$1.$Derek purchased a house for $$450,000.$ He made a down payment of $25\mathrm{.}00\%$ of the value of the house and received a mortgage for the rest of the amount at $4\mathrm{.}02\%$ compounded semi$-$annually amortized over $20$ years. The interest rate was fixed for a $5$ year period.

a$.$ Calculate the monthly payment amount.

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 monthly payment amount if the mortgage was renewed for another $5$ years at $3\mathrm{.}62\%$ compounded semi$-$annually?

Round to the nearest cent