1. (15 pts) The average life of a bond is defined as E-txPCFt = y.PCFt where PCF, is the principal cash flow at time t, and is the maturity of the bond. a. [1 pt.) What is the average life of a zero-coupon bond? Show work b. (1 pt.) What is the average life of an interest only bond? Show work c. 12 pts) Consider a fully amortizing level-payment fixed-rate mortgage that does not default, nor is it ever curtailed or prepaid. Show that limt = 1+1 where c is the mortgage contract rate. d. (11 pts) Compute the realized average life of a 30 yr., 5/1 ARM with initial rate of 4%, and a margin of 2%. The underlying index is (date in yrs., index in %):(0,2), (1,3), (2,3), (3,2.5), (4,3), (5,5), (6,5), and (7-30,6). The loan is never prepaid, nor curtailed, nor defaults. There are no rate or payment caps. Annotate any excel and show all work. 1. (15 pts) The average life of a bond is defined as E-txPCFt = y.PCFt where PCF, is the principal cash flow at time t, and is the maturity of the bond. a. [1 pt.) What is the average life of a zero-coupon bond? Show work b. (1 pt.) What is the average life of an interest only bond? Show work c. 12 pts) Consider a fully amortizing level-payment fixed-rate mortgage that does not default, nor is it ever curtailed or prepaid. Show that limt = 1+1 where c is the mortgage contract rate. d. (11 pts) Compute the realized average life of a 30 yr., 5/1 ARM with initial rate of 4%, and a margin of 2%. The underlying index is (date in yrs., index in %):(0,2), (1,3), (2,3), (3,2.5), (4,3), (5,5), (6,5), and (7-30,6). The loan is never prepaid, nor curtailed, nor defaults. There are no rate or payment caps. Annotate any excel and show all work