Question

Allen’s uncle sold him a car for $6400. The gentleman’s agreement was that Allen would pay back his uncle in monthly payments for two years. The payments would include interest calculated as simple interest at an annual rate of 3.9% for two years. (a) What was the amount of interest that Allen’s uncle charged him? (b) What was the total amount that Allen owed his uncle? (c) What were Allen’s monthly payments? Express the payments rounded to the nearest cent

Answer 1

a) $499.20

b) $6,899.20

c) $287.47

Explanation:

First, calculate the interest accumulated in 2 years.

Amount(a): $6400

Interest(i): 3.9% or
`(3.9)/(100)=0.039`

years(y): 2

We can say;
`a+a(i)(y)`

`6400+(6400)(0.039)(2)\\=6,899.20`

Calculate how much he would have to pay per month to fully pay in 2 years.

`2years((12months)/(1year) )=24months`

We can say that,
`payment/month=(total)/(months)`

`p/m=(6,899.20)/(24) \\\\p/m=287.47`

Therefore, he has to pay at least $287.47/month to pay off in two years.