## Thinking Mathematically (6th Edition)

Published by Pearson

# Chapter 8 - Personal Finance - 8.6 Cars - Exercise Set 8.6 - Page 547: 13

#### Answer

(a) $\$19,600$(b) The amount saved after 6 years is$\$145,609$

#### Work Step by Step

(a) We can find the total annual expense for a Cadillac. $expense = (\$0.98~/mi)(20,000~mi) = \$19,600$ (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 $\$19,600$.$A = \frac{P~[(1+\frac{r}{n})^{nt}~-1]}{\frac{r}{n}}A = \frac{(\$19,600)~[(1+\frac{0.085}{1})^{(1)(6)}~-1]}{\frac{0.085}{1}}$ $A = \$145,609$The amount saved after 6 years is$\$145,609$

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