avin and Holly purchased a $$730,000$ condominium in Toronto. They paid $20\%$ of the amount as a down payment and secured a $25-$year mortage for the balance. They negotiated a fixed interest rate of $3\mathrm{.}1\%$ compounded semi$-$annually for a $5-$year term with repayments made at the end of every month. Their mortgage contract also stated that they may prepay up to $15\%$ of the original principal every year without at interest penalty. At the end of the first year, in addition to the regular monthly payment, they made a lump$-$sum payment of $$25,000.$

a$.$ What was the size of the monthly payment?

Round to the nearest cent

b$.$ What was the principal balance at the end of the first year, prior to make the lump sum payment?

Round to the nearest cent

c$.$ By how much did the amortization period shorten after they made the lump sum payment at the end of the first year?

months