Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 8 - Personal Finance - 8.6 Cars - Exercise Set 8.6: 11

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 $\$42,142$
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