Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 9 - Section 9.1 - Exponential Functions - Exercise Set - Page 672: 41

Answer

$7\%$ compounded monthly.

Work Step by Step

Investment $P=\$12,000$. Time $t=3$ years. $7\%$ Compounded monthly $(n=12)$ Rate of interest $r=7\%=0.07$. Compounded interest formula $A=P\left ( 1+\frac{r}{n} \right )^{nt}$ Substitute all values. $A_1=12,000\left ( 1+\frac{0.07}{12} \right )^{12\cdot 3}$ $A_1=12,000\left ( \frac{12+0.07}{12} \right )^{36}$ $A_1=12,000\left ( \frac{12.07}{12} \right )^{36}$ $A_1=12,000\left ( 1.23292558748 \right )$ $A_1=14795.1070497$. $6.85\%$ compounded continuously. Rate of interest $r=6.85\%=0.0685$. Interest formula $A=Pe^{rt}$ Substitute all values. $A_2=12,000\cdot e^{0.0685\cdot 3}$ $A_2=12,000\cdot e^{0.2055}$ $A_2=14737.6677715$ By comparing both values $A_1>A_2$.
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