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}=(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=(r)/(12)=(0.10)/(12)\approx0.0083`

Then, the monthly payment will be:

`\begin{gathered} A=(897.30)/((1)/(r_m)-(1)/(r_m(1+r_m)^n)) \\ A=(897.30)/((12)/(0.1)-(1)/((0.1)/(12)(1+(0.1)/(12))^(36))) \\ A=(897.30)/(120-(1)/(0.0083\cdot(1.0083)^(36))) \\ A=(897.30)/(120-(1)/(0.0083\cdot1.348)) \\ A=(897.30)/(120-89.38) \\ A=(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