Question

One method to determine the monthly payment for a car loan is based on using future-value simple interest. To use this method, first find the sum of the principal of the loan and the total simple interest to be paid on the loan. Then, divide the sum by the number of months in the loan period.

Keri is planning to get a $12,000 loan to buy a used car. Let r be the annual interest rate and t be the length of the loan, in years.


1. Which expression represents the total simple interest, in dollars, that Keri will pay?


2. Which formula can be used to find m, the monthly payment on Keri’s car loan?

Answer 1

A & C

Explanation:

1. 12,000rt

2. m = 12,000 + 12,000rt/ 12t

Answer 2

1) 120rt

2)
`\frac{10(100+rt)}t}`

Explanation:

Principal amount = $12,000

r = rate of interest

t = t years(time)

1) Simple interest =
`(P * R * t)/(100)`

=
`(12000 * r * t)/(100)`

= 120rt

2) For finding the monthly payment we will use the future value formula as described in the question.

Total amount = Principal + Total interest

= 12000 + 120rt

t years = 12t months

Monthly payment =
`(Total amount)/(no. of months)`

=
`(12000+120rt)/(12t)`

=
`\frac{10(100+rt)}t}`