A private equity group had bought a pool of 30-year fixed-rate mortgages with a remaining life of 5 years from a company in distress at a discount paying yearly $1M. The private equity group is worried about raising interest rates and decides to fund the purchase of the pool using a 5-year and a 2-year balloon loan, where all interest rate is paid at maturity and where the interest rate of the loan is the spot rate at maturity plus 0.25%, respectively. (Think of these balloon loans as zero coupon bonds with a yield of spot at maturity plus 0.25%.) The spot rate curve for years 1 thru 5 is as follows: 1%, 2%, 2.6%, 3%, 3.3%. (2) What are the interest payments of the two loans and final payment of each of the loans per an initial amount of $100? 6) What is the present value of the mortgage pool and the duration of each of the loans? c) What is the duration of the mortgage pool? (a) What amount of each of the two loans would mitigate duration risk