An insurance companys losses of a particular type per year are to a reasonable approximation normally distributed with a mean of $150 million and a standard deviation of $50 million. (Assume that the risks taken on by the insurance company are entirely non-systematic.) The one-year risk-free rate is 5% per annum with annual compounding. Estimate the cost of the following: (a) A contract that will pay in one-years time 60% of the insurance companys costs on a pro rata basis (b) A contract that pays $100 million in one-years time if losses exceed $200 million.