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# Final - Stat 490 Final 1 A participant in a pension plan is...

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Stat 490 Final December 14, 2010 1. A participant in a pension plan is subject to three decrements: (1) is retirement, (2) is death, (3) is other termination. All terminations have a constant force of decrement as follows: i. = 0.08 ii. = 0.03 iii. = 0.14 Calculate the following items: i. ii. iii. iv.

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2. Li Life Insurance Company offers a special whole life insurance policy to (70). The policy pays a death benefit of 100,000 upon death from all causes. It also pays an additional death benefit of A upon death caused by an accident. You are given: a. Mortality for all deaths follows the Illustrative Life Table. b. Mortality for accidental deaths follows a constant force model with 0.01 . c. 0.06 i d. Death benefits are paid at the moment of death. e. The Actuarial Present Value of the death benefit from all causes is equal to the Actuarial Present Value of the additional death benefit paid upon accidental death. Calculate A , the additional death benefit paid upon death from accidental causes.
3. A person with a long term care policy can be classified as being in three states: i. Not in a Nursing Home ii. In a Nursing Home iii. Deceased (Dead) The following transitional probabilities indicated the probabilities of moving between the three states in a year: Not in a Nursing Home In A Nursing Home Deceased Not in A Nursing Home 0.6 0.3 0.1 In a Nursing Home 0.1 0.5 0.4 Deceased 0.0 0.0 1.0 Nelkenbaum Nursing Homes currently have 2000 residents. Ronny, the company’s actuary, wants to estimate the number of current residents who will still be in the nursing home at the end of three years. a. Calculate the expected number of current residents that will still be in a nursing home at the end of three years. b. Calculate the variance of the number of current residents that will still be in a nursing home at the end of three years. c. Assuming a normal distribution and using a 95% confidence interval, determine the range of the number of current residents that will still be in a nursing home at the end of three years.

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4. Scientists have recently discovered records from the Pre-Historic Actuarial Society.
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