How can I calculate these on excel?

1.[10 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. [1 pt] 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.