Fast.

On 1 January 2003, an insurance company issued a 35 year with-profits endowment assurance policy to a life aged 30 exact for a sum assured of 60,000. The sum assured (together with any bonuses attaching) is payable at maturity or immediately on death, if earlier. Level premiums are payable annually in advance throughout the policy term or until earlier death. Compound reversionary bonuses vest at the end of each policy year (ie the death benefit does not include any bonus relating to the policy year of death) The company calculates the premium on the following basis: Mortality AM92 Ultimate Interest: 6% per annum loitial expenses: 250 plus 60% of the first year's premium, incurred at outset Renewal expenses 2.5% of the second and each subsequent year's premium, incurred at the beginning of the respective policy years Bonuses: 1.92308% per annum (8] 0 Show that the annual premium is approximately 1.146. ) Express, in stochastic form, the gross future loss random variable for this policy at duration 1, where t is an integer and 0