A financial services company is selling a university scholarship plan. Under the plan, if a client's newborn child lives to age 18, qualifies for and enters university, the child will be awarded a $15,000 scholarship on its 18th birthday. Alternatively, if the child qualifies for university and enters the following year (i.e., the child takes a 'gap year'), the plan will pay $3,000 on its 18th birthday and $15,000 on its 19th birthday. If the child qualifies for university, takes a 'gap year', and then doesn't enter university the following year, the plan only pays $3,000 on the child's 18th birthday. The financial services company wants to calculate an appropriate premium for this scholarship plan. The financial services company estimates that the rate of return of government bonds (risk-free rate of return) over the next eighteen or nineteen years will be 6% p.a. (compounded annually). It views the probability of a newborn child surviving to age 18 as 0.95, and the probability that this child will qualify and enter university immediately as 0.55; the probability of qualifying for university and taking a gap year is 0.15. The probability that an 18 year old child survives to age 19 is 0.99. Of the group of surviving 19 year old children who took a gap year at age 18, it is believed 80% will choose to enter university. The financial services company incurs a cost of $75 to issue and service the policy at the date of issue. The cost of servicing a claim is $25 each time a claim occurs. The company wants the policy to earn a profit of 15% of premium in eighteen years' time.

a. Draw a detailed contingent cash flow diagram, from t he perspective of the financial services company, that models the scholarship plan.

b. What premium should the financial services company charge for this product? Carefully set out all your working. Round your answer to three decimal places.