Lexi$$s father is setting up a retirement plan. He will make fixed monthly contributions to a pension fund until the retirement in $25$ years from now. Assume that the fund earns an APR $9\%$ return $($annualized$).$ After retirement, Lexi$$s father is planning to withdraw a fixed amount $$2,500$ each month for the next $20$ years. How much would he have to pay into the fund each month before he retires?