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. 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