You work for a construction company that wants to purchase a truck for $P. The company can finance the truck by either withdrawing cash from a savings account, which earns 9% APR (nominal annual rate compounded monthly), or by borrowing $P from the car dealer for 4 years at 12% APR (nominal annual rate compounded monthly). The loan would be paid in equal monthly installments. Your supervisor has requested that you analyze both financing alternatives. In particular, she has requested that you:

1. Calculate, i.e., write an expression for, the total interest that would be lost (over the 4 year duration of the loan) if the money is withdrawn from the savings account.

2. Calculate, i.e., write an expression for, the total interest that would be paid if the company decides to borrow from the car dealer.

3. After looking at the answers to parts (a) and (b), the companys accountant suggests that you borrow from the dealer because the answer to part (b) is less than the answer to part (a). Your supervisor, on the other hand, thinks that you should withdraw the money from the savings account because it pays less than 12% APR. Explain which financing alternative is preferable. Defend your reasoning with quantitative analysis/numerical calculations.

4. If the company borrows from the dealer, write an expression for the principal amount paid with the 37th loan payment?