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5. A 10-year endowment insurance is issued to a life aged 40. The sum insured is payable at the end of the year of death or on survival to the maturity date. The sum insured is $100,000 on death, or $50,000 on survival to age 50. Premiums are payable annually in advance. Assume the following premium basis: (i) expenses of 5% of each gross premium including the first, (ii) interest is 5% per year, (iii) Standard Select Survival Model. (a) Calculate the gross premium. (b) Calculate :V, the policy value in force at the start of the ninth year, just before the ninth premium is due