Answer
$\$1082.43.$
Work Step by Step
According to the Compound Interest Formula, where $P$ is the principal, the amount deposited, $r$ is the annual interest rate, $n$ is the number of times the interest is compounded annually, $t$ is the number of years, $A$ is the amount you get back after $t$ years: $A=P\cdot(1+\frac{r}{n})^{n\cdot t}.$
Here we have: $t=2\text{ years}$
$r=4\%=0.04$
$P=\$1000$
$n=2$ (since it is compounded semiannual)
Substitute these values into the formula above to obtain:
Here $A=1000\cdot(1+\frac{0.04}{2})^{2\cdot 2}= \$1082.43.$
