Answer
(a) The value of the annuity is $\$50,226$
(b) The interest is $\$32,226$
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
$A = \frac{P~[(1+\frac{r}{n})^{nt}-1]}{\frac{r}{n}}$
$A = \frac{(\$50)~[(1+\frac{0.06}{12})^{(12)(30)}-1]}{\frac{0.06}{1}}$
$A = \$50,226$
The value of the annuity is $\$50,226$
(b) The total amount of money deposited into the annuity is $\$50 \times 360$, which is $\$18,000$
The interest is the difference between the value of the annuity and the total amount deposited. We can calculate the interest.
$interest = \$50,226 - \$18,000 = \$32,226$
The interest is $\$32,226$.
