T . 1. [10 pts) The average life of a bond is defined as =1tx PCFt, = PCFt I where PCFt is the principal cash flow at time t, and T 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. [1 pt] Consider a fully amortizing level-payment fixed-rate mortgage that does not default, nor is it ever curtailed or prepaid. Show that T +1 limt = C-0 2 where c is the mortgage contract rate. d. (7 pts] Compute and graph the average life of a 30 yr. FA FRM in the range of note rates from 2% to 30%. Assume the loan is never prepaid, nor curtailed, nor defaults. Show all work