5. An insurance company's losses on a particular policy are 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-year's time, 60% of the insurance company's costs. (b) A contract that pays $ 100 million in one-year's time if losses exceed $200 million (and zero otherwise). Hints: In (a), the expected cost to the insurance company depends only on the mean losses; the expected cost should then be discounted to the present. In (b), the expected cost to the company is $100 million times the probability that the losses exceed $200 (you must calculate this probability from the mean and standard deviation given in the problem). Once you have computed the expected cost, you must discount it to the present. A discount rate of 5% with annual compounding implies a one-year PV factor of 1/1.05