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: 33



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: $A=P\cdot(1+\frac{r}{n})^{n\cdot t}.$ The investment is compounded annually, hence $n=1$. Thus, the formula above becomes: $A=P\cdot(1+\frac{r}{1})^{1\cdot t}\\ A=P\cdot(1+r)^{t}.$ The given situation has $t=5$ years $A=3P$ because the investment triples after $5$ years. Using the formula above gives: $3\cdot P=P\cdot(1+r)^5\\3=(1+r)^5.\\\sqrt[5] {3}=\sqrt[5] {(1+r)^5}\\\sqrt[5] 3=1+r\\r=\sqrt[5] 3-1$. Use a calculator to obtain: $r=\sqrt[5] 3-1\\r=1.245731-1\\r=0.245731\\r\approx24.57\%$
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