(i) A life insurance company issues a with-profit whole life assurance policy to lives age 40 exact. The benefit is payable at the end of year of death and is equal to the basic sum assured plus any attaching bonuses. Level annual premiums are paid in advance ceasing after 20 years or on the death of the policy holder if earlier. Premium basis: Mortality AM92 select, Interest rate: 6% p.a. Commission: 50% of the first premium 5% of the second and subsequent premiums. Initial:1Expenses:,000 Renewal: At the start of each year the policy is in existence. 100 at the start of the first year and increases each year (starting in the second year) at a rate of 1.923% p.a. Claim: 500 inflating at 1.923% p.a. The first increase will takeplace at the end of the first year. Bonus: Simple bonus rate of 2% p.a. of the basic sum assured. Bonuses are applied at the start of each year including the first year. The basic sum assured is 100,000. Show that the annual premium is approximately 2,112. [19 minutes.] (ii) Over the first 15 years of the policy the actual bonuses paid were 1% p.a. instead of 2% p.a. Calculate the gross prospective reserve at the end of the 15 th policy anniversary. Prospective reserving basis: Mortality: AM92 ultimate Interest rate: 4% p.a. Commission: 5% of monthly premiums Bonus: Simple bonus rate of 2% of basic sum assured. Expenses: Renewal: 150 p.a. [12 minute: Claim: 750 (i) A life insurance company issues a with-profit whole life assurance policy to lives age 40 exact. The benefit is payable at the end of year of death and is equal to the basic sum assured plus any attaching bonuses. Level annual premiums are paid in advance ceasing after 20 years or on the death of the policy holder if earlier. Premium basis: Mortality AM92 select, Interest rate: 6% p.a. Commission: 50% of the first premium 5% of the second and subsequent premiums. Initial:1Expenses:,000 Renewal: At the start of each year the policy is in existence. 100 at the start of the first year and increases each year (starting in the second year) at a rate of 1.923% p.a. Claim: 500 inflating at 1.923% p.a. The first increase will takeplace at the end of the first year. Bonus: Simple bonus rate of 2% p.a. of the basic sum assured. Bonuses are applied at the start of each year including the first year. The basic sum assured is 100,000. Show that the annual premium is approximately 2,112. [19 minutes.] (ii) Over the first 15 years of the policy the actual bonuses paid were 1% p.a. instead of 2% p.a. Calculate the gross prospective reserve at the end of the 15 th policy anniversary. Prospective reserving basis: Mortality: AM92 ultimate Interest rate: 4% p.a. Commission: 5% of monthly premiums Bonus: Simple bonus rate of 2% of basic sum assured. Expenses: Renewal: 150 p.a. [12 minute: Claim: 750
