Answer
(a) The periodic deposit is $\$1405$
(b) The total amount of money deposited into the annuity is $\$168,600$
The interest is $\$81,400$
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
$A = \frac{P~[(1+\frac{r}{n})^{nt}~-1]}{\frac{r}{n}}$
$P = \frac{A~(\frac{r}{n})}{~(1+\frac{r}{n})^{nt}~-1}$
$P = \frac{(\$250,000)~(\frac{0.075}{12})}{~(1+\frac{0.075}{12})^{(12)(10)}~-1}$
$P = \$1405$
The periodic deposit is $\$1405$
(b) The total amount of money deposited into the annuity is $\$1405 \times 120$, which is $\$168,600$
The interest is the difference between the value of the annuity and the total amount deposited. We can calculate the interest.
$interest = \$250,000 - \$168,600 = \$81,400$
The interest is $\$81,400$
