# Exam MLC Models for Life MLC - SOA of Actuaries Exam MLC Models for Life Contingencies Tuesday,...

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Society of Actuaries Exam MLC

Models for Life Contingencies

Tuesday,

April 29, 2014 8:30 a.m. 12:45 p.m.

MLC Canadian Institute of Actuaries

INSTRUCTIONS TO CANDIDATES

General Instructions 1. Write your candidate number here ____________. Your

name must not appear. 2. Do not break the seal of this book until the supervisor tells

you to do so. 3. Tables and numerical values necessary for solving some of

the questions on this examination will be distributed by the Supervisor.

4. This examination has a total of 96 points. It consists of:

Section A: 20 multiple-choice questions, each worth 2 points for a total of 40 points, and

Section B: 7 written-answer questions, worth a total of

56 points. The point value for each written-answer question is indicated at the beginning of the question.

You may divide your time between the two sections of the examination (written-answer, and multiple-choice) as you choose. You should keep in mind the relative weight of the two sections.

5. Failure to stop writing after time is called will result in the

disqualification of your answers or further disciplinary action. 6. While every attempt is made to avoid defective questions,

sometimes they do occur. If you believe a question is defective, the supervisor or proctor cannot give you any guidance beyond the instructions on the exam booklet.

Multiple-Choice Instructions 1. A separate answer sheet for the multiple-choice questions is

inside the front cover of this book. During the time allotted for this examination, record all your answers on the back of the answer sheet. NO ADDITIONAL TIME WILL BE ALLOWED FOR THIS PURPOSE. No credit will be given for anything indicated in the examination book but not transferred to the answer sheet. Failure to stop writing or coding your answer sheet after time is called will result in the disqualification of your answer sheet or further disciplinary action.

2. On the front of the answer sheet, space is provided to write

and code candidate information. Complete the information requested by printing in the squares and blackening the circles (one in each column) corresponding to the letters or numbers printed. For each empty box blacken the small circle immediately above the A circle. Fill out the boxes titled:

(a) Name

(include last name, first name and middle initial) (b) Candidate Number

(Candidate/Eligibility Number, use leading zeros if needed to make it a five digit number)

(c) Test Site Code

(The supervisor will supply the number.) (d) Examination Part

(Code the examination that you are taking by blackening the circle to the left of "Exam MLC")

(e) Booklet Number

(The booklet number can be found in the upper right-hand corner of this examination book. Use leading zeros if needed to make it a four digit number.)

In box titled Complete this section only if instructed to do so, fill in the circle to indicate if you are using a calculator and write in the make and model number. In the box titled Signature and Date sign your name and write today's date. If the answer sheet is not signed, it will not be graded. Leave the boxes titled Test Code and Form Code blank.

On the back of the answer sheet fill in the Booklet Number in the space provided.

CONTINUED ON INSIDE FRONT COVER

2014 by the Society of Actuaries Printed in the U.S.A. 475 N. Martingale Road Exam MLC - Front Cover Schaumburg, IL 60173-2226

3. Your score will be based on the number of questions which you answer correctly. No credit will be given for omitted answers and no credit will be lost for wrong answers: hence, you should answer all questions even those for which you have to guess.

4. Five answer choices are given with each multiple-choice

question, each answer choice being identified by a key letter (A to E). Answer choices for some questions have been rounded. For each question, blacken the circle on the answer sheet which corresponds to the key letter of the answer choice that you select.

5. Use a soft-lead pencil to mark the answer sheet. To facilitate

correct mechanical scoring, be sure that, for each question, your pencil mark is dark and completely fills only the intended circle. Make no stray marks on the answer sheet. If you have to erase, do so completely.

6. Do not spend too much time on any one question. If a

question seems too difficult, leave it and go on. 7. Clearly indicated answer choices in the test book can be an

aid in grading examinations in the unlikely event of a lost answer sheet.

8. Use the blank portions of each page for your scratch work.

Extra blank pages are provided at the back of the examination book.

9. After the examination, the supervisor will collect this book

and the answer sheet separately. DO NOT ENCLOSE THE ANSWER SHEET IN THE BOOK OR IN THE ESSAY ANSWER ENVELOPE. All books and answer sheets must be returned. THE QUESTIONS ARE CONFIDENTIAL AND MAY NOT BE TAKEN FROM THE EXAMINATION ROOM.

Written-Answer Instructions 1. Write your candidate number at the top of each sheet. Your

name must not appear. 2. Write on only one side of a sheet. Start each question on a

fresh sheet. On each sheet, write the number of the question you are answering. Do not answer more than one question on a single sheet.

3. The answer should be confined to the question as set. 4. When you are asked to calculate, show all your work

including any applicable formulas. 5. When you finish, insert all your written-answer sheets into the

Essay Answer Envelope. Be sure to hand in all your answer sheets because they cannot be accepted later. Seal the envelope and write your candidate number in the space provided on the outside of the envelope. Check the appropriate box to indicate Exam MLC.

6. Be sure your essay answer envelope is signed because if it is

not, your examination will not be graded. 7. For all parts of all problems, to maximize the credit earned,

candidates should show as much work as possible, considering the time allotted for the question. Answers lacking justification will receive no credit. Answers should be organized so that the methods, logic, and formulas used are readily apparent. Candidates should not round their answers excessively; enough precision should be provided so that their answers can be accurately graded.

In some cases, candidates are asked to show that a calculation

results in a particular number. Typically the answer given will be rounded; candidates should provide a greater level of accuracy than the number given in the question. This structure of question is intended to assist the candidate by giving an indication when the calculation has been done incorrectly, providing an opportunity to explore an alternative approach. It also allows a candidate who cannot obtain the correct answer to use the answer given to proceed with subsequent parts of the problem. (Candidates who are able to solve the problem should use their exact answer for subsequent parts.)

For questions requiring candidates to derive or write down a

formula or equation, the resulting expression should be simplified as far as possible, and where numerical values are provided in the problem, they should be used.

Exam MLC Inside Front Cover

Tournez le cahier dexamen pour la version franaise

Exam MLC

SECTION A Multiple-Choice

Exam MLC: Spring 2014 1 GO ON TO NEXT PAGE

**BEGINNING OF EXAMINATION**

1. You are given the following information from a life table:

(i) x xl xd xp xq

95 0.40 96 0.20 97 72 1.00

(ii) 90 1000l = and 93 825l =

(iii) Deaths are uniformly distributed over each year of age.

Calculate the probability that (90) dies between ages 93 and 95.5. (A) 0.195

(B) 0.220

(C) 0.345

(D) 0.465

(E) 0.668

Exam MLC: Spring 2014 2 GO ON TO NEXT PAGE

USE THIS PAGE FOR YOUR SCRATCH WORK

EXTRA BLANK PAPER IS PROVIDED AT THE END OF THE EXAM BOOK

Exam MLC: Spring 2014 3 GO ON TO NEXT PAGE

2. You are given the following extract from a table with a 3-year select period:

(i) x [ ]xq [ ] 1xq + [ ] 2xq + 3xq + 3x +

60 0.09 0.11 0.13 0.15 63 61 0.10 0.12 0.14 0.16 64 62 0.11 0.13 0.15 0.17 65 63 0.12 0.14 0.16 0.18 66 64 0.13 0.15 0.17 0.19 67

(ii) 64 5.10e =

Calculate [61].e (A) 5.30

(B) 5.39

(C) 5.68

(D) 5.85

(E) 6.00

Exam MLC: Spring 2014 4 GO ON TO NEXT PAGE

USE THIS PAGE FOR YOUR SCRATCH WORK

EXTRA BLANK PAPER IS PROVIDED AT THE END OF THE EXAM BOOK

Exam MLC: Spring 2014 5 GO ON TO NEXT PAGE

3. A continuous Markov process is modeled by the following multiple state diagram:

State 0 State 1

State 2

You are given the following constant transition intensities:

(i) 01 0.08 =

(ii) 02 0.04 =

(iii) 10 0.10 =

(iv) 12 0.05 = For a person in State 1, calculate the probability that the person will continuously remain in State 1 for the next 15 years. (A) 0.032

(B) 0.105

(C) 0.151

(D) 0.250

(E) 0.350

Exam MLC: Spring 2014 6 GO ON TO NEXT PAGE

USE THIS PAGE FOR YOUR SCRATCH WORK

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