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: 43

Answer

$\$104,334.67$.

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 the loaner gets back after $t$ years: $A=P\cdot(1+\frac{r}{n})^{n\cdot t}.$ Here it is compounded annually, hence $n=1$, therefore $A=P\cdot(1+\frac{r}{1})^{1\cdot t}\\ A=P\cdot(1+r)^{t}.$ Also, $t=5$ years $P=\$90000$ $r=3\%$ Substitute these values into the formula above to obtain: $A=\$90000 \cdot (1+0.03)^5=\$104,334.67$.
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