Jim and Nancy just got married today. They want to start saving so they can buy a house five years from today. The average house in their town today sells for $$120,000.$ Housing prices are expected to increase $3$ percent a year. When they buy their house five years from now, Jim and Nancy expect to get a $30-$year $(360-$month$)$ mortgage with a $7$ percent nominal interest rate. They want the monthly payment on their mortgage to be $$500$ a month.

Jim and Nancy want to buy an average house in their town. They are starting to save today for a down payment on the house. The down payment plus the mortgage will equal the expected price of the house. Their plan is to deposit $$2,000$ in a brokerage account today and then deposit a fixed amount at the end of each of the next five years. Assuming that the brokerage account has an annual return of $10$ percent, how much do Jim and Nancy need to deposit at the end of each year in order to accomplish their goal?