Answer
(a) The amount saved after 40 years is $\$171,271$
(b) The interest is $\$135,271$
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
$A = \frac{P~[(1+\frac{r}{n})^{nt}~-1]}{\frac{r}{n}}$
$A = \frac{(\$75)~[(1+\frac{0.065}{12})^{(12)(40)}~-1]}{\frac{0.065}{12}}$
$A = \$171,271$
The amount saved after 40 years is $\$171,271$
(b) The total amount of money deposited into the annuity is $\$75 \times 480$, which is $\$36,000$
The interest is the difference between the value of the annuity and the total amount deposited. We can calculate the interest.
$interest = \$171,271 - \$36,000 = \$135,271$
The interest is $\$135,271$
