After graduating from college, Sarah took a position as a stockbroker in Dallas. Her goal was to set aside funds for the next six years in order to make. down payment on a house in 2025. Based on median house price data, she learned that a three-bedroom, two-bath house currently costs $315,000. Sarah will make a down payment of 20% when she decides to buy.

Because it will be five years before Sarah buys a house, the $315,000 price will surely not be the same in the future. In the recent past, homes in Dallas appreciated by 9% annually. When saving for her down payment on the home, Sarah will invest the funds in a balanced account containing stocks, bonds, and government securities would realistically achieve an annual rate of return of 10% annually.

a. Taking into consideration the fact that the home prices will grow at 9% annually, what will be the future median home selling price in Dallas in five years? What amounts will Sarah have to accumulate as a down payment if she does decide to buy a house in Dallas?

b. Based on your answer from part a, how much will have to be deposited into Sarah's investment account (which earns 10% per year) at the beginning of each month to accumulate the required down payment in six years?