A loan of $$36,000$ is being amortized over $60$ months at an nominal interest rate of $15\%$ compounded monthly. Find,

$($a$)$ the monthly payment.

$($b$)$ the principal outstanding at the beginning of the ${48}^{th}$ month.

$($c$)$ the interest in the ${48}^{th}$ payment.

$($d$)$ the portion of the repaid principal in the ${48}^{th}$ payment.

$($e$)$ The total interest paid,$($i$.$e$.$ finance charge$).$