$1.$ You want to buy a new sports coupe for $$78,500,$ and the finance office at the dealership has quoted you a loan with an APR of $4\mathrm{.}9$ for $60$ months to buy the car.a$)$ How much total interest is paid over the life of the loan?b$)$ Suppose you plan on trading the car in for a new one after two years. Compute the loan balance when you trade the car in$.$