ABC Bank originates a pool of containing 100 three-year fixed-rate mortgages with loan amount of $100,000 each. All mortgages in the pool carry a rate of 6% with annual payments. The servicing fee is charged 0.5%. ABC Bank would like to sell the pool to investors via Mortgage Pass Through (MPT) security. Suppose that 100,000 shares will be issued and the market interest rate is 5.5%.

Questions [10 points each question]

1.Assume that there are no prepayment and no default, how much an investor would like to pay for each share of the MPT security?

2.What is the price of each share of the MPT if there are a constant prepayment rate of 1.5% each year and no default?

3.What is the price of each share of the MPT if there are a constant default rate of 1.5% each year (assuming the recovering rate is 50%) and no prepayment?

4.What is the price of each share of the MPT if there are a constant annual default rate of 1.5% (assuming the recovering rate is 50%) and another constant annual prepayment of 1.5%?