Answer
(a) The periodic deposit is $\$401$
(b) The total amount of money deposited into the annuity is $\$3208$
The interest is $\$292$
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
$A = \frac{P~[(1+\frac{r}{n})^{nt}~-1]}{\frac{r}{n}}$
$P = \frac{A~(\frac{r}{n})}{~(1+\frac{r}{n})^{nt}~-1}$
$P = \frac{(\$3500)~(\frac{0.05}{2})}{~(1+\frac{0.05}{2})^{(2)(4)}~-1}$
$P = \$401$
The periodic deposit is $\$401$
(b) The total amount of money deposited into the annuity is $\$401 \times 8$, which is $\$3208$
The interest is the difference between the value of the annuity and the total amount deposited. We can calculate the interest.
$interest = \$3500 - \$3208 = \$292$
The interest is $\$292$
