## Thinking Mathematically (6th Edition)

(a) We can save $\$6000$in annual fuel expenses by owning a hybrid. (b) The amount saved after 6 years is$\$42,142$
(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\$