Broverman FM Study Guide 2017 - Sample Excerpt - ACTEX / Mad River

EXCERPTS FROM S. BROVERMAN STUDY GUIDE FOR SOA EXAM FM 2017

Table of Contents Introductory Comments Section 12 - Bond Amortization, Callable Bonds Problem Set 7 - Annuities Whose Payments Follow a Geometric Progression

? S. Broverman, 2017

S. BROVERMAN EXAM FM/2 STUDY GUIDE

2017

TABLE OF CONTENTS

INTRODUCTORY NOTE

SECTION 1 - Calculus Review and Effective Rates of Interest and Discount

1

PROBLEM SET 1

13

SECTION 2 - Nominal Rates of Interest and Discount

19

PROBLEM SET 2

31

SECTION 3 - Force of Interest, Inflation, Risk of Default

37

PROBLEM SET 3

47

SECTION 4 - Annuity-Immediate and Annuity-Due

55

PROBLEM SET 4

63

SECTION 5 - Annuity Valuation At Any Time Point

71

PROBLEM SET 5

79

SECTION 6 - Annuities With Differing Interest and Payment Periods

85

PROBLEM SET 6

93

SECTION 7 - Annuities Whose Payments Follow a Geometric Progression

101

PROBLEM SET 7

105

SECTION 8 - Annuities Whose Payments Follow an Arithmetic Progression

117

PROBLEM SET 8

127

SECTION 9 - Amortization of a Loan

139

PROBLEM SET 9

147

SECTION 10 - The Sinking Fund Method of Loan Repayment

165

PROBLEM SET 10

169

SECTION 11 - Bond Valuation

175

PROBLEM SET 11

185

SECTION 12 - Bond Amortization, Callable Bonds

193

PROBLEM SET 12

201

? S. Broverman, 2017

SECTION 13 - Measures of the Rate of Return on a Fund

211

PROBLEM SET 13

219

SECTION 14 - Term Structure, Forward Rates

227

PROBLEM SET 14

235

SECTION 15 - Duration and Immunization

243

PROBLEM SET 15

253

SECTION 16 - Interest Rate Swaps

263

PROBLEM SET 16

271

PROBLEM SET 17 Calculator Exercises

277

PRACTICE EXAM 1

287

PRACTICE EXAM 2

307

PRACTICE EXAM 3

327

PRACTICE EXAM 4

343

PRACTICE EXAM 5

361

PRACTICE EXAM 6

381

? S. Broverman, 2017

INTRODUCTORY NOTE

This study guide is designed to help with the preparation for Exam FM of the Society of Actuaries. The SOA has revised the syllabus for Exam FM starting with the June, 2017 sitting of the exam. This study guide is based on the revised syllabus.

Among the references indicated by the SOA in the exam syllabus for Exam FM is the 6th edition of Mathematics of Investment and Credit by S. Broverman. Along with the SOA listed Text References, there are three SOA Study Notes as part of the readings for the FM exam. The notation and ordering of material will be mostly consistent with those references. This study guide covers all of the mathematical content of the two Study Notes titled "Using Duration and Concexity to Approximate Change in Present Value" and "Interest Rate Swaps". The third Study Note is titles "Determinants of Interest Rates". There is minimal mathematical content in that Study Note, but this study guide covers much of the content of that Study Note. It is recommended that those preparing for the FM exam read those Study Notes.

Many examples in this study guide are labeled "SOA", and some, "EA1". This indicates that the example is from a previous SOA or Enrolled Actuaries exam. The review part of this study guide is divided into 16 sections, each with a problem set, plus a Problem Set 17 which has exercises specifically for practice on the BA II PLUS calculator. This is followed by 6 practice exams. The exam is scheduled to be 3 hours long with 35 multiple choice questions. In addition, at the start of each section of notes is a reference to the appropriate sections in Mathematics of Investment and Credit in which the material is covered.

Because of the time constraint on the exam, a crucial aspect of exam taking is the ability to work quickly. I believe that working through many problems and examples is a good way to build up the speed at which you work. It can also be worthwhile to work through problems that have been done before, as this helps to reinforce familiarity, understanding and confidence. Working many problems will also help in being able to more quickly identify topic and question types.

I have attempted, wherever possible, to emphasize shortcuts and efficient and systematic ways of setting up solutions. There are also occasional comments on interpretation of the language used in some exam questions. While the focus of the study guide is on exam preparation, from time to time there will be comments on underlying theory in places that I feel those comments may provide useful insight into a topic.

This study guide contains over 70 detailed examples throughout the sections of review notes, and about 240 exercises in the problem sets. There are 35 questions on each of the 6 practice exams. Some of the questions on the practice exams have been taken from past SOA exams. SOA exam questions are copyrighted material of the SOA. The author gratefully acknowledges the permission granted by the SOA to use those questions in this study guide.

? S. Broverman, 2017

Although many examples in the review notes and some of the exercises are from old SOA exams, some of the problem set exercises are more in depth than actual exam questions, but the practice exam questions have been created in an attempt to replicate the level of depth and difficulty of actual exam questions. It is worthwhile to occasionally check the SOA websites to see if any new sample questions have been posted.

It has been my intention to make this study guide self-contained and comprehensive for Exam FM. While the ability to derive formulas used on the exam is usually not the focus of an exam question, it can be useful in enhancing the understanding of the material and may be helpful in memorizing formulas. There will be some references in the review notes to derivations, but you are encouraged to review the official reference material for more detail on formula derivations. In order for this study guide to be most effective, you should be reasonably familiar with differential and integral calculus.

Of the various calculators that are allowed for use on Exam FM, I think that the BA II PLUS is probably the best choice. It has several easily accessible memories. It is probably the most functional of all the calculators allowed. Throughout the notes you will find boxed examples labeled "Calculator Notes, BA II PLUS". I am the author of a couple of study notes available at the SOA website which cover applications of the BA II PLUS and BA-35 calculators in some detail (the BA-35 is no longer displayed at the Texas Instruments website, so it is possible that TI no longer produces it). These study notes are available at . The study notes provide examples of keystroke sequences for solving the more frequently encountered types of calculations for that calculator. Students are strongly urged to review the calculator functions in the calculator guidebooks.

The calculator guidebook should come with the calculator when it is purchased, or can be downloaded from the Texas Instruments website: .

If you have any questions, comments, criticisms or compliments regarding this study guide, you may contact me at the address below. I apologize in advance for any errors, typographical or otherwise, that you might find, and it would be greatly appreciated if you would bring them to my attention. I will be maintaining a website for errata that can be accessed from (at the Exam FM link) .

It is my sincere hope that you find this study guide helpful and useful in your preparation for the exam. I wish you the best of luck on the exam.

Samuel A. Broverman Department of Statistics, University of Toronto 100 St. George Street Toronto, Ontario CANADA M5S 3G3 E-mail: 2brove@ or sam@utstat.toronto.edu Internet:

January, 2017

? S. Broverman, 2017

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