Answer
(a) The periodic deposit is $\$1122$
(b) The total amount of money deposited into the annuity is $\$22,440$
The interest is $\$2560$
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
$A = \frac{P~[(1+\frac{r}{n})^{nt}~-1]}{\frac{r}{n}}$
$P = \frac{A~(\frac{r}{n})}{~(1+\frac{r}{n})^{nt}~-1}$
$P = \frac{(\$25,000)~(\frac{0.045}{4})}{~(1+\frac{0.045}{4})^{(4)(5)}~-1}$
$P = \$1122$
The periodic deposit is $\$1122$
(b) The total amount of money deposited into the annuity is $\$1122 \times 20$, which is $\$22,440$
The interest is the difference between the value of the annuity and the total amount deposited. We can calculate the interest.
$interest = \$25,000 - \$22,440 = \$2560$
The interest is $\$2560$
