Question $4(11$ marks$)$

Samuel has just purchased an apartment by taking out a $30-$year mortgage loan with monthly repooments. The relevant interest rate is $12\%($APR$)$ compounded monthly. The principal $($loan amount$)$ of the mortgage is $$5,500,000.$ Monthly mortgage repayment will occur at the end of every month.

$($a$)$ What is the monthly mortgage repayment $C?$

$(4$ marks$)$

$($b$)$ After $150$ repayments, what is the outstanding loan amount?

$(4$ marks$)$

$($c$)$ In Samuel's ${151}^{st}$ mortgage repayment, what is the interest payment and principal payment?

$(3$ marks$)$