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A 3-year unitised with-profits endowment is to be issued to a man aged exactly 55. The policy includes the following features: Allocation rate of 85% in year 1 and 100% thereafter. Premium of 5,000 paid at start of each year. Death benefit, paid at the end of the year of death, equal to the end year unit fund value plus terminal bonus, or 15,000, if higher. Maturity benefit equal to the end-year unit fund value plus terminal bonus. Surrender is permitted at the end of the first and second years, equal to the unit fund value plus terminal bonus less a surrender penalty of 80 per surrender. A policy fee is deducted at the start of each year except the first, equal to 1.5% of the unit fund value immediately after the premium for that year has been paid. Calculate the net present value for this policy on the following assumptions: 500 . Initial expenses: 30 Renewal expenses: 50 per termination (death, surrender or maturity) Termination expenses: Initial commission: 5% of the first year's premium 1% of the second and third year's premiums Renewal commission: Investment and actuarial management expenses: 0.25% of the end-year unit fund value each year 80% of AM92 Select Mortality: Surrender probability: 10% of all policies in force at the end of each year 4% per annum Regular bonus interest: 1% of the unit fund value after 1 year Terminal bonus rates: 3% of the unit fund value after 2 years 6.5% of the unit fund value after 3 years Non-unit interest: 2% per annum Risk discount rate: 8% per annum All expected investment returns are assumed to be distributed to the policyholder through the regular and terminal bonuses. [13]

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