Long-Term Actuarial Mathematics Sample Multiple Choice ...

1 Long-Term Actuarial Mathematics Sample Multiple Choice Questions July 31, 2019. There are 237 Sample Multiple Choice questions in this Study Note for the Long-Term Actuarial Mathematics exam. The questions are sorted by the Society of Actuaries' recommended resources for this exam. All question numbers follow the format of where X identifies the source and Y is the question number from that source. If the X is a number, then it refers to the chapter of Actuarial Mathematics for Life Contingent Risks, 2nd Edition. If the X is LM then it refers to Chapter 12 of Loss Models, From Data to Decisions, 5th Edition which is Study Note LTAM-22-18. If the X is S# where the # is a number, then these questions refer to chapter # of the Supplemental Note on Long-Term Actuarial Mathematics which is Study Note LTAM-21-18.

2 Many of these questions are questions that have previously appeared on MLC exams from 2012. through 2017. These are identified by a parenthetical expression at the end of such questions. Questions that have been modified have been modified to: Replace the Illustrative Life Table (ILT) which was used on the MLC exam with the Standard Ultimate Life Table (SULT) which will be used with the LTAM exam. All problems that previously used the ILT have been converted to the SULT. Change language to reflect the current terms used on the LTAM exam. For example, the current term used is net premium where on the earlier MLC exams, the term used was benefit premium. Where benefit premium appeared in old exam questions, it has been replaced by net premium.

3 Additionally, questions from previous MLC exams from 2012 to 2017 which covered material that is no longer covered by the Long-Term Actuarial Mathematics exam have been eliminated. The student should note that Multiple Choice questions from MLC exams in 2012 and 2013. which are included in these Sample questions were intended to average six minutes each. For the Multiple Choice questions for the MLC exam in 2014 and later were intended to average five minutes each. The Multiple Choice questions on the Long-Term Actuarial Mathematics exam are intended to average five minutes each. Therefore, the questions based on the 2012 and 2013. MLC exams may be slightly longer that the student will encounter on the Long-Term Actuarial Mathematics exam.

4 That being said, these questions are representative of the types of questions that might be asked of candidates sitting for the Long-Term Actuarial Mathematics exam. These questions are intended to represent the depth of understanding required of candidates. The distribution of questions by topic is not intended to represent the distribution of questions on future exams. Finally, there are new Sample Multiple Choice questions which primarily cover the material that has been added to the Long-Term Actuarial Mathematics exam. July 31, 2019 Page 1. Versions: July 2, 2018 Original Set of Questions Published July 24, 2018 Correction to question August 27, 2018 Correction to question September 17, 2018 Added 72 questions from the 2016 and 2017 Multiple Choice MLC.

5 Exams. October 13, 2018 Correction to questions , and February 6, 2019 Questions , , , and were previously misclassified so they were renumbered to move them to the correct chapter. July 31, 2019 Questions and were previously misclassified so they were renumbered to move them to the correct chapter. July 31, 2019 Page 2. Which of the following is not true with regard to underwriting? (A) Life insurance policies are typically underwritten to prevent adverse selection. (B) The distribution method affects the level of underwriting. (C) Single premium immediate annuities are typically underwritten to prevent adverse selection. (D) Underwriting may result in an insured life being classified as a rated life due to the insured's occupation or hobby.

6 (E) A pure endowment does not need to be underwritten to prevent adverse selection. July 31, 2019 Page 3. Over the last 30 years, life insurance products and the management of the associated risks have radically changed and become more complex. Which of the following is not a reason for this change? (A) More sophisticated policyholders. (B) More competition among life insurance companies. (C) More computational power. (D) More complex risk management techniques. (E) Separation of the savings elements and the protection elements of life insurance products. July 31, 2019 Page 4. You are given: 1. t 4. (i) S 0 (t ) 1 , for 0 t .. 1. (ii) 65 . 180. Calculate e106 , the curtate expectation of life at age 106.

7 (A) (B) (C) (D) (E) [This was Question 3 on the Fall 2012 Multiple Choice exam.]. July 31, 2019 Page 5. Scientists are searching for a vaccine for a disease. You are given: (i) 100,000 lives age x are exposed to the disease. (ii) Future lifetimes are independent, except that the vaccine, if available, will be given to all at the end of year 1. (iii) The probability that the vaccine will be available is (iv) For each life during year 1, q x (v) For each life during year 2, q x 1 if the vaccine has been given, and q x 1 if it has not been given. Calculate the standard deviation of the number of survivors at the end of year 2. (A) 100. (B) 200. (C) 300. (D) 400. (E) 500.

8 [This was Question 20 on the Spring 2013 Multiple Choice exam.]. July 31, 2019 Page 6. You are given that mortality follows Gompertz Law with B = and c = Calculate f50 (10) . (A) (B) (C) (D) (E) July 31, 2019 Page 7. t2. You are given t q0 for 0 < t < 100. 10, 000. Calculate e75:10 . (A) (B) (C) (D) (E) July 31, 2019 Page 8. You are given the following: (i) e40:20 18. (ii) e60 25. (iii) q 20 40. (iv) q40 Calculate e41 . (A) (B) (C) (D) (E) July 31, 2019 Page 9. You are given the survival function: 1. x 3. S0 ( x ) 1 , 0 x 60. 60 . Calculate 1000 35 . (A) (B) (C) (D) (E) [This was Question 2 on the Spring 2016 Multiple Choice exam.]. July 31, 2019 Page 10. You are given the following survival function of a newborn: x 1 250 , 0 x 40.

9 S0 x 2. 1 x , 40 x 100. 100 . Calculate the probability that (30) dies within the next 20 years. (A) (B) (C) (D) (E) [This was Question 2 on the Fall 2016 Multiple Choice exam.]. July 31, 2019 Page 11. In a population initially consisting of 75% females and 25% males, you are given: (i) For a female, the force of mortality is constant and equals . (ii) For a male, the force of mortality is constant and equals . (iii) At the end of 20 years, the population consists of 85% females and 15% males. Calculate the probability that a female survives one year. (A) (B) (C) (D) (E) [This was Question 3 on the Fall 2016 Multiple Choice exam.]. July 31, 2019 Page 12. You are given: (i) An excerpt from a select and ultimate life table with a select period of 3 years: x l[ x] l [ x ] 1 l [ x] 2 l x 3 x 3.

10 60 80,000 79,000 77,000 74,000 63. 61 78,000 76,000 73,000 70,000 64. 62 75,000 72,000 69,000 67,000 65. 63 71,000 68,000 66,000 65,000 66. (ii) Deaths follow a constant force of mortality over each year of age. Calculate 1000 23. q [60] . (A) 104. (B) 117. (C) 122. (D) 135. (E) 142. [This was Question 2 on the Fall 2012 Multiple Choice exam.]. July 31, 2019 Page 13. You are given: (i) The following extract from a mortality table with a one-year select period: x l[ x] d [ x] l x 1 x 1. 65 1000 40 66. 66 955 45 67. (ii) Deaths are uniformly distributed over each year of age. (iii) e [ 65] Calculate e[66] . (A) (B) (C) (D) (E) [This was Question 19 on the Spring 2013 Multiple Choice exam.]