Question

When you purchased your car, you took out a five-year annual-payment loan with an interest rate of 5.9 % per year. The annual payment on the car is $ 5,100. You have just made a payment and have now decided to pay off the loan by repaying the outstanding balance. What is the payoff amount for the following scenarios? a. You have owned the car for one year (so there are four years left on the loan)? b. You have owned the car for four years (so there is one year left on the loan)?

Answer #1

Answer a.

Annual Payment = $5,100

Annual Interest Rate = 5.9%

Remaining Period = 4 years

Loan Outstanding = $5,100 * PVIFA(5.90%, 4)

Loan Outstanding = $5,100 * (1 - (1/1.059)^4) / 0.059

Loan Outstanding = $5,100 * 3.4731

Loan Outstanding = $17,712.81

Amount repaid is $17,712.81

Answer b.

Annual Payment = $5,100

Annual Interest Rate = 5.9%

Remaining Period = 1 years

Loan Outstanding = $5,100 * PVIF(5.90%, 1)

Loan Outstanding = $5,100 / 1.059

Loan Outstanding = $4,815.86

Amount repaid is $4,815.86

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