1. [15 pts] The average life of a bond is defined as

where PCF_t 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. [2 pts] Consider a fully amortizing level-payment fixed-rate mortgage that does not default, nor is it ever curtailed or prepaid. Show that

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.