Marie and Alex just paid $250,000 for a house. They made a down payment of $50,000 and assumed a 30-year $200,000 mortgage with a fixed annual interest rate of 7.50% compounded monthly. The house will serve as a residence for several years, but Marie and Alex also view it as an investment, as property values in the neighborhood are projected to increase at a rate of 5% per year in the near future. Suppose the couple sells the house after eight years. Neglecting income tax deductions, do they come out ahead on their investment?

This question doesn't sound like one encountered in most mathematics courses. First, while it is a problem in words, it is not the dreaded word problem that many of us remember from high school mathematics courses. Second, the problem is relevant and immediate; it is unlikely that a student would respond to this question with the familiar “what does this have to do with my life?” Third, while the solution involves fairly elementary mathematics, it is a multi-step process that requires organizing several pieces of information. Fourth, the solution requires some understanding of home mortgages and appreciation of property values; these topics are not considered mathematics, but they represent applications of mathematics. Finally, the problem invites discussion and extensions: What assumptions were made in arriving at an answer? How would the answer change if Marie and Alex are in a 28% tax bracket and income tax deductions are considered?