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: 46



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 we have: $t=0.5\text{ years}$ $r=3\%=0.03$ $A=\$3000$ $n=12$ (since it is compounded monthly) Substitute these values into the formula above to obtain: $\$3000=P\cdot(1+\frac{0.03}{12})^{12\cdot 0.5}\\ \$3000=P\cdot(1+0.0025)^{6}\\ \dfrac{3000}{(1+0.0025)^{6}}=P\\ \$2955.39114=P\\ P\approx \$2955.39$
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