Please show work in excel.

The average life of a bond is defined as == 1 / = 1 where PCFt is the principal cash flow at time t, and T is the maturity of the bond.

a. What is the average life of a zero-coupon bond?

b. What is the average life of an interest only bond?

c. Consider a fully amortizing level-payment fixed-rate mortgage that does not default, nor is it ever curtailed or prepaid. Show that lim0 = + 1 / 2

where c is the mortgage contract rate.

d. 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, curtailed, or defaults.