Susan is considering purchasing two-year tuition fee insurance for her daughter Sherry, who is a university student. This two-year policy will make a payment of $12,000 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 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 Susan dying in the first year is 0.01.

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 65% and the assumed probability of Sherry withdrawing from her studies is 35%.

The life insurance company incurs initial expenses of $50 per policy at the beginning of the term of insurance.

The life insurance company incurs claim costs of $75 when a death payment is made, at the end of the year in which death occurs.

Interest rates are assumed to be j₁ = 3.6% p.a.

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

b. Find the fair value of the insurance premium P. Round your answer to two decimal places.

c. The life insurance company has set a goal of achieving a target profit of 5% 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 profit-loaded premium P' in these circumstances. Round your answer to two decimal places.