A 40-year-old male has purchased a 25-year endowment insurance with death benefit payable at the end of the year of death. The death benefit in the first year is $100,000. Use AM92 ultimate mortality with 6% interest p.a. (a) Assuming that only the death benefit increases by 1.9231% on each policy anniversary, calculate the expected present value of the increasing death benefit and the $100,000 survival benefit. (4 marks) (b) Given that the premiums are paid yearly in advance until the end of insurance or earlier death, calculate the annual premium. (2 marks) (c) Assume that the premiums are still paid yearly in advance until the end of insurance or earlier death. The death benefit is $100,000 in the first year but now increases arithmetically by $2000 each year. If the survival benefit also increases geometrically by 1.9231% on each policy anniversary, calculate the policy value of this new endowment product when the owner of the product is aged 60 exact. (6 marks) A 40-year-old male has purchased a 25-year endowment insurance with death benefit payable at the end of the year of death. The death benefit in the first year is $100,000. Use AM92 ultimate mortality with 6% interest p.a. (a) Assuming that only the death benefit increases by 1.9231% on each policy anniversary, calculate the expected present value of the increasing death benefit and the $100,000 survival benefit. (4 marks) (b) Given that the premiums are paid yearly in advance until the end of insurance or earlier death, calculate the annual premium. (2 marks) (c) Assume that the premiums are still paid yearly in advance until the end of insurance or earlier death. The death benefit is $100,000 in the first year but now increases arithmetically by $2000 each year. If the survival benefit also increases geometrically by 1.9231% on each policy anniversary, calculate the policy value of this new endowment product when the owner of the product is aged 60 exact. (6 marks)