Microeconomics questions

Example 6.9 A life insurer is about to issue a 25-year endowment insurance with a basic sum insured of $250 000 to a select life aged exactly 30. Premiums are payable annually throughout the term of the policy. Initial expenses are $1200 plus 40% of the first premium and renewal expenses are 1% of the second and subsequent premiums. The insurer allows for a compound reversionary bonus of 2.5% of the basic sum insured, vesting on each policy anniversary (including the last). The death benefit is payable at the end of the year of death. Assume the Standard Select Survival Model with interest at 5% per year. (a) Derive an expression for the future loss random variable, Lo, for this policy. (b) Calculate the annual premium for this policy. (c) Let Lo(k) denote the present value of the loss on the policy given that K1301 = k for k