Search a real estate website for a home you are interested in buying. Please limit your selection to homes under $$500,000$ for the purposes of our math. Calculate putting $20\%$ down for your home purchase. The remaining amount of the mortgage you will need to buy the home will have an interest rate of $3\%.$ The mortgage will require monthly payments for $30$ years. What is the cost of the house you selected, the down payment, and the monthly payment?