Athens First S&L originated a pool containing $75$ ten$-$year fully amortizing fixed interest rate mortgages with an average balance of $$100,000$ each. All mortgages in the pool carry an interest rate of $12\%$ and have annual payments.

$1.$ Athens First S&L would now like to sell the pool to FNMA. Assuming a constant annual prepayment rate of $10\%($for simplicity assume that prepayments are based on the pool balance at the end of the preceding year and begin at the end of year $1,$ except in the final year where the prepayments should be zero since all remaining principal will be paid in the final year$’$s scheduled principal$),$  what is the price that Athens First S&L could obtain if market interest rates are $11\%?$