Question 1:

Consider a 5-year $10,000 endowment assurance issued to a select life aged 30 under the following bonus schemes:-

(a) Simple reversionary bonuses of 5% p.a., 6%interest rate p.a.
(b) Compound reversionary bonuses of 2.885% p.a. and 7% interest rate p.a.

Find the EPV of the benefits under each method assuming that the benefits are added to the policy at the end of each year.

Question 2:

A with-profit 15-year endowment assurance policy is issued to a life aged 50 with basic sum assured of $80,000, payable at the end of the term or the year of earlier death and projected (but not guaranteed) super-compound bonuses of b=0.96175% p.a on initial sum assured and C=2b on bonuses. Premiums are payable annually in advance.

(a) Calculate the annual premium under this policy.

(b) Find the policy value 10 years after the policy is issued.

(c) If the insurer calculated the net premium reserve following the principles for with-profit policies (which include past bonuses, but make no allowance for future bonuses), what will be the profit at 10 years after the policy is issued?

Basis AM92 Ultimate mortality, 6% p.a interest