Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 5 - Exponential and Logarithmic Functions - 5.7 Financial Models - 5.7 Assess Your Understanding - Page 321: 19



Work Step by Step

According to the Compound Interest Formula, where $P$ is the principal, the amount deposited, $r$ is the annual interest rate, $n$ is the number of times the interest is compounded annually, $t$ is the number of years, $A$ is the amount you get back after $t$ years: $A=P\cdot(1+\frac{r}{n})^{n\cdot t}$ Here we have: $t=2\text{ years}$ $r=4\%=0.04$ $A=\$600$ $n=4$ (since it is compounded quarterly) Substitute these values into the formula above to obtain: $\$600=P\cdot\left(1+\frac{0.04}{4}\right)^{4\cdot 2}$ Hence, $P=\dfrac{\$600}{\left(1+\frac{0.04}{4}\right)^{4\cdot 2}}\approx\$554.09$
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