Karim Soltan is shopping for a new vehicle, and has noticed thatmany vehicle manufacturers are offering special deals to sell offthe current year’s vehicles before the new models arrive. Karim’slocal Ford dealership is advertising 3.9% financing for a full 48months (i.e., 3.9% compounded monthly) or up to $4000 cash back onselected vehicles.

The vehicle that Karim wants to purchase costs $24 600 includingtaxes, delivery, licence, and dealer preparation. This vehiclequalifies for $1800 cash back if Karim pays cash for the vehicle.Karim has a good credit rating and knows that he could arrange avehicle loan at his bank for the full price of any vehicle hechooses. His other option is to take the dealer financing offeredat 3.9% for 48 months.

Karim wants to know which option requires the lower monthlypayment. He knows he can use annuity formulas to calculate themonthly payments.

Questions
a. Suppose Karim buys the vehicle on July 1. What monthly paymentmust Karim make if he chooses the dealer’s 3.9% financing optionand pays off the loan over 48 months? (Assume he makes each monthlypayment at the end of the month and his first payment is due onJuly 31.)
b. Suppose the bank offers Karim a 48-month loan with the interestcompounded monthly and the payments due at the end of each month.If Karim accepts the bank loan, he can get $1800 cash back on thisvehicle.

Help Karim work out a method to calculate the bank rate ofinterest required to make bank financing the same cost as dealerfinancing. First, calculate the monthly rate of interest that wouldmake the monthly bank payments equal to the monthly dealerpayments. Then calculate the effective rate of interest representedby the monthly compounded rate. If the financing from the bank isat a lower rate of interest compounded monthly, choose the bankfinancing. The reason is that the monthly payments for the bank’sfinancing would be lower than the monthly payments for the dealer’s3.9% financing.
(i) How much money would Karim have to borrow from the bank to paycash for this vehicle?
(ii) Using the method above, calculate the effective annual rate ofinterest and the nominal annual rate of interest required to makethe monthly payments for bank financing exactly the same as fordealer financing.
c. Suppose Karim decides to explore the costs of financing a moreexpensive vehicle. The more expensive vehicle costs $34 900 intotal and qualifies for the 3.9% dealer financing for 48 months or$2500 cash back. What is the highest effective annual rate ofinterest at which Karim should borrow from the bank instead ofusing the dealer’s 3.9% financing?