Question

2. You are considering buying a new car from a local dealer (Dealer 1) for $30,000. Dealer 1 will finance the entire purchase price at 6% interest over 5 years. Interest is compounded monthly and you must make monthly payments.

What is the most you would be willing to offer another dealer (Dealer 2) for the same car who is offering a financing plan with a 2% interest rate over 5 years?

Hint: If the loan payments are the same you can assume you would be indifferent between buying from the two dealers.

Please explain your answer, including any TVM formulas used.

Answer 1

Monthly installment for the financing plan with 6% interest rate over 5 years:

PV = -30,000; N = 5*12 = 60; rate = 6%/12 = 0.5%, solve for PMT.

Monthly installment = 579.98

If 579.98 per month is the most, you are willing to offer then the maximum price which you are willing to pay to the second dealer who offers a 2% interest over 5 years, financing plan is:

PMT = -579.98; N = 60; rate = 2%/12 = 0.167%, solve for PV.

Maximum price = 33,089.46