## Thinking Mathematically (6th Edition)

(a) After 384 years, the value of the investment would be $\$5,027,378,918$(b) After 384 years, the value of the investment would be$\$5,224,999,925$
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 (a) We can find the total value of the investment after 384 years when invested at a rate of 5% compounded monthly. $A = P~(1+\frac{r}{n})^{nt}$ $A = (\$24)~(1+\frac{0.05}{12})^{(12)(384)}A = \$5,027,378,918$ After 384 years, the value of the investment would be $\$5,027,378,918$(b) We can find the total value of the investment after 384 years when invested at a rate of 5% compounded 360 times per year.$A = P~(1+\frac{r}{n})^{nt}A = (\$24)~(1+\frac{0.05}{360})^{(360)(384)}$ $A = \$5,224,999,925$After 384 years, the value of the investment would be$\$5,224,999,925$