Consider a whole life policy to a select life aged 50 years with benefits payable immediately on death. The policy has the following characteristics: - Sum insured is $250,000 - Premiums payable annually in advance for the life of the policy - Initial expenses of 70% of the first premium - Annual expenses of 2% of each premium (starting from second premium) - Claims expenses of 1% of the sum insured - Profit loading of 3% of each premium. Basis: AM92 Select at 4% p.a. a) Calculate the EPV of benefits under this policy. (3 marks) b) Give an expression for the EPV of premiums in terms of the gross annual premium, P. (2 marks) c) Give an expression for the EPV of expenses in terms of P. (4 marks) d) Give an expression for the EPV of the profit loading in terms of P. (2 marks) e) Calculate the gross annual premium P. (2 marks) Consider a whole life policy to a select life aged 50 years with benefits payable immediately on death. The policy has the following characteristics: - Sum insured is $250,000 - Premiums payable annually in advance for the life of the policy - Initial expenses of 70% of the first premium - Annual expenses of 2% of each premium (starting from second premium) - Claims expenses of 1% of the sum insured - Profit loading of 3% of each premium. Basis: AM92 Select at 4% p.a. a) Calculate the EPV of benefits under this policy. (3 marks) b) Give an expression for the EPV of premiums in terms of the gross annual premium, P. (2 marks) c) Give an expression for the EPV of expenses in terms of P. (4 marks) d) Give an expression for the EPV of the profit loading in terms of P. (2 marks) e) Calculate the gross annual premium P. (2 marks)