A $$$$100,000$ mortgage is to be amortized by making monthly payments for $15$ years. Interest is $8\mathrm{.}6\%$ compounded semi $-$annually for a five$-$year term.

$($a$)$

Compute the size of the monthly payment.

$($b$)$

Determine the balance at the end of the five$-$year term.

$($c$)$

If the mortgage is renewed for a five$-$year term at $3\%$ compounded semi dash annually $,$what is the size of the monthly payment for the renewal$$ term?