Michael purchased a house for $$475,000.$ 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 $6\mathrm{.}92\%$ compounded semi$-$annually amortized over $20$ years. The interest rate was fixed for a $7$ year period.

a$.$ Calculate the monthly payment amount.

Round to the nearest cent

b$.$ Calculate the principal balance at the end of the $7$ year term.

Round to the nearest cent

c$.$ Calculate the monthly payment amount if the mortgage was renewed for another $7$ years at $4\mathrm{.}52\%$ compounded semi$-$annually?

Round to the nearest cent