#### Answer

(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 $\$5,224,999,925$

#### 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
(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 $\$5,224,999,925$