Question 1

Consider each of the following policies, issued to a life aged exactly x :

(i) a regular premium whole life assurance

(ii) a single premium term assurance (t n

(iii) a single premium whole life annuity

(iv) a regular premium deferred annuity (t n

Where appropriate:

? the sum assured is S , payable immediately on death

? the annuity benefit is paid continuously at the rate of R pa

? the premium is either a single premium P or is a regular premium payable

continuously at the rate of P pa

? the policy term / deferment period is n years

The force of interest ? is assumed to remain constant throughout the term of the each

contract.

For each of these policies construct Thiele's differential equation for V (t) , the reserve

at time t , by considering the change in (V) during the short time interval (t,t)

Determine which of the following assertions relating to a multiple decrement table are correct: The dependent probabilities of decrement can never exceed the corresponding independent probabilities. Forces of decrement can never exceed 1 in value. The total of all the decrement numbers summed over all ages equals the initial radix of the table. The active male membership of a large pension scheme follows the experience of the multiple decrement table below. Age Active lives Age retirements ll-health Withdrawals Deaths retirements Y (al) x (a)' (ad )x (ad) (ad ) 16 10,000 0 0 750 5 17 9,245 0 0 600 5 18 8,640 0 500 5 . .= 39 3,150 0 30 7 40 3,111 20 g 2,200 100 25 0 20 64 2,055 200 30 0 25 65 1,800 1,800 Assume that decrements occur continuously, except for age retirements at age 65, which all occur on the 65th birthday. Stating any other assumptions that you make, calculate the following: (i) The probability that a man who joins the scheme on his 18th birthday, will retire for any reason after his 63rd birthday. (ii) The independent probability of withdrawal between the ages of 17 and 18. (iii) The expected present value of a lump sum retirement benefit of f 10,000 payable on retirement at age 65, for a member now aged exactly 18, calculated using 4% po interest. (iv) The expected present value of a lump sum death benefit of f20,000 payable immediately on death while an active member if this occurs after the 63rd birthday, for a member now aged exactly 40, using 4% po interest