Answer
(a) We can save $\$2625$ in annual fuel expenses by owning a hybrid.
(b) The amount saved after 6 years is $\$18,726$
Work Step by Step
(a) We can find the number of gallons of fuel consumed by a hybrid car.
$\frac{15,000~mi}{60~mi/gal} = 250~gallons$
We can calculate the annual fuel expenses for a hybrid car.
$cost = (250~gal)(\$3.50/gal) = \$875$
We can find the number of gallons of fuel consumed by an SUV.
$\frac{15,000~mi}{15~mi/gal} = 1000~gallons$
We can calculate the annual fuel expenses for an SUV.
$cost = (1000~gal)(\$3.50/gal) = \$3500$
We can save $\$2625$ in annual fuel expenses by owning a hybrid.
(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
Since the fuel savings are $\$2625$ per year, the monthly fuel savings are $\$218.75$. The periodic deposit $P$ is $\$218.75$.
$A = \frac{P~[(1+\frac{r}{n})^{nt}~-1]}{\frac{r}{n}}$
$A = \frac{(\$218.75)~[(1+\frac{0.057}{12})^{(12)(6)}~-1]}{\frac{0.057}{12}}$
$A = \$18,726$
The amount saved after 6 years is $\$18,726$
