You have decided to buy a house. The price will be $$500,000$ and you will put $$50,000$ down. Your annual interest rate will be $6\%$ and the loan calls for monthly payments for $30$ years. You also know that your loan payment will include monthly escrow collected by your lender to cover property taxes, property insurance, and private mortgage insurance $($PMI$)$ that the bank will make you pay because you are not making a $20\%$ down payment. The annual cost of property taxes will be $$4,000.$ The annual cost of property insurance will be $$2,000.$ The annual cost of PMI will be $$3,000.$ What will your total monthly payment be including the escrow amounts?