STAT 490 F11 Homework

STAT 490 F11 Homework - Chapter 1 1. A with profits whole...

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December 9, 2011 Version 3 Chapter 1 1. A with profits whole life insurance policy on (30) has a death benefit of 100,000 at the time that it is issued. The policy pays a reversionary bonus at the end of each policy year which are equal to 2.5% of the death benefit (including any death benefit provided by previously paid bonuses) during the policy year. Determine the death benefit that would be paid if the insured died during the fifth policy year. 2. A with profits whole life insurance policy on (30) has a death benefit of 100,000 at the time that it is issued. The policy pays a reversionary bonus at the end of each policy year. The bonus is equal to 2.5% of the death benefit at issue plus 3.5% of any death benefit that resulted from previously paid bonuses. Determine the death benefit that would be paid if the insured died during the fifth policy year. 3. Kelli has worked for Chupp Insurance Company for 23 years when she retires on December 31, 2011. Her salary during the last five years has been: Year Salary 2007 180,000 2008 200,000 2009 210,000 2010 220,000 2011 160,000 Calculate Kelli ’s annual pension benefit under each of the following plans: a. Her pension benefit is 2% per year of service of her final salary. b. Her pension benefit is 2% per year of service of her average salary over her last five years of service. c. Her pension benefit is 1.8% per year of service of her highest salary over the last five years of service.
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December 9, 2011 Version 3 Chapter 2 4. You are given: 1 5 0 ( ) 1 1 ,0 125 125 t F t t        Calculate: a. 0 () St b. 0 Pr[ ] Tt c. 0 Pr[ ] d. x e. Probability that a newborn will live to age 25. f. Probability that a person age 25 will live to age 75. g. Probability that a person age 25 will die between age 50 and age 75. h. i. x j. 25 k. 100 l. tx p m. 10 50 p n. q o. 10 50 q p. 10 50 10 50 pq q. 50 p r. | u t x q s. x ft t. [] x ET u. x e v. x Var T w. Standard Deviation of 50 T x. 120 EK y. 120 Var K 5. You are given that mortality follows Gompertz Law with B = 0.00027 and c = 1.1. Calculate: a. x b. 25 c. 100 d. 0 e. 0 Pr[ ] f. 0 Pr[ ] g. x h. Probability that a newborn will live to age 25. i. Probability that a person age 25 will live to age 75. j. Probability that a person age 25 will die between age 50 and age 75. k. l. p m. 10 50 p n. q o. 10 50 q p. 10 50 10 50 q. 50 p r. | u t x q s. x
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December 9, 2011 Version 3 6. You are given that that x c for all 0 x where c is a constant. This mortality law is known as a constant force of mortality. a. tx p b. q c. d. x e e. x e f. 10 10 p g. 10 100 p h. 10 500 p i. Would this be a reasonable model for human mortality? Why or why not? 7. You are given 2 0 10,000 t t q for 0 < t < 100. Calculate: a. 0 () Fx b. 0 Sx c. x St d. 0 fx e. 0 [] ET f. 0 Var T g. 40 0 q h. 40 0 p i. 0 Pr(40 60) T  j. x k. 75 l. p m. q n. 75 t q o. 75 t p p. x q. 75 r. x e s. 0 e t. 75 e u. | u t x q v. 10|5 75 q
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December 9, 2011 Version 3 8. You are given that 2 100 x x for 0 100 x  . Calculate 0 () Fx and 10 50 p .
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STAT 490 F11 Homework - Chapter 1 1. A with profits whole...

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