On 1 January 2015, a life insurance company issued four-year increasing term assurance policies with level premiums payable annually in advance for the term of the policy, but ceasing on earlier death. The initial sum assured is 140,000, increasing by 20,000 at each policy anniversary (the first increase taking place at the beginning of the second policy year). The death benefit is payable at the end of the year of death. If the policyholder survives to the end of the term of the contract. 50% of the total premiums paid (accrued with no interest) is payable. The company calculates the premium on the following basis: Mortality Rate of interest Initial expense Initial commission AM92 Select 6% per annum 275 30% of the first year's premium, incurred at the outset 55 per annum, incurred at the time of payment of the second and subsequent years premiums 2.5% of the second and subsequent years premiums. Renewal expense Renewal commission For a male life aged 56 exact at inception of the policy: (0) Set out, in stochastic form, the gross future loss random variable at the outset of this policy using where applicable, Tx. Ky and elements of the premium basis that are relevant. 131 (ii) Calculate, showing all your workings, the office premium using annuity and assurance functions and setting the expected present value of the gross future loss random variable equal to zero. [4]