Question

Kevin bought a new car for $22,000. He made a down payment of $9,500 and has monthly payments of $308.10 for 4 years. He is able to pay off his loan at the end of 30 months. Using the actuarial method, find the unearned interest and payoff amount.

Answer 1

The answer has been presented in the supporting sheet. For detailed answer refer to the supporting sheet.

Answer Firstly we have to calculate the interest rate of loan monthly = i% Amount of loan/ installment amount = Present value annuity (i%,48) (22000-9500)/308.1 = ((1-(1+i%)^-48)/i%) 40.57124 = ((1-(1+i%)^-48)/i%) From present value table this annuity is for.70833 % motnly Yearly interest rate -8.5% (.70833%*12) Amount of loan paid off at the end of 30 months = monthly installment * ((1-(1+(8.5%/12)) ^-18)/(8.5%/12)) = 308.1* ((1-(1+(8.5%/12))^-18)/(8.5%/12)) = 308.1*16.84389 = $ 5189.6 - Thus amount of loan to be payoff = $ 5189.6 Unearned interest = (monthly installment *18) - amount pay off = = (308.1*18) - 5189.6 = $ 356.2 Thus the amount of unearned interest = $ 356.2