In order to buy a car, you borrow $$27,500$ from a friend at $7\%/$year compounded monthly for $4$ years. You plan to repay the loan with $48$ equal monthly payments.

a$)$ How much are the monthly payments?

b$)$How much interest is in the $23$rd payment?

c$)$What is the remaining balance after the $37$th payment?

d$)$Three and a half years into the loan, you decide to pay it off. You have not made the payment due at that time. What is the payoff amount of the loan?