## Thinking Mathematically (6th Edition)

Published by Pearson

# Chapter 8 - Personal Finance - 8.4 Compound Interest - Exercise Set 8.4: 35

The first investment would earn $\$649,083$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 30 years when we invest at a rate of 10% compounded annually.$A = P~(1+\frac{r}{n})^{nt}A_1 = (\$50,000)~(1+\frac{0.10}{1})^{(1)(30)}$ $A_1 = \$872,470.11$After 30 years, there will be$\$872,470.11$ in the account. We can find the total amount in the account $A_2$ after 30 years when we invest at a rate of 5% compounded monthly. $A = P~(1+\frac{r}{n})^{nt}$ $A_2 = (\$50,000)~(1+\frac{0.05}{12})^{(12)(30)}A_2 = \$223,387.22$ After 30 years, there will be $\$223,387.22$in the account. We can find the difference between the first investment and the second investment.$A_1-A_2 = \$872,470.11-\$223,387.22A_1-A_2 = \$649,083$ The first investment would earn $\$649,083\$ more than the second investment.

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