A with-profit whole life assurance policy was issued to a life then aged 25 with:

• basic (initial) sum assured of S = $100,000;
• bonuses added to sum assured at the end of each year (if still alive) at rate b = 1.9231% pa compound;
• benefits payable at the end of the year of death;
• level premiums payable annually in advance.

It is now the 5th anniversary of the policy just before the payment of the premium due today.

(a) Evaluate the annual premium for this policy.

(b) Write down an expression for the net future loss random variable at present and calculate its expected value.

(c) Evaluate the net premium reserve at present following the principles for with-profit policy that includes all past bonuses but make no allowance for future bonuses.

Basis: AM92 Select mortality, 6% pa interest