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: 7

Answer

The monthly payments are $\$405$ The interest is $\$3665$

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 Since the down payment is $\$9000$, the amount of the loan is $\$20,635$ $PMT = \frac{P~(\frac{r}{n})}{[1-(1+\frac{r}{n})^{-nt}~]}$ $PMT = \frac{(\$20,635)~(\frac{0.0662}{12})}{[1-(1+\frac{0.0662}{12})^{-(12)(5)}~]}$ $PMT = \$405$ The monthly payments are $\$405$ We can find the total amount paid. $\$405 \times 60 = \$24,300$ The interest is the difference between the total amount paid and the amount of the loan. $I = \$24,300 - \$20,635 = \$3665$ The interest is $\$3665$
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