Ann would like to buy a house. It costs $800,000. Her down payment will be $40,000. She will take out a mortgage for $760,000. It will be a 30 year, fully amortizing, FRM, with constant monthly payments and monthly compounding. The annual interest rate is 4.00%. She must pay 2.5% in fees at the time of the loan.

She forecasts four possible scenarios for house price appreciation (HPA).

Optimistic Case: 4.5% annual HPA, hence 4.5/12% monthly HPA

Base Case: 2.5% annual HPA, hence 2.5/12% monthly HPA

Pessimistic Case: 0% annual HPA, hence 0/12% monthly HPA

Very Bad Case: -6% annual HPA, hence -6/12% monthly HPA

1. Assume Ann will make the required monthly payment every month for 30 years.

(a) How much home equity will Ann have after 10 years (120 months) of payments under each of the four scenarios?

(b) After 30 years?