fall2010Homework 2

# fall2010Homework 2 - 1 A participant in a pension plan is...

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November 12, 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. = 0.05 ii. = 0.01 iii. = 0.10 Calculate the following items: a. b. c. d. e. f. g. h. i. j. k. l.

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November 12, 2010 2. Your professor is 54 years old. My teaching career is subject to two decrements as follows: i. Decrement 1 is mortality. The associated single decrement table for future mortality follows De Moivre’s law with ω = 50. ii. Decrement 2 is retirement. The associated single decrement table for future retirement follows De Moivre’s law with ω = 20. Calculate the following items: a. b. c. d. e. f. g. h. i. j. k. l. m. n. o.
November 12, 2010 3. (Spreadsheet) One thousand whole life policies are issued to males (20). The policies are subject to two decrements as follows: i. Mortality (1) where is the mortality rate in the Excel File on Class Website ii. Lapse (2) where is the lapse rate in the following table x 20 0.20 21 0.10 22 0.08 23 0.07 24 0.06 25+ 0.05 In a spreadsheet complete the following table: x 20 21 120 4. Using the table created in Problem 3, calculate the following: i. ii. The probability of termination by lapse between the end of the 5 th duration and the end of the 10 th duration. iii. The number of policies still in force at attained age 65. iv. v.

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November 12, 2010 5. You are given: i. ii. iii. Assuming that each decrement is uniformly distributed over each year of age in the associated single decrement table, calculate 6. You are given: i. ii. iii. Assuming that each decrement in the multiple decrement table is uniformly distributed over each year of age, calculate 7. You are given the following for a double decrement table: i. ii. Assuming that each decrement in the multiple decrement table is uniformly distributed over each year of age, calculate 0.4 8. You are given: i. ii. Decrement (1) is uniformly distributed over the year. Decrement (2) occurs at time 0.6. Calculate . 9. For a double decrement table with x 40 0.24 0.10 0.25 y 41 -- -- 0.20 2y Calculate
November 12, 2010 10. For iPhones, the phone may cease service for mechanical failure or for other reasons (lost, stolen, dropped in a pitcher of beer, etc). You are given the following double decrement table: Year of Service For an iPhone at the beginning of the year of service, probability of Mechanical Failure Failure for Other Reasons Survival through the year of service 1 0.2 0.30 -- 2 -- 0.40 -- 3 -- -- 0.20 You are also given: i. The number of iPhones that terminate for other reasons in year 3 is 40% of the number of iPhones that survive to the end of year 2. ii. The number of iPhones that terminate for other reasons in year 2 is 80% of the number of iPhones that survive to the end of year 2. Calculate the probability that an iPhone will cease to function due to mechanical failure during the three year period following its entry into service.

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