Assume that a 25-year-old man has these probabilities of dying during the next five years: Age...
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Assume that a 25-year-old man has these probabilities of dying during the next five years: Age at death Probability 25 I 0.00039 26 0.00044 27 0.00051 28 0.00057 29 0.00060 a) What is the probability that the man does not die in the next five years? (2 marks) b) An online insurance site offers a term insurance policy that will pay $100,000 if a 25-year-old man dies within the next five years. The cost is $175 per year. So the insurance company will take in $875 from this policy if the man does not die within five years. If he does die, the company must pay $100,000. Let X denote the cash intake of the insurance company which depends on how many premiums the man paid. Find the distribution of X. (3 marks) Hint: if a 25-year-old man dies in the first year, the cash intake of the insurance company is -(100,000 -175)=-$99,825 under the policy; if he dies in the second year, the cash intake of the company is -(100,000 -2 175)= -$99,650 etc. If the man does not die within five years, the cash intake of the company is 5 175 = 875. c) What is the insurance company's mean cash intake? (2 marks) d) Suppose the insurance company insures one hundreds 25-year-old men under the terms of Question b). What is the probability that the insurance company will receive at least one claim? For simplicity, assume independence. (3 marks) Assume that a 25-year-old man has these probabilities of dying during the next five years: Age at death Probability 25 I 0.00039 26 0.00044 27 0.00051 28 0.00057 29 0.00060 a) What is the probability that the man does not die in the next five years? (2 marks) b) An online insurance site offers a term insurance policy that will pay $100,000 if a 25-year-old man dies within the next five years. The cost is $175 per year. So the insurance company will take in $875 from this policy if the man does not die within five years. If he does die, the company must pay $100,000. Let X denote the cash intake of the insurance company which depends on how many premiums the man paid. Find the distribution of X. (3 marks) Hint: if a 25-year-old man dies in the first year, the cash intake of the insurance company is -(100,000 -175)=-$99,825 under the policy; if he dies in the second year, the cash intake of the company is -(100,000 -2 175)= -$99,650 etc. If the man does not die within five years, the cash intake of the company is 5 175 = 875. c) What is the insurance company's mean cash intake? (2 marks) d) Suppose the insurance company insures one hundreds 25-year-old men under the terms of Question b). What is the probability that the insurance company will receive at least one claim? For simplicity, assume independence. (3 marks)
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Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
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