Q5. For a fully discrete 20-year term insurance of 100,000 on (30), you are given that: The mortality rate follows the Illustrative Life Table with i = 0.06. Expenses, payable at the beginning of the year, are 20% of the gross pre- mium plus 150 in the first year and 5% of the gross premium in years 2 and later. (a) Determine the gross premium using equivalence principle. (2 marks) (b) Suppose that this identical policy is issued on M lives with independent future lifetimes, each age 30. Demonstrate that the accumulated value of the premiums at time k minus the death benefit and expenses spent up to time k per survivor is equivalent to the total reserve at the end of time k. (7 marks) Q5. For a fully discrete 20-year term insurance of 100,000 on (30), you are given that: The mortality rate follows the Illustrative Life Table with i = 0.06. Expenses, payable at the beginning of the year, are 20% of the gross pre- mium plus 150 in the first year and 5% of the gross premium in years 2 and later. (a) Determine the gross premium using equivalence principle. (2 marks) (b) Suppose that this identical policy is issued on M lives with independent future lifetimes, each age 30. Demonstrate that the accumulated value of the premiums at time k minus the death benefit and expenses spent up to time k per survivor is equivalent to the total reserve at the end of time k. (7 marks)