An FI originates a pool of 500 30-year mortgages, each averaging $150,000 with an annual mortgage coupon rate of 8 percent. Assume that the GNMA credit risk insurance fee is 6 basis points and that the FI's servicing fee is 19 basis points.

a. What is the present value of the mortgage pool?    

b. What is the monthly mortgage payment?

c. For the first two payments, what portion is interest and what portion is principal repayment?

d. What are the expected monthly cash flows to GNMA bondholders?

e. What is the present value of the GNMA pass through bonds? Assume that the risk- adjusted market annual rate of return is 8 percent compounded monthly.

f. Would actual cash flows to GNMA bondholders deviate from expected cash flows as in part (d)? Why or why not?

g. What are the expected monthly cash flows for the FI and GNMA?

h. If all of the mortgages in the pool are completely prepaid at the end of the second month, what is the pool's weighted-average life? Hint: Use your answer to part (c).

i. What is the price of the GNMA pass through security if its weighted-average life is equal to your solution for part (h)? Assume no change in market interest rates.

j. What is the price of the GNMA pass through with a weighted-average life equal to your solution for part (h) if market yields decline by 50 basis points?