Answer
(a) $\$19,600$
(b) The amount saved after 6 years is $\$145,609$
Work Step by Step
(a) We can find the total annual expense for a Cadillac.
$expense = (\$0.98~/mi)(20,000~mi) = \$19,600$
(b) 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
The periodic deposit $P$ is $\$19,600$.
$A = \frac{P~[(1+\frac{r}{n})^{nt}~-1]}{\frac{r}{n}}$
$A = \frac{(\$19,600)~[(1+\frac{0.085}{1})^{(1)(6)}~-1]}{\frac{0.085}{1}}$
$A = \$145,609$
The amount saved after 6 years is $\$145,609$
