Answer
(a) We can save $\$6000$ in annual fuel expenses by owning a hybrid.
(b) The amount saved after 6 years is $\$42,142$
Work Step by Step
(a) We can find the number of gallons of fuel consumed by a hybrid car.
$\frac{40,000~mi}{40~mi/gal} = 1000~gallons$
We can calculate the annual fuel expenses for a hybrid car.
$cost = (1000~gal)(\$4/gal) = \$4000$
We can find the number of gallons of fuel consumed by an SUV.
$\frac{40,000~mi}{16~mi/gal} = 2500~gallons$
We can calculate the annual fuel expenses for an SUV.
$cost = (2500~gal)(\$4/gal) = \$10,000$
We can save $\$6000$ 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 $\$6000$ per year, the monthly savings are $\$500$. The periodic deposit $P$ is $\$500$.
$A = \frac{P~[(1+\frac{r}{n})^{nt}~-1]}{\frac{r}{n}}$
$A = \frac{(\$500)~[(1+\frac{0.052}{12})^{(12)(6)}~-1]}{\frac{0.052}{12}}$
$A = \$42,142$
The amount saved after 6 years is $\$42,142$
