Answer
The balance in the account after 6 years will be $\$12,942.95$
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 5% compounded semiannually.
$A = P~(1+\frac{r}{n})^{nt}$
$A = (\$6000)~(1+\frac{0.05}{2})^{(2)(2)}$
$A = \$6622.88$
After 2 years, there will be $\$6622.88$ in the account. Then, an additional $\$4000$ is deposited, so there will be a total of $\$10,622.88$ in the account.
We can find the total amount in the account after 4 more years when we invest at a rate of 5% compounded semiannually.
$A = P~(1+\frac{r}{n})^{nt}$
$A = (\$10,622.88)~(1+\frac{0.05}{2})^{(2)(4)}$
$A = \$12,942.95$
After 4 more years, there will be $\$12,942.95$ in the account.
The balance in the account after 6 years will be $\$12,942.95$
