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: 15



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: $t=2\text{ years}$ $r=6\%=0.06$ $A=\$100$ $n=12$ (since it is compounded monthly) Substitute these values into the formula above to obtain: $\$100=P\cdot\left(1+\frac{0.06}{12}\right)^{12\cdot 2}$ Hence, $P=\frac{100}{\left(1+\frac{0.06}{12}\right)^{12\cdot 2}}\approx\$88.72 $
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