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Last year, you obtained a loan to purchase a used car. The loan carries a 5% int

ID: 2794480 • Letter: L

Question

Last year, you obtained a loan to purchase a used car. The loan carries a 5% interest rate per year; the annual interest payment is $5,000. You just made the second payment, so there are three payments left to fully repay the loan. The next payment is due exactly one year from now. You receive a call from your bank. The representative tells you that they would like to reward you as a loyal customer and offer you two alternative options to repay your loan Option 1: You make one payment today of $14,000 to fully repay the loan. Option 2: You make one payment of $16,000 exactly 3 years from now and no other payments in between. Are these options interesting to you? If yes, which one would you prefer and why? If no, why would you decline?

Explanation / Answer

To compare the various options, we compare the present value of the costs

Original option. The present value of the payments = 5000/1.05^1 + 5000/1.05^2 + 5000/1.05^3

= $13616.24

Option 1: PV of the payment = $14000

Option 2: PV of the payment = 16000/ 1.05^3 = $13821.4

Since the present value of the costs of the original option is lowest, I would prefer the original option and decline the others.