Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 4 - Exponential and Logarithmic Functions - Section 4.7 Financial Models - 4.7 Assess Your Understanding - Page 347: 42


$t \approx16.62\text{ years}$

Work Step by Step

The formula for the amount $A$ after $t$ years due to a principal $P$ invested at an annual interest rate $r$ compounded $n$ times per year can be computed as: $A=P(1+\dfrac{r}{n})^{nt}$ When the compounding is continuous, use the formula $A=Pe^{rt}$ We need to compute with continuous compounding. Thus we use formula: $A=Pe^{rt}~~~(1)$ We are given that $A=\$80000; \\ P=\$25000 ; \\r=7\%=0.07$ Plugging these values into formula (1), we obtain: $\$80000=\dfrac{$80000}{\$25000}=e^{0.07t} \\ \\ln{3.2}=0.07t\\ t=\dfrac{\ln (3.2)}{0.07}=16.6164\approx16.62\text{ years}$
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