Paul and Paula are purchasing a home for a price of $$500,000.$ To avoid paying mortgage insurance, they will make a down payment of $20\%$ of the price or $$100,000.$ They will finance the remaining $$400,000$ with a $30-$year, monthly payment, amortized mortgage at a fixed $7\mathrm{.}2\%$ nominal interest rate, with the first payment due in one month. What will the size of their monthly payment be$?$