Question A life insurance company offers a two-year term life insurance for males aged 30 years. This two-year policy pays $500,000 if the policyholder dies during its term. The $500,000 will be paid at the end of the year in which death occurs. Policyholders pay one single premium of $P at the beginning of this policy. The life insurance company incurs the following expenses. At age 30, the assumed probability of dying during this year is 0.0007. At age 31, the assumed probability of dying during this year is 0.0008. The life insurance company incurs initial expenses of $100 per policy at the beginning of the term of insurance. The life insurance company incurs claim costs of $200 when a death payment is made, at the end of the year in which death occurs. Interest rates are assumed to be ji = 4% p.a. for year 1 and ji = 4.2% p.a. for year 2. a. [4 marks) Carefully draw a contingent cash flow diagram that models this life insurance policy from the perspective of the life insurance company. b. [6 marks) Find the fair value of the insurance premium P. Round your answer to two decimal places. c. [4 marks] The life insurance company has set a goal of achieving a target profit of 10% of premiums on these two-year term policies. This profit amount should be realised at the end of year 2 (whether a death benefit is paid or not). Find the value of the premium P' in these circumstances. Round your answer to two decimal places. Question A life insurance company offers a two-year term life insurance for males aged 30 years. This two-year policy pays $500,000 if the policyholder dies during its term. The $500,000 will be paid at the end of the year in which death occurs. Policyholders pay one single premium of $P at the beginning of this policy. The life insurance company incurs the following expenses. At age 30, the assumed probability of dying during this year is 0.0007. At age 31, the assumed probability of dying during this year is 0.0008. The life insurance company incurs initial expenses of $100 per policy at the beginning of the term of insurance. The life insurance company incurs claim costs of $200 when a death payment is made, at the end of the year in which death occurs. Interest rates are assumed to be ji = 4% p.a. for year 1 and ji = 4.2% p.a. for year 2. a. [4 marks) Carefully draw a contingent cash flow diagram that models this life insurance policy from the perspective of the life insurance company. b. [6 marks) Find the fair value of the insurance premium P. Round your answer to two decimal places. c. [4 marks] The life insurance company has set a goal of achieving a target profit of 10% of premiums on these two-year term policies. This profit amount should be realised at the end of year 2 (whether a death benefit is paid or not). Find the value of the premium P' in these circumstances. Round your answer to two decimal places
