Answer
(a) The amount saved after 10 years is $\$956,793$
(b) The interest is $\$356,793$
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
$A = \frac{P~[(1+\frac{r}{n})^{nt}~-1]}{\frac{r}{n}}$
$A = \frac{(\$15,000)~[(1+\frac{0.09}{4})^{(4)(10)}~-1]}{\frac{0.09}{4}}$
$A = \$956,793$
The amount saved after 10 years is $\$956,793$
(b) The total amount of money deposited into the annuity is $\$15,000 \times 40$, which is $\$600,000$
The interest is the difference between the value of the annuity and the total amount deposited. We can calculate the interest.
$interest = \$956,793 - \$600,000 = \$356,793$
The interest is $\$356,793$
