Consider a fully discrete n-year deferred whole life insurance of $b issued to (x). If (x) dies in the first n years, the death benefit is equal to policy value at the end of the year of death. Level annual premiums are payable during deferral period (i.e. no premiums will be paid after n years).

a) Show that the net premium is equal to

where is the policy value at time n.

Hint: Use the recursive formula for teh first n years.

b) Does the premium depend on the mortality during the deferral period? Why or why not?