You are just graduating college and are beginning to think about your personal finances $($or perhaps you already have been!$).$ You decide that you would like to purchase a house $10$ years from now and wish to create a savings plan to meet that goal. You start your job next year and you save by depositing money into an account at the end of each year. Suppose that house prices today are $$300,000$ and grow at a rate of $3\%$ per year. Further suppose that your starting annual salary next year is $$61,800.$ Your salary grows at a rate of $3\%$ per year, and money invested in the stock market may be invested at a $5\%$ annual rate of return. Assume that money invested in the stock market can be withdrawn freely $($i$.$e$.$ with no tax implications$).$

What will the price of a house be at the end of the tenth year?