The Green Mortgage Company has originated a pool containing $75$ ten$-$year fixed interest rate mortgages with an average balance of $$100,400$ each. All mortgages in the pool carry a coupon of $12$ percent. $($For simplicity, assume that all mortgage payments are made annually at $12\%$ interest.$)$ Green would now like to sell the pool to FNMA.

Required:

a$.$ Assuming a constant annual prepayment rate of $10$ percent $($for simplicity, assume that prepayments are based on the pool balance at the end of each year$),$ what will be the price that Green should obtain on the date of issuance if market interest rates were $(1)11$ percent? $(2)12$ percent? $(3)9$ percent?