Sam is considering purchasing two-year tuition fee insurance for her daughter Emily, who is a university student. This two-year policy will make a payment of $20,000 if Sam dies during the term and Emily chooses to continue her study; this two-year policy will make a payment of $8,000 if Sam dies during the term and Emily chooses to withdraw from her studies. 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 Sam dying in the first year is 0.005.

The assumed probability of Sam dying in the second year is 0.008.

If Sam dies, the assumed probability of Emily continuing her studies is 57.5% and the assumed probability of Sherry withdrawing from her studies is 42.5%.

The life insurance company incurs initial expenses of $500 per policy at the beginning of the term of insurance.

The life insurance company incurs claim costs of $175 when a death payment is made, at the end of the year in which death occurs.

Interest rates are assumed to be j1 = 4.25% p.a.

[4 marks] Carefully draw a contingent cash flow diagram that models this life insurance policy from the perspective of the life insurance company.

[6 marks] Find the fair value of the insurance premium P . Round your answer to two decimal places