#### Answer

The ending balance in the account will be $\$8544.49$

#### 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 at the end of 2 years when we invest at a rate of 8% compounded monthly.
$A = P~(1+\frac{r}{n})^{nt}$
$A = (\$5000)~(1+\frac{0.08}{12})^{(12)(2)}$
$A = \$5864.44$
After 2 years, there will be $\$5864.44$ in the account. Then, $\$1500$ is withdrawn, so there will be a total of $\$4364.44$ in the account.
We can find the total amount in the account after 1 more year when we invest at a rate of 8% compounded monthly.
$A = P~(1+\frac{r}{n})^{nt}$
$A = (\$4364.44)~(1+\frac{0.08}{12})^{(12)(1)}$
$A = \$4726.69$
After 1 more year, there will be $\$4726.69$ in the account. Then, $\$2000$ is put in the account, so there will be a total of $\$6726.69$ in the account.
We can find the total amount in the account after 3 more years when we invest at a rate of 8% compounded monthly.
$A = P~(1+\frac{r}{n})^{nt}$
$A = (\$6726.69)~(1+\frac{0.08}{12})^{(12)(3)}$
$A = \$8544.49$
The ending balance in the account will be $\$8544.49$