Question $6$: $($Value $5$ marks$)$

When Gary purchased a home, he borrowed $$200,000$ as a mortgage to be amortized by making

monthly payments for $25$ years. Interest is fixed at $3\mathrm{.}39\%$ compounded semi$-$annually for a three$-$year

term.

$($a$)$ Compute the monthly payment.

$($b$)$ Determine the balance at the end of the three$-$year term.

$($c$)$ If the mortgage is renewed for a four$-$year term at $5\mathrm{.}24\%$ compounded semi$-$annually, what is the

size of the monthly payment for the renewal term?

Show all inputs and any other necessary work below.