College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 6 - Section 6.7 - Financial Models - 6.7 Assess Your Understanding - Page 475: 33


$ 24.573\%$

Work Step by Step

The amount A after t years due to a principal P invested at an annual interest rate r, expressed as a decimal, compounded n times per year is $A=P\displaystyle \cdot\left(1+\frac{r}{n}\right)^{nt}$ --- We want $A=3P$, after $t=5$ years, with $n=1$ compounding period per year. $3P =P\displaystyle \left(1+\frac{r}{1}\right)^{5(1)} \quad/\div P$ $3=(1+r)^{5} \quad/ \sqrt[5]{...}$ $\sqrt[5]{3}=1+r\quad/-1$ $r=\sqrt[5]{3}-1\approx 0.24573$ $ r\approx 24.573\%$
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