Interest & hire purchase

Shop prices and GST

<p class="paragraph-header">Repeated percentage change</p>
<p>Repeated percentage changes act on the current amount. With initial value \(P\), rate \(r\%\) per year and \(n\) years:</p>
<div class="content-block content-block--table"><div class="table-container"><table style="width: 100%;"><thead><tr><th style="text-align: center; --cell-justify: center"><strong>Model</strong></th><th style="text-align: center; --cell-justify: center"><strong>Amount after the stated time</strong></th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">Annual compound growth</td><td style="text-align: center; --cell-justify: center">\(P\left(1+\dfrac r{100}\right)^n\)</td></tr><tr><td style="text-align: center; --cell-justify: center">Annual depreciation</td><td style="text-align: center; --cell-justify: center">\(P\left(1-\dfrac r{100}\right)^n\)</td></tr><tr><td style="text-align: center; --cell-justify: center">Simple interest</td><td style="text-align: center; --cell-justify: center">\(P\left(1+\dfrac{nr}{100}\right)\)</td></tr></tbody></table></div></div>
<p>Compound interest earns interest on earlier interest; simple interest is calculated on the original principal. Interest earned is the final amount minus \(P\).</p>
<p>Match the rate to the number of periods. To find an original value, divide the final value by the complete multiplier. Round money only at the end: to cents unless the question requests the nearest dollar.</p>

Repeated percentage changes act on the current amount. With initial value \(P\), rate \(r\%\) per year and \(n\) years:

Compound interest earns interest on earlier interest; simple interest is calculated on the original principal. Interest earned is the final amount minus \(P\).

Match the rate to the number of periods. To find an original value, divide the final value by the complete multiplier. Round money only at the end: to cents unless the question requests the nearest dollar.

Model	Amount after the stated time
Annual compound growth	\(P\left(1+\dfrac r{100}\right)^n\)
Annual depreciation	\(P\left(1-\dfrac r{100}\right)^n\)
Simple interest	\(P\left(1+\dfrac{nr}{100}\right)\)