You have decided to buy a new home in SE Washington, DC for $500,000. In order to avoid paying private mortgage insurance, you make a down payment of 20% of the purchase price and finance the remaining 80% with a 30-year fixed rate mortgage. The first loan payment is one month after the mortgage is signed. The interest rate on the loan is 12% per year. Assume interest rates are compounded monthly. What is your monthly mortgage payment?