Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 8 - Personal Finance - 8.4 Compound Interest - Exercise Set 8.4 - Page 521: 7

Answer

See below:

Work Step by Step

(a). Step 1: Rate is expressed as a decimal while calculating the interest. Thus, to convert the rate percent into a decimal, rate percent is divided by 100. \[\begin{align} & r=4.5percent \\ & =\frac{4.5}{100} \\ & =0.045 \end{align}\] Step 2: The rate is divided by 12, because the amount is compounded monthly. So, n is taken as \[12\]. The amount can be computed by using the formula:: \[\begin{align} & A=P{{\left( 1+\frac{r}{n} \right)}^{n\times t}} \\ & =\$4,500{{\left(1+\frac{0.045}{12}\right)}^{12\times3}}\\&=\$4,500\times{{\left(1.00375\right)}^{36}}\\&=\$5,149.116\end{align}\] Step 3: Rounding off the amount to the nearest cent: \[\$5,149.116=\$5,149.12\] After rounding off the amount (A) to the nearest cent, the amount will become \[\$5,149.12\]. (b). The interest can be computed by subtracting the original principal from the amount. The amount of money calculated in the first part is\[\$5,149.12\]. Thus, to calculate the interest, following formula is used: \[\begin{align} & \text{Interest}=\text{Amount}-\text{Principal} \\ & =\$5,149.12-\$4,500\\&=\$649.12\end{align}\] The interest calculated is \[\$649.12\].
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