Paula Hunt bought a new car for $25,000. A dealer\'s financing was available thr
ID: 2613446 • Letter: P
Question
Paula Hunt bought a new car for $25,000. A dealer's financing was available through a local bank at an interest rate of 15%pa but compounded monthly. Dealer financing required a 10% down payment and 48 equal monthly payments. Because the interest rate was rather high, Paula checked her credit union for possible financing. The loan officer at the credit union quoted on 10.5% interest for a, new car loan and 12% for a used car. But to be eligible for the loan, Paula has to be a member of the union for at least 6 months. Since she joined the union 2 months ago, she had to wait 4 more months to apply for the loan. Now she decided to go ahead with the dealer's financing, and 4 months later refinanced the balance through the credit union at an interest of 12%, compounded monthly. She will pay the credit union 44 equal monthly payments. Compute the monthly payment to the dealer. Compute he monthly payment to the union.Explanation / Answer
Annual Compounded rate = 15%
Monthly rate = (1+15%)^ (1/12) - 1 = 0.011715 = 1.1715%
Down payment = 22500 * 10% = 2500
Loan Value = 25000 - 2500 = 22500
With I = 1.1715% , present value = 22500 and n =48 ; monthly payments = $615.50
Amortization Schedule For 4 Months
Month
Opening Balance
Interest
Payment
Closing Balance
1
22,500.00
263.59
615.50
22,148.09
2
22,148.09
259.46
615.50
21,792.05
3
21,792.05
255.29
615.50
21,431.85
4
21,431.85
251.07
615.50
21,067.42
Hence refinancing value = 21067.42 from Union @ 12% p.a. compounded monthly
Monthly interest rate = (1+12%)^ (1/12) - 1 = 0.95%
With I = 0.95% , present value = 21067.42 and n =44 ; monthly payments = $ 588.06
Month
Opening Balance
Interest
Payment
Closing Balance
1
22,500.00
263.59
615.50
22,148.09
2
22,148.09
259.46
615.50
21,792.05
3
21,792.05
255.29
615.50
21,431.85
4
21,431.85
251.07
615.50
21,067.42