Question $2(15$ marks$)$ A loan of $$5000$ is repaid by $60$ month payments of $$100,$ with the first payment due in a month.

$($a$)$ What is the interest rate per annual? $[5$ marks$]$

$($b$)$ With the interest found in part $($a$),$ how many year will it take to pay off the loan if the payment is only $$80$ per month? $[5$ marks$]$

$($c$)$ Suppose that we wanted to kill off the loan after $4$ years. How much we need to pay each month? $[5$ marks$]$