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 322: 55


$\$1019.82 $ billion. $\$232.82$

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: $t=20\text{ years}$ $r=1.3\%=0.013$ $P=\$787$ $n=2$ (since it is compounded semiannually) Substitute these values into the formula above to obtain: $A=\$787\cdot(1+\frac{0.013}{2})^{2\cdot 20}\approx\$1019.82 .$ billion. Then the interest is $\$1019.82-\$787=\$232.82$
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