Answer
(a) The value of the annuity is $\$9076$
(b) The interest is $\$4076$
Work Step by Step
(a) This is the formula we use to calculate the value of an annuity:
$A = \frac{P~[(1+\frac{r}{n})^{nt}-1]}{\frac{r}{n}}$
$A$ is the future value of the annuity
$P$ is the amount of the periodic deposit
$r$ is the interest rate
$n$ is the number of times per year the interest is compounded
$t$ is the number of years
$A = \frac{P~[(1+\frac{r}{n})^{nt}~-1]}{\frac{r}{n}}$
$A = \frac{(\$100)~[(1+\frac{0.045}{2})^{(2)(25)}~-1]}{\frac{0.045}{2}}$
$A = \$9076$
The value of the annuity is $\$9076$
(b) The total amount of money deposited into the annuity is $\$100 \times 50$, which is $\$5000$
The interest is the difference between the value of the annuity and the total amount deposited. We can calculate the interest.
$interest = \$9076 - \$5000 = \$4076$
The interest is $\$4076$
