BOA originates 100 Fully Amortizing Fixed Rate Mortgages, each has a $1,000 balance, 5% interest rate (no fees), 25-year term, and annual payments. BOA immediately issues IO and PO strips backed by the pool of these mortgages and sells them to investors who discount payoffs at 4%.

7a. What profits does BOA make immediately? (the answer will be a few million dollars, an 8-digit number)

Payment: N=25 ,I=5 ,PV= -1000 ,FV=0,Solve for PMT=70.95

Price per mortgage=70.95 "/ 0.04 * (1 - 1.04^25) = 2954.78

Profits per mortgage=2954.78-1,000=1954.78

Profits from the pool=100*1954.78=195,478

7b. What is the value of all PO strips?

7c. What would be the value of all PO strips if the expected prepayment rate was 15% per year?

7d. What would be the value of all PO strips if instead the expected default rate was 10% per year? Assume that in case of default, BOA recovers 85% of balance (i.e. default is prepayment but you receive only 80% of the `prepaid balance).

PLEASE CHECK MY WORK FOR 7a AND HELP WITH THE REST OF THE SUB-QUESTIONS. THANK YOU!