Question

My son recently purchased a new car that was priced at $28,000. He was given two purchase options. The first was a 0% loan for 48 months on the full purchase price. However, if he paid cash he would get a 10% discount on the car making the purchase price $25,200.

     a) What is the loan payment if he takes the 0% loan?

     b) Comparing the first option to the second option, what is the actual interest rate for the 0% loan (find the monthly and annual effective interest rates)?

Answer 1

Under first option he won't get any discount the price which he has to pay is $28000. This amount he will be paying in 48 months. So he will be required to pay =$28000/48 = $583.33 per month.

Let r be the discounting rate.

If he buys car in cash he gets a discount of 10%. Effective price =$25200.

When r = 0.44% per month

PVIFA = 43.18

Therefore interest rate on 0% loan is 0.44% per month or, 5.28% per annum.

A. Under 0% loan he will be required to pay = $ 583.33 per month.

B. Monthly rate of interest = 0.44%

Annual rate of interest = 5.28%

Effective rate of interest

Effective interest rate = 5.4% per annum