Answer
After 21 years, there will be $\$28,210$ in the account.
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 after 21 years when we invest at a rate of 5% compounded semiannually.
$A = P~(1+\frac{r}{n})^{nt}$
$A = (\$10,000)~(1+\frac{0.05}{2})^{(2)(21)}$
$A = \$28,210$
After 21 years, there will be $\$28,210$ in the account.
