Question

Lawrence Wagner purchased a log splitter with an installment loan that has an APR of 10 percent. The log splitter sells for $997. The store financing requires a 10 percent down payment and 36 monthly payments. What is the finance charge?

Answer 1

We have a purchase at a price of $997.

The downpayment is 10%, so it represents $99.70

$\text{downpayment}=\frac{10}{100}\cdot997=0.1\cdot997=99.70$

Then, the amount that is financed is:

$997-99.70=897.30$

We then can calculate the monthly payments using the annuity formula.

As there are monthly payments, we have to calculate a monthly interest rate:

$r_m=\frac{r}{12}=\frac{0.10}{12}\approx0.0083$

Then, the monthly payment will be:

$\begin{gathered} A=\frac{897.30}{\frac{1}{r_m}-\frac{1}{r_m(1+r_m)^n}} \\ A=\frac{897.30}{\frac{12}{0.1}-\frac{1}{\frac{0.1}{12}(1+\frac{0.1}{12})^{36}}} \\ A=\frac{897.30}{120-\frac{1}{0.0083\cdot(1.0083)^{36}}} \\ A=\frac{897.30}{120-\frac{1}{0.0083\cdot1.348}} \\ A=\frac{897.30}{120-89.38} \\ A=\frac{897.30}{30.62} \\ A=29.30 \end{gathered}$

We can calculate the total financed payments as:

$A\cdot n=29.30\cdot36=1054.80$

The finance charge will be the difference between the total financed payments and the financed value:

$I=1054.80-897.30=157.50$

Answer: Finance charge = $157.50