You are considering buying a car worth $$30,000.$ The dealer, who is anxious to sell the car, offers you an attractive financing package. You have to make a down$-$payment of $$3,200,$ and pay the rest over $3$ years with monthly payments. The dealer will charge you interest at a constant APR of $2\%,$ which is lower than the market interest rate.a$.$ What is the monthly payment to the dealer? $1$b$.$ The dealer offers you a second option: you pay cash, but get a $$2,500$ discount. Should you go for the loan or should you pay cash? Assume that the market annual interest rate $($APR$)$ is at $5\mathrm{.}5\%.$