Problem1

Derive from first principles an expression for the variance of the benefits payable under an endowment assurance with benefits payable at the end of the year of death. Use a sum assured of S.

Problem 2

Find an expression for the variance of the present value of a continuous annuity payable so long as (x) is alive.  

Problem

Find an expression for the variance of the present value of a deferred annuity payable annually in advance to a life aged x (using n for deferment).

Problem 3

Prove the following: fx(t)=tPxμx+t

Problem 4

Calculate the expected present value of a whole life assurance payable at the end of the year of death to a policyholder aged 45 exact, if the sum assured of $10,000 increases at the end of each year by 1.923% if the policyholder is then alive. Use AM92 ultimate mortality and 6% interest.

Revise your answer to allow for a fixed increase of $1,000 at the end of each year instead of the 1.923% compound increase.

Problem 5

Calculate the net premium payable under a 8 year term assurance issued to (x) using ELT15 (female) mortality and an interest rate of 4.5% pa. The policyholder is aged exactly 23 at the start of the policy. Repeat for a pure endowment with same term. Assume the premium in both cases is paid as a lump sum at the start of the policy.

Problem 6

A life company issues a 15 year endowment assurance, with death benefit payable immediately on death, to someone currently aged exactly 45. Calculate the net premium payable monthly in arrear for this policy assuming the sum assured is $50,000 and the basis used for pricing is:

- AM92 select mortality
- 6% interest per annum