Question

The formula m = 12,000 + 12,000rt 12t  gives Keri's monthly loan payment, where r is the annual interest rate and t is the length of the loan, in years. Keri decides that she can afford, at most, a $275 monthly car payment. Give an example of an interest rate greater than 0% and a loan length that would result in a car payment Keri could afford. Provide support for your answer.

Answer 1

The Given Formula is m = [ 12,000 + (12,000rt) ] / 12t

This given the monthly payment of loan (m) provided we have the interest rate (r) and term in years (t)

In the question we were asked to give the examples of an interest rate greater than 0% and length that would result in monthly car payment that Keri can afford.

We can arrive at the answer by trial and error method. We subtitute random interest rates and term and check at the possible combinations

Preparing a table with the results of Trial and Error method combinations

Interest Rate	Term (years)	Monthly payment
5%	5	250
5%	4	300
4%	5	240
4%	4	290
3%	5	230
3%	4	280

From the above, it is clear that Keri can afford a loan repayment with Interest rate of 5% or 4% or 3% with 5 year term where the monthly payments would be 250 or 240 or 230 respectively

Working Note :

Taking 5% interest rate and 5 years

m = [ 12000 + (12000*5%*5) ] / 12(5)

= [ 12000 + 3000 ] / 60

= [ 15000 ] / 60

= 250

The remaining trial and error combinations are also done similar way and results are posted in the above table