleries/15-280/compound-interest-etc021-thumb128.jpg"><li><li data-index="3"><img title="Click to view" src="../../../std-galleries/15-280/compound-interest-etc022-thumb128.jpg"><li><li data-index="4"><img title="Click to view" src="../../../std-galleries/15-280/compound-interest-etc023-thumb128.jpg"><li><li data-index="5"><img title="Click to view" src="../../../std-galleries/15-280/compound-interest-etc024-thumb128.jpg"><li><li data-index="6"><img title="Click to view" src="../../../std-galleries/15-280/compound-interest-etc027-thumb128.jpg"><li><li data-index="7"><img title="Click to view" src="../../../std-galleries/15-280/compound-interest-etc028-thumb128.jpg"><li><li data-index="8"><img title="Click to view" src="../../../std-galleries/15-280/compound-interest-etc031-thumb128.jpg"><li><li data-index="9"><img title="Click to view" src="../../../std-galleries/15-280/compound-interest-etc032-thumb128.jpg"><li></li></ol> <h4>Loans & Annuities Videos</h4> <p>The following series of videos explain all the key points and go through worked examples</p> <div class="panel panel-has-colored-body panel-orange"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>6. Introduction to Loans & Annuities</p> </div> </div> <div class="panel-body"> <p>Here we look at understanding and carrying out compound interest calculations, how it works and what it means.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/703323941"></iframe></div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-expandable panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>7. Focus on loans</p> </div> </div> <div class="panel-body"> <p>Working through examples of solving problems with loans.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/703335121"></iframe></div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-expandable panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>8. Focus on savings annuities</p> </div> </div> <div class="panel-body"> <p>Working through examples of solving problems with savings annuities.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/703354616"></iframe></div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-expandable panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>9. Focus on gift annuities</p> </div> </div> <div class="panel-body"> <p>Working through examples of solving problems with gift annuities.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/703383928"></iframe></div> </div> <div class="panel-footer"> <div> </div> </div> </div> <p>....</p> </div> <div class="panel-footer"> <div> <p>text</p> </div> </div> </div> <div class="panel panel-has-colored-body panel-violet"> <div class="panel-heading"><a class="expander pull-right" href="#"><span class="fa fa-plus"></span></a> <div> <p>Summary - coming soon</p> </div> </div> <div class="panel-body"> <p>These slides summarise the essential understanding and skills in this topic. They are what we have previously included as 'Flash Cards' or 'revision cards</p> <p>Insert rotating gallery here</p> </div> <div class="panel-footer"> <div> <p>text</p> </div> </div> </div> <div class="panel panel-has-colored-body panel-green"> <div class="panel-heading"><a class="expander pull-right" href="#"><span class="fa fa-plus"></span></a> <div> <p>Test yourself</p> </div> </div> <div class="panel-body"> <div> <h4>Self Checking Quiz</h4> <p>Practice your understanding on these quiz questions. Check your answers when you are done and read the worked solutions when you get stuck. If you find there are still some gaps in your understanding then go back to the videos above<em>.</em></p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="tib-quiz" data-stats="15-906-2786"><div class="label label-default q-number">1</div><div class="exercise shadow-bottom"><div class="q-question"><p>You invest $4000 in an account that pays compound interest at 5% for 6 years. Work out the value of your investment after 6 years if interest is compounded...</p><p>a) Annually</p><p>b) Monthly</p><p>c) Quarterly</p><p>Give your answers to the nearest dollar.</p></div><div class="q-answer"><p>a) $ <input type="text" style="height: auto;" data-c="5360"> <span class="review"></span> </p><p>b) $ <input type="text" style="height: auto;" data-c="5396"> <span class="review"></span> </p><p>c) $ <input type="text" style="height: auto;" data-c="5389"> <span class="review"></span> </p></div><div class="q-explanation"><p>Use the compound interest formula</p><p><span class="math-tex">\(4000\times\left(1+\frac{5}{\frac{k}{100}}\right)^{\left(6\times k\right)}\)</span></p><p>a) k = 1, b) k = 12, c) k = 4</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">2</div><div class="exercise shadow-bottom"><div class="q-question"><p>You invest $42300 in an account that pays compound interest at 2.5% for 10 years. Work out the value of your investment after 10 years if interest is compounded...</p><p>a) Semi Annually</p><p>b) Monthly</p><p>c) Quarterly</p><p>Give your answers to the nearest dollar.</p></div><div class="q-answer"><p>a) $ <input type="text" style="height: auto;" data-c="54230"> <span class="review"></span> </p><p>b) $ <input type="text" style="height: auto;" data-c="54300"> <span class="review"></span></p><p>c) $ <input type="text" style="height: auto;" data-c="54272"> <span class="review"></span></p></div><div class="q-explanation"><p>Use the compound interest formula</p><p><span class="math-tex">\(42300\times\left(1+\frac{6}{\frac{k}{100}}\right)^{\left(10\times k\right)}\)</span></p><p>a) k = 2, b) k = 12, c) k = 4</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">3</div><div class="exercise shadow-bottom"><div class="q-question"><p>You invest $3500 at an interest rate of 6%pa compounding monthly. How long will it take for your investment to double? Give your answer correct to the nearest month.</p></div><div class="q-answer"><p> <input type="text" style="height: auto;" data-c="139"> <span class="review"></span> months</p></div><div class="q-explanation"><p>You are trying to solve the equation..</p><p><span class="math-tex">\(3500\cdot\left(1+\frac{6}{\frac{12}{100}}\right)^{x}=7000\)</span></p><p>You can use your finance app and solve for n with</p><p>n = ? (what you are looking for)</p><p>I = 6%</p><p>PV = -3500</p><p>PMT = 0</p><p>FV = 7000</p><p>P/Y = 12</p><p>C/Y = 12</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">4</div><div class="exercise shadow-bottom"><div class="q-question"><p>An investment of $5000 is put in a savings account for 8 years with interest compounding quarterly. At the end the investment is worth $9500. What was the interest rate for the investment? Give your answer to 3sf.</p></div><div class="q-answer"><p> <input type="text" style="height: auto;" data-c="8.10"> <span class="review"></span> %</p></div><div class="q-explanation"><p>You are trying to solve the equation..</p><p><span class="math-tex">\(5000\cdot\left(1+\frac{x}{\frac{4}{100}}\right)^{8\times4}=9500\)</span></p><p>You can use your finance app and solve for I with</p><p>n = 32</p><p>I = ? (what you are looking for)</p><p>PV = -5000</p><p>PMT = 0</p><p>FV = 9500</p><p>P/Y = 12</p><p>C/Y = 12</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">5</div><div class="exercise shadow-bottom"><div class="q-question"><p>You buy are car for $12000. Its value depreciates at 8% a year. What is the value of the car after</p><p>a) 1 year</p><p>b) 3 years</p><p>c) 10 years</p><p>Give your answers to 3sf</p></div><div class="q-answer"><p>a) $ <input type="text" style="height: auto;" data-c="11000"> <span class="review"></span></p><p>b) $ <input type="text" style="height: auto;" data-c="9340"> <span class="review"></span></p><p>c) $ <input type="text" style="height: auto;" data-c="5210"> <span class="review"></span></p></div><div class="q-explanation"><p>Use the formula as follows</p><p><span class="math-tex">\(12000\cdot\left(1-\frac{8}{100}\right)^{x}\)</span></p><p>a) x = 1</p><p>b) x = 3</p><p>c) x = 10</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">6</div><div class="exercise shadow-bottom"><div class="q-question"><p>A new car valued at $25000 depreciates in value at 5% every year. After how many years will the car first be worth less than half of its original value?</p></div><div class="q-answer"><p> <input type="text" style="height: auto;" data-c="14"> <span class="review"></span> years</p></div><div class="q-explanation"><p>You are trying to solve the equation...</p><p><span class="math-tex">\(25000\cdot\left(1-\frac{5}{100}\right)^{x}=12500\)</span></p><p>Enter the function in your GDC</p><p><span class="math-tex">\(y=25000\cdot\left(1-\frac{5}{100}\right)^{x}\)</span></p><p>Look for the first value of x where the value of the car is less than 12500</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">7</div><div class="exercise shadow-bottom"><div class="q-question"><p>You take a loan of $5000 at 3.2%pa compounding monthly, being paid back monthly over a period of 6 years. What are your monthly payments? Give your answer to 2 decimal places. (money)</p></div><div class="q-answer"><p>$ <input type="text" style="height: auto;" data-c="76.42"> <span class="review"></span> per month</p></div><div class="q-explanation"><p>Use your finance app and solve for PMT with</p><p>n = 72 (6 x 12 every month for 6 years - this is the number of payments made)</p><p>I = 3.2%</p><p>PV = 5000</p><p>PMT = ? (what you are looking for)</p><p>FV = 0 (nothing left when the loan is paid)</p><p>P/Y = 12 monthly payments</p><p>C/Y = 12 Interest calculated monthly</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">8</div><div class="exercise shadow-bottom"><div class="q-question"><p>You take a loan of $8000 at x% pa compounding quarterly, being paid back quarterly over a period of 8 years. Your monthly repayments are $260, what is the interest rate? Give your answer to 2 decimal places.</p></div><div class="q-answer"><p>$ <input type="text" style="height: auto;" data-c="0.96"> <span class="review"></span> %</p></div><div class="q-explanation"><p>Use your finance app and solve for I with</p><p>n = 32 (8 x 4 every quarter for 8 years - this is the number of payments made)</p><p>I = ? (what you are looking for)</p><p>PV = 8000</p><p>PMT = -260 (what you are looking for)</p><p>FV = 0 (nothing left when the loan is paid)</p><p>P/Y = 4 quarterly payments</p><p>C/Y = 4 calculated quarterly</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><p>...</p><div class="label label-default q-number">9</div><div class="exercise shadow-bottom"><div class="q-question"><p>You are saving for a big trip. You have 3 years to save $10000. A bank offers a savings annuity at 3%pa compounding monthly. How much do you need to put in each month to reach your target? Give your answer to 2 decimal places. (money)</p></div><div class="q-answer"><p>$ <input type="text" style="height: auto;" data-c="265.81"> <span class="review"></span> per month</p></div><div class="q-explanation"><p>Use your finance app and solve for PMT with</p><p>n = 36 (3 x 12 every month for 3 years - this is the number of payments made)</p><p>I = 3%</p><p>PV = 0 (you start with nothing)</p><p>PMT = ? (what you are looking for)</p><p>FV = 10000 (your target)</p><p>P/Y = 12 monthly payments</p><p>C/Y = 12 Interest calculated monthly</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><p>...</p><div class="label label-default q-number">10</div><div class="exercise shadow-bottom"><div class="q-question"><p>You are given a gift of $20000 to be paid out to you every quarter, with interest compounded monthly over a period of 10 years. The interest rate is 2.5%pa. How much will you receive each quarter? Give your answer to 2 decimal places. (money)</p></div><div class="q-answer"><p>$ <input type="text" style="height: auto;" data-c="566.80"> <span class="review"></span> per month</p></div><div class="q-explanation"><p>Use your finance app and solve for PMT with</p><p>n = 40 (10 x 4 every quarter for 10 years - this is the number of payments made)</p><p>I = 2.5%</p><p>PV = 20000 (your original gift)</p><p>PMT = ? (what you are looking for)</p><p>FV = 0 (at the end you have received all the money)</p><p>P/Y = 4 quarterly payments</p><p>C/Y = 12 Interest calculated monthly</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="totals"><span class="score"></span><button class="btn btn-success btn-block text-center check-total"><i class="fa fa-check-square-o"></i> Check</button></div></div><hr> </section> </div> </div> <div class="panel-footer"> <div> <p>text</p> </div> </div> </div> <div class="panel panel-has-colored-body panel-default"> <div class="panel-heading"><a class="expander pull-right" href="#"><span class="fa fa-plus"></span></a> <div> <p>Exam Style Questions - coming soon</p> </div> </div> <div class="panel-body"> <div> <p>The following are exam style questions on this topic that you should try on your own before checking against the video solution.</p> <div class="panel panel-has-colored-body panel-default"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 1</p> </div> </div> <div class="panel-body"> <div> <p>Put in a good quality image of the first exam question - this is a <strong>non expandable panel</strong> (solution goes in the hidden box)</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <p>Solution is embedded in a hidden box</p> </section> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-default panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 2</p> </div> </div> <div class="panel-body"> <div> <p>Put in a good quality image of the first exam question - this is an expandable panel. (solution goes in the hidden box)</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <p>Solution is embedded in a hidden box</p> </section> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-default panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 3</p> </div> </div> <div class="panel-body"> <div> <p>Put in a good quality image of the first exam question - this is an expandable panel. (solution goes in the hidden box)</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <p>Solution is embedded in a hidden box</p> </section> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> repeat expandable panels as necessary</div> </div> <div class="panel-footer"> <div> <p>text</p> </div> </div> </div> <div class="panel panel-has-colored-body panel-red"> <div class="panel-heading"><a class="expander pull-right" href="#"><span class="fa fa-plus"></span></a> <div> <p>Just for Fun</p> </div> </div> <div class="panel-body"> <div> <p>This session might include an idea for an exploration or a thought provoking question. This section can also be deleted (easily done via the code page) If it has nothing in it it should be deleted</p> </div> </div> <div class="panel-footer"> <div> <p>text</p> </div> </div> </div> <p>...</p> <div class="page-container panel-self-assessment" data-id="2786"> <div class="panel-heading">MY PROGRESS</div> <div class="panel-body understanding-rate"> <div class="msg"></div> <label class="label-lg">Self-assessment</label><p>How much of <strong>1.4 & 1.7 Compound Interest, Loans and Annuities</strong> have you understood?</p><div class="slider-container text-center"><div id="self-assessment-slider" class="sib-slider self-assessment " data-value="1" data-percentage=""></div></div> <label class="label-lg">My notes</label> <textarea name="page-notes" class="form-control" rows="3" placeholder="Write your notes here..."></textarea> </div> <div class="panel-footer text-xs-center"> <span id="last-edited" class="mb-xs-3"> </span> <div class="actions mt-xs-3"> <button id="save-my-progress" 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