An insurer issues a 25-year endowment insurance with sum insured $100, 000 to a select life aged 30. The premiums are payable annually throughout the term of the insurance. The insurer incurs initial expenses of $2, 000 plus 50% of the first premium, and the renewal expenses of 2.5% of each subsequent premium. The death benefit is payable immediately on death.

Basis:

Mortality: AM92 Select

Rate of interest: 6%

a. Write down the expression for the gross future loss random variable at the inception of the contract.

b. Calculate the gross premium using the equivalence premium principle.