Answer
(a) The periodic deposit is $\$355$
(b) The total amount of money deposited into the annuity is $\$170,400$
The interest is $\$829,600$
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
$A = \frac{P~[(1+\frac{r}{n})^{nt}~-1]}{\frac{r}{n}}$
$P = \frac{A~(\frac{r}{n})}{~(1+\frac{r}{n})^{nt}~-1}$
$P = \frac{(\$1,000,000)~(\frac{0.0725}{12})}{~(1+\frac{0.0725}{12})^{(12)(40)}~-1}$
$P = \$355$
The periodic deposit is $\$355$
(b) The total amount of money deposited into the annuity is $\$355 \times 480$, which is $\$170,400$
The interest is the difference between the value of the annuity and the total amount deposited. We can calculate the interest.
$interest = \$1,000,000 - \$170,400 = \$829,600$
The interest is $\$829,600$
