This question illustrates how having a balloon mortgage may lead to a negative equity that increases the risk of default. Ann would like to buy a house. It costs $2,500,000. Her down payment will be $50,000. She will take out a mortgage for the remainder. It will be a 30 year, fully amortizing, FRM, with constant monthly payments and monthly compounding. The annual interest rate is 4.50%. She will pay $5,000 in closing costs at origination. She will also pay 1.75% of the balance in buy-down points at origination. Ann is pessimistic and forecasts house prices to fall by 0.5% every month.

For questions 7 and 8, assume all is the same as above EXCEPT there is a $500,000 balloon due in 30 years (recalculate the mortgage payment accordingly).

7. How much home equity will she have after 10 years (120 months)?

8. How much home equity will she have after 29 years (348 months)?