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: 5

Answer

The monthly payments for the new-car option are $\$277$ more than the monthly payments for the used-car option.

Work Step by Step

We can use this formula to calculate the payments for a loan: $PMT = \frac{P~(\frac{r}{n})}{[1-(1+\frac{r}{n})^{-nt}~]}$ $PMT$ is the amount of the regular payment $P$ is the amount of the loan $r$ is the interest rate $n$ is the number of payments per year $t$ is the number of years We can find the monthly payments for the new-car option. $PMT = \frac{P~(\frac{r}{n})}{[1-(1+\frac{r}{n})^{-nt}~]}$ $PMT = \frac{(\$28,000)~(\frac{0.0612}{12})}{[1-(1+\frac{0.0612}{12})^{-(12)(4)}~]}$ $PMT = \$659$ The monthly payments for the new-car option are $\$659$ We can find the monthly payments for the used-car option. $PMT = \frac{P~(\frac{r}{n})}{[1-(1+\frac{r}{n})^{-nt}~]}$ $PMT = \frac{(\$16,000)~(\frac{0.0686}{12})}{[1-(1+\frac{0.0686}{12})^{-(12)(4)}~]}$ $PMT = \$382$ The monthly payments for the used-car option are $\$382$ We can find the difference in the monthly payments. $\$659 - \$382 = \$277$ The monthly payments for the new-car option are $\$277$ more than the monthly payments for the used-car option.
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