When you purchased your$$ house, you took out a$30-$year annual$-$payment mortgage with an interest rate of $5\%$ per year. The annual payment on the mortgage is $ $12,198.$ You have just made a payment and have now decided to pay the mortgage off by repaying the outstanding balance.

a$.$ What is the payoff amount if you have lived in the house for $13$ years$($so there are $17$ years left on the$$ mortgage$)?$

b$.$ What is the payoff amount if you have lived in the house for $20$ years$($so there are $10$ years left on the$$ mortgage$)?$

c$.$ What is the payoff amount if you have lived in the house for $13$ years$($so there are $17$ years left on the$$ mortgage$)$ and you decide to pay off the mortgage immediately before the $13$ th payment is$$ due?