A loan of $$5,000,$ with a monthly interest rate of $1\mathrm{.}5\%,$ is repaid through $60$ monthly payments of $$100,$ with the first payment due in one month.

$($a$)$ What is the interest rate per annum?

$[5$ marks$]$

$($b$)$ How many years will it take to pay off the loan if the payment is only $$80$ per month.

$[5$ marks$]$

$($c$)$ Suppose we want to pay off the loan after $4$ years. How much do we need to pay each month?