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