Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 8 - Personal Finance - 8.4 Compound Interest - Exercise Set 8.4: 33

Answer

The first investment would earn \$2,069,131 more than the second investment.

Work Step by Step

This is the formula we use when we make calculations with compound interest: $A = P~(1+\frac{r}{n})^{nt}$ $A$ is the final amount in the account $P$ is the principal (the amount of money invested) $r$ is the interest rate $n$ is the number of times per year the interest is compounded $t$ is the number of years We can find the total amount in the account $A_1$ after 40 years when we invest at a rate of 12% for 40 years. $A = P~(1+\frac{r}{n})^{nt}$ $A_1 = (\$25,000)~(1+\frac{0.12}{1})^{(1)(40)}$ $A_1 = \$2,326,274.26$ After 40 years, there will be \$2,326,274.26 in the account. We can find the total amount in the account $A_2$ after 40 years when we invest at a rate of 6% for 40 years. $A = P~(1+\frac{r}{n})^{nt}$ $A_2 = (\$25,000)~(1+\frac{0.06}{1})^{(1)(40)}$ $A_2 = \$257,142.95$ After 40 years, there will be \$257,142.95 in the account. We can find the difference between the first investment and the second investment. $A_1-A_2 = \$2,326,274.26-\$257,142.95$ $A_1-A_2 = \$2,069,131$ The first investment would earn \$2,069,131 more than the second investment.
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