After reading consumer car guides and receiving advice from family and friends, Aysha has chosen the new car she wants to purchase. She now wants to research her financing options to choose the best way to pay for the car.
Aysha knows that with taxes, license, delivery, and dealer preparation fees, her car will cost $17 650. She has saved $7500 toward the purchase price but must borrow the rest. she has narrowed her financing choices to three options: dealer financing, credit union financing, and bank financing.
(i) The car dealer has offered 48-month financing at 8.5% compounded monthly.
(ii) The credit union has offered 36-month financing at 9% compounded quarterly. It has also offered 48-month financing at 9.3% compounded quarterly.
(iii) The bank has offered 36-month financing at 8.8% compounded semi-annually. It has also offered 48-month financing at 9.1% compounded semi-annually.
Aysha desires the financing option that offers the best interest rate. However, she also wants to explore the financing options that allow her to pay off her car loan more quickly.
Questions
1. Aysha wants to compare the 48-month car loan options offered by the car dealer, the credit union, and the bank.
(a) What is the effective annual rate of interest for each 48-month option?
(b) How much interest will Aysha save by choosing the best option as against the worst option?
2. Suppose Aysha wants to try to pay off her car loan within three years.
(a) What is the effective annual rate of interest for both of the 36-month options?
(b) How much interest will Aysha save by choosing the better option?