When you purchased your$$ house, you took out a $30-$year $$annual$-$payment mortgage with an interest rate of $10\%$ per year. The annual payment on the mortgage is $$$$13,000.$ 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 $23$ years$($so there are $7$ 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? Assume the same payment of $$$$13$ comma $13,000$ per year and an interest rate of $10\%$ per year.