When you purchased a house, you took out a $$500,000,30-$year monthly$-$payment mortgage with an interest rate of $12\%.$ You have now decided to pay the mortgage off by repaying the outstanding balance. Calculate the annual payment.

What is the payoff amount if:

a$.$ You decided to pay off the mortgage immediately after the ${20}^{th}$ payment is made.

b$.$ You decided to pay off the mortgage immediately before the ${25}^{th}$ payment is due.