Chapter 9.7, Problem 16HP

a.

To determine

The monthly payment.

Answer to Problem 16HP

  $\$316.82$

Explanation of Solution

Given:

She will finance $16000 at an annual interest rate of 7% over a period of 60 months.

Below formula relates the monthly payment P , annual interest rate r in decimal form, and t is the time in years

  $\text{Amount financed}=P\left[\frac{1-{\left(1+\frac{r}{12}\right)}^{-12t}}{\frac{r}{12}}\right]$

Calculation:

In order to find her monthly payment, substitute $\text{Amount financed}=16000$ , the interest rate $r=7\%=0.07$ and time $t=\frac{60}{12}=5$ years, in the given formula and solve for P as shown below

  $\begin{array}{c}\text{Amount financed}=P\left[\frac{1-{\left(1+\frac{r}{12}\right)}^{-12t}}{\frac{r}{12}}\right]\\ 16000=P\left[\frac{1-{\left(1+\frac{0.07}{12}\right)}^{-12\left(5\right)}}{\frac{0.07}{12}}\right]\\ 16000=P\left[\frac{1-{\left(1+\frac{0.07}{12}\right)}^{-60}}{\frac{0.07}{12}}\right]\\ \Rightarrow P\approx 316.82\end{array}$

Thus, her monthly payment is approximately $\$316.82$ .

b.

To determine

The amount she will have paid on the car, assuming that she does not pay ahead.

Answer to Problem 16HP

  $\$19009.20$

Explanation of Solution

Given:

She will finance $16000 at an annual interest rate of 7% over a period of 60 months.

Below formula relates the monthly payment P , annual interest rate r in decimal form, and t is the time in years

  $\text{Amount financed}=P\left[\frac{1-{\left(1+\frac{r}{12}\right)}^{-12t}}{\frac{r}{12}}\right]$

Calculation:

If she does not pay ahead anything, then she will have to pay $\$316.82$ for 60 months.

So the total she will have to pay is

  $\$316.82\times 60=\$19009.20$

Thus, she will have to pay $\$19009.20$ for the car.