Answer
(a) The amount saved after 10 years is $\$693,031$
(b) The interest is $\$293,031$
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
$A = \frac{P~[(1+\frac{r}{n})^{nt}~-1]}{\frac{r}{n}}$
$A = \frac{(\$10,000)~[(1+\frac{0.105}{4})^{(4)(10)}~-1]}{\frac{0.105}{4}}$
$A = \$693,031$
The amount saved after 10 years is $\$693,031$
(b) The total amount of money deposited into the annuity is $\$10,000 \times 40$, which is $\$400,000$
The interest is the difference between the value of the annuity and the total amount deposited. We can calculate the interest.
$interest = \$693,031 - \$400,000 = \$293,031$
The interest is $\$293,031$
