order to buy a car, you borrow $$21,000$ from the bank at $6\mathrm{.}17\%$ annual effective interest rate $($AEIR$)$ or a monthly interest rate of $0\mathrm{.}5\%$ compounded monthly over $48$ months. You plan to repay the loan with equal monthly payments

$($a$)$ How much are the monthly payments?

$($b$)$ How much is the remaining balance after paying $12$ equal monthly payments?