Aaron purchased a house for $$450,000.$ He made a downpayment of $20\%$ of the value of the house and received a mortgage for the rest of the amount at $4\mathrm{.}75\%$ compounded semi$-$annually for $25$ years. The interest rate was fixed for a $5-$year term a$.$ Calculate the size of the monthly payments.

Round to the nearest cent

b$.$ Calculate the principal balance at the end of the $5-$year term..

Round to the nearest cent

c$.$ Calculate the size of the monthly payments if after the first $5-$year term the mortgage was renewed for another $5-$year term at $4\mathrm{.}50\%$ compounded semi$-$annually?