Long-Term Actuarial Mathematics Sample Multiple Choice Questions

243 Pages·2017·1.84 MB·English

Long-Term Actuarial Mathematics
Sample Multiple Choice Questions
July 19, 2021
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 X.Y. 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.
The current syllabus of the LTAM exam is now Actuarial Mathematics for Life Contingent Risks,
3nd Edition with no study notes. The material previously in the study notes is now in 3rd edition
of the text. We have not renumbered the sample questions as the entire syllabus will be
revamped in the near future.
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been replaced by net premium.
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. 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.

July 19, 2021 Page 1
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 19, 2021 Page 2
Versions:
July 2, 2018 Original Set of Questions Published
July 24, 2018 Correction to question 6.25
August 27, 2018 Correction to question LM.3
September 17, 2018 Added 72 questions from the 2016 and 2017 multiple choice MLC
exams.
October 13, 2018 Correction to questions 4.21, 6.32 and 6.39.
February 6, 2019 Questions 4.5, 5.3, 5.5, and 5.8 were previously misclassified so they
were renumbered to move them to the correct chapter.
July 31, 2019 Questions 6.6 and 6.17 were previously misclassified so they were
renumbered to move them to the correct chapter.
July 19, 2021 Question LM.4 was clarified to indicate a “linear” confidence interval
and to change the notation to be consistent with the current syllabus.
Question LM.6 was removed.

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1.1
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.
(E) A pure endowment does not need to be underwritten to prevent adverse selection.

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1.2.
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.

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2.1.
You are given:
1
 t 4
(i) S (t)1  , for 0t 
0  

1
(ii)  
65 180

Calculate e , the curtate expectation of life at age 106.
106

(A) 2.2

(B) 2.5

(C) 2.7

(D) 3.0

(E) 3.2

[This was Question 3 on the Fall 2012 Multiple Choice exam.]

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2.2
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 0.2.

(iv) For each life during year 1, q 0.02.
x

(v) For each life during year 2, q 0.01 if the vaccine has been given, and q 0.02 if
x1 x1
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

[This was Question 20 on the Spring 2013 Multiple Choice exam.]
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2.3.
You are given that mortality follows Gompertz Law with B = 0.00027 and c = 1.1.

Calculate f (10).
50

(A) 0.048

(B) 0.050

(C) 0.052

(D) 0.054

(E) 0.056

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t2
2.4.
You are given q  for 0 < t < 100.
t 0 10,000

Calculate e .
75:10

(A) 6.6

(B) 7.0

(C) 7.4

(D) 7.8

(E) 8.2
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2.5.
You are given the following:
(i) e 18
40:20
(ii) e 25
60
(iii) q 0.2
20 40
(iv) q 0.003
40

Calculate e .
41

(A) 36.1

(B) 37.1

(C) 38.1

(D) 39.1

(E) 40.1

July 19, 2021 Page 10