When you purchased your$$ house, you took out a $30-$year $$annual$-$payment mortgage with an interest rate of $6\%$ per year. The annual payment on the mortgage is $$$$13000.$ 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 $10$ years$($so there are $20$ years left on the$$ mortgage$)?$

b$.$ What is the payoff amount if you have lived in the house for $21$ years$($so there are $9$ years left on the$$ mortgage$)?$

c$.$ What is the payoff amount if you have lived in the house for $10$ years$($so there are $20$ years left on the$$ mortgage$)$ and you decide to pay off the mortgage immediately before the $10$th payment is$$ due? Assume the same payment of $$$$13000$ per year and an interest rate of $6\%$ per year.