#### Answer

The value of the account after 16 years will be $\$9187$

#### 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 10 years when we invest at a rate of 7% compounded semiannually.
$A = P~(1+\frac{r}{n})^{nt}$
$A = (\$3000)~(1+\frac{0.07}{2})^{(2)(10)}$
$A = \$5969.37$
After 10 years, there will be $\$5969.37$ in the account.
We can find the total amount in the account after 6 more years when we invest at a rate of 7.25% compounded quarterly.
$A = P~(1+\frac{r}{n})^{nt}$
$A = (\$5969.37)~(1+\frac{0.0725}{4})^{(4)(6)}$
$A = \$9187$
After 6 more years, there will be $\$9187$ in the account.
The value of the account after 16 years will be $\$9187$