## Thinking Mathematically (6th Edition)

Published by Pearson

# Chapter 8 - Personal Finance - 8.6 Cars - Exercise Set 8.6: 2

#### Answer

The monthly payments are $\$732$The interest is$\$5136$

#### 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 $PMT = \frac{P~(\frac{r}{n})}{[1-(1+\frac{r}{n})^{-nt}~]}$ $PMT = \frac{(\$30,000)~(\frac{0.08}{12})}{[1-(1+\frac{0.08}{12})^{-(12)(4)}~]}PMT = \$732$ The monthly payments are $\$732$We can find the total amount paid.$\$732 \times 48 = \$35,136$The interest is the difference between the total amount paid and the amount of the loan.$I = \$35,136 - \$30,000 = \$5136$ The interest is $\$5136\$

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