QUESTION 2 [9 marks] Susan is considering purchasing a two-year tuition fee insurance for her daughter Sherry, who is a university student. This two-year policy will make a payment of $20,000 if Susan dies during the term and Sherry chooses to continue her study; this two-year policy will make a payment of $6,000 if Susan dies during the term and Sherry chooses to withdraw from her stud- ies. The insurance benefit 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 has calculated its premium on the following basis. The assumed probability of Susan dying in the first year is 0.009. . The assumed probability of Susan dying in the second year is 0.012. If Susan dies, the assumed probability of Sherry continuing her studies is 50% and the assumed probability of Sherry withdrawing from her studies is 50%. Interest rates are assumed to be ji = 3% p.a. a. [4 marks] Carefully draw a contingent cash flow diagram that mod- els this life insurance policy from the perspective of the life insurance company. b. [5 mark] Find the fair value of the insurance premium P. Round your answer to two decimal places. QUESTION 2 [9 marks] Susan is considering purchasing a two-year tuition fee insurance for her daughter Sherry, who is a university student. This two-year policy will make a payment of $20,000 if Susan dies during the term and Sherry chooses to continue her study; this two-year policy will make a payment of $6,000 if Susan dies during the term and Sherry chooses to withdraw from her stud- ies. The insurance benefit 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 has calculated its premium on the following basis. The assumed probability of Susan dying in the first year is 0.009. . The assumed probability of Susan dying in the second year is 0.012. If Susan dies, the assumed probability of Sherry continuing her studies is 50% and the assumed probability of Sherry withdrawing from her studies is 50%. Interest rates are assumed to be ji = 3% p.a. a. [4 marks] Carefully draw a contingent cash flow diagram that mod- els this life insurance policy from the perspective of the life insurance company. b. [5 mark] Find the fair value of the insurance premium P. Round your answer to two decimal places