Bill needs a new car and can afford monthly car payments of $400. The interest rate on new car loans is 7%, APR and payments are made at month-end. Bill wonders whether to arrange a 48- or 60-month loan. With either loan, Bill will borrow the maximum amount and buy the most expensive car possible. The average annual rate of depreciation of a car's value is 18%. Bill can invest his spare cash in a mutual fund expected to pay 5%, compounded monthly.
a. What is the maximum he can spend on a car if he arranges a 48-month loan? What if he arranges a 60-month loan?
b. Compare Bill's wealth (the value of his car plus his investments) after 5 years if he arranges a 48-month loan to his wealth if he arranges a 60-month loan.