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.
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