Tim Smith is shopping for a used luxury car. He has found one priced at $$32,000.$ The dealer has told Tim that if he can come up with a down payment of $$$$6,100,$ the dealer will finance the balance of the price at a $7\%$ annual rate over $4$ years $(48$months$).$

a$.$Assuming that Tim accepts the$$ dealer's offer, what will his monthly$($end$-$of$-$month$)$ payment amount$$ be$?$

b$.$Use a financial calculator or spreadsheet to help you figure out what$$ Tim's monthly payment would be if the dealer were willing to finance the balance of the car price at an annual rate of $3\mathrm{.}9\%?$