Answer
(a) $\$5600$
(b) The amount saved after 6 years is $\$41,289$
Work Step by Step
(a) We can find the total annual expense for a Toyota Corolla.
$expense = (\$0.40~/mi)(14,000~mi) = \$5600$
(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 $\$5600$.
$A = \frac{P~[(1+\frac{r}{n})^{nt}~-1]}{\frac{r}{n}}$
$A = \frac{(\$5600)~[(1+\frac{0.082}{1})^{(1)(6)}~-1]}{\frac{0.082}{1}}$
$A = \$41,289$
The amount saved after 6 years is $\$41,289$
