SOA Exam FM - studymanuals.com

1 12th EditionHarold Cherry, FSA, MAAA NO RETURN IF OPENEDA ctuarial Study MaterialsS OA Exam FMStudy ManualLearning Made EasierStudyPlus+ gives you digital access* to: Flashcards & Formula Sheet Actuarial Exam & Career Strategy Guides Technical Skill eLearning Tools Samples of Supplemental Texts & Study Tools And more!*See inside for keycode access and login instructionsWith StudyPlus+12th EditionHarold Cherry, FSA, MAAA NO RETURN IF OPENEDA ctuarial Study MaterialsS OA Exam FMStudy ManualLearning Made EasierStudyPlus+ gives you digital access* to: Flashcards & Formula Sheet Actuarial Exam & Career Strategy Guides Technical Skill eLearning Tools Samples of Supplemental Texts & Study Tools And more!*See inside for keycode access and login instructionsWith StudyPlus+TO OUR READERS:Please check s web site at for errata and updates.

2 If you have any comments or reports of errata, please e-mail us at Copyright 2017 by Actuarial Study Materials ( ), PO Box 69, Greenland, NH 03840. All rights reserved. Reproduction in whole or in part without express written permission from the publisher is strictly MATHEMATICS7 SECTION1 Interest Rates and Discount Rates9 1a Basic Concepts9 Calculator Notes16 Calculator Notes #1: Formatting; Present Values and Future Values17 Summary of Concepts and Formulas in Sections 1a(i) to 1a(v)23 Past Exam Questions on Sections 1a(i) to 1a(v)24 Calculator Notes #2: Discount Rates; Nominal Rates38 Summary of Concepts and Formulas in Sections 1a(vi) to 1a(ix)40 Past Exam Questions on Sections 1a(vi) to 1a(ix)41 1b Why Do We Need a Force of Interest?47 1c Defining the Force of Interest47 1d Finding the Fund in Terms of the Force of Interest50 1e The Simplest Case: A Constant Force of Interest52 1fPower Series54 Calculator Notes #3: Force of Interest57 Summary of Concepts and Formulas in Sections 1b to 1f58 Past Exam Questions on Sections 1b to 1f59 1g The Variable Force of Interest Trap71 Summary of Concepts and Formulas in Section 1g74 Past Exam Questions on Section 1g75 1h Equivalent Rates82 Calculator Notes #4.

3 Equivalent Rates85 Summary of Concepts and Formulas in Section 1h88 Past Exam Questions on Section 1h89 SECTION2 Practical Applications93 2a Equations of Value, Time Value of Money, and Time Diagrams93 2b Unknown Time and Unknown Interest Rate98 Summary of Concepts and Formulas in Sections 2a and 2b103 Past Exam Questions on Sections 2a and 2b104 ContentsSECTION3 Annuities113 3a The Geometric Series Trap113 3b Annuity-Immediate and Annuity-Due115 3c The Great Confusion: Annuity-Immediate and Annuity-Due119 Calculator Notes #5: Annuities124 Summary of Concepts and Formulas in Sections 3a to 3c129 Past Exam Questions on Sections 3a to 3c130 3d Deferred Annuities (or Playing Now you see )138 3e A Short-Cut Method for Annuities with Block Payments140 3fPerpetuities143 Summary of Concepts and Formulas in Sections 3d to 3f146 Past Exam Questions on Sections 3d to 3f147 3g Thea2n/anTrick (and Variations)158 Summary of Concepts and Formulas in Section 3g160 Past Exam Questions on Section 3g161 3h Balloon Payments and Drop Payments165 3iWhat If the Rate Is Unknown?

4 167 Summary of Concepts and Formulas in Sections 3h and 3i169 Past Exam Questions on Sections 3h and 3i170 3jWhat If the Rate Varies?177 Summary of Concepts and Formulas in Sections 3j179 Past Exam Questions on Section 3j180 SECTION4 Complex Annuities183 4a Annuities with Off-Payments Part I183 4b Annuities with Off Payments Part II185 4c Avoiding themthlyAnnuity Trap192 Summary of Concepts and Formulas in Sections 4a to 4c194 Past Exam Questions on Sections 4a to 4c195 4d Continuous Annuities210 4e Double-dots Cancel (and so do upperm s )211 4fA Short Note on Remembering Annuity Formulas213 4g ThesnTrap When Interest Varies213 Summary of Concepts and Formulas in Sections 4d to 4g215 Past Exam Questions on Sections 4d to 4g216 4h Payments in Arithmetic Progression221 Calculator Notes #6.

5 Annuities in Arithmetic Progression228 4iRemembering Increasing Annuity Formulas231 Summary of Concepts and Formulas in Sections 4h to 4i234 Past Exam Questions on Sections 4h and 4i236 4jPayments in Geometric Progression257 Summary of Concepts and Formulas in Sections 4j259 Past Exam Questions on Section 4j260ivCopyright 2017 ASM, 12th editionContents 4k The Amazing Expanding Money Machine (Or ContinuousVarying Annuities)270 Summary of Concepts and Formulas in Sections 4k273 Past Exam Questions on Section 4k274 4lA Short-Cut Method for the Palindromic Annuity277 Summary of Concepts and Formulas in Sections 4l279 Past Exam Questions on Section 4l280 4m The 0% Test: A Quick Check of Symbolic Answers282 SECTION5 Comparing Investments285 5a Net Present Value and Internal Rate of Return285 5b Is the Yield Rate Unique?

6 288 Calculator Notes #7: Cash Flow Worksheet289 5c Reinvestment Rates291 Summary of Concepts and Formulas in Sections 5a to 5c293 Past Exam Questions on Sections 5a to 5c294 5d Yield Rate Earned by a Fund303 5e Dollar-Weighted and Time-Weighted Interest Rates305 Summary of Concepts and Formulas in Sections 5d and 5e309 Past Exam Questions on Section 5d and 5e310 5fPortfolio Methods and Investment Year Methods317 SECTION6 Loans319 6a Amortizing a Loan319 Calculator Notes #8: Amortization Schedules327 Summary of Concepts and Formulas in Section 6a330 Past Exam Questions on Section 6a331 6b Don t be Sunk by Sinking Funds355 6c General Approach to SF Problems356 Summary of Concepts and Formulas in Sections 6b and 6c359 Past Exam Questions on Sections 6b and 6c360 6d Outstanding Balance, Interest Paid, and Principal Repaid under the Sinking FundMethod369 Summary of Concepts and Formulas in Section 6d372 Past Exam Questions on Section 6d373 6e Varying Series of Payments375 Summary of Concepts and Formulas in Section 6e378 Past Exam Questions on Section 6e379 6fEqual Principal Repayments (A Special Case of Varying Payments)

7 386 Summary of Concepts and Formulas in Section 6f388 Past Exam Questions on Section 6f389 SECTION7 Bonds393 7a Bonds and Other Investments393 7b Finding the Price of a Bond393 Copyright 2017 ASM, 12th editionvContentsCalculator Notes #9: Bonds399 Summary of Concepts and Formulas in Sections 7a and 7b400 Past Exam Questions on Sections 7a and 7b401 7c Premium and Discount415 Summary of Concepts and Formulas in Section 7c420 Past Exam Questions on Section 7c421 7d Price Between Coupon Dates427 7e Determination of Yield Rates431 Summary of Concepts and Formulas in Sections 7d and 7e433 Past Exam Questions on Sections 7d and 7e434 7fCallable Bonds436 Summary of Concepts and Formulas in Section 7f440 Past Exam Questions on Section 7f441 SECTION8 Financial Instruments443 8a Bonds, Preferred Stock.

8 And Common Stock443 8b Price of a Share of Stock444 8c Other Financial Instruments446 Summary of Concepts and Formulas in Sections 8a to 8c448 Past Exam Questions on Section 8a to 8c449 SECTION9 Determinants of Interest Rates453 9a What is Interest?453 9b Quotation Bases for Interest Rates454 9c Components of the Interest Rate: No Inflation or Default Risk457 9d Components of the Interest Rate: No Inflation but with Default Risk458 9e Components of the Interest Rate: Known Inflation461 9fComponents of the Interest Rate: Uncertain Inflation462 9g Savings and Lending Interest Rates464 9h Government and Corporate Bonds465 9iThe Role of Central Banks468 SECTION10 Duration, Convexity, and Immunization471 10a Duration of a Single Cash Flow471 10b Macaulay Duration474 10c Macaulay Duration as a Measure of Price Sensitivity477 10d Modified Duration479 10e Duration of a Portfolio483 10f Change in Duration As Time Goes By484 Summary of Concepts and Formulas in Sections 10a to 10f486 Practice Questions on Sections 10a to 10f487 10g Convexity492 10h Redington Immunization495 10i Full Immunization500 10j A Note on Rebalancing502viCopyright 2017 ASM, 12th editionContents 10k Immunization by Exact Matching ( Dedication )

9 502 Summary of Concepts and Formulas in Sections 10g to 10k506 Practice Questions on Sections 10g to 10k507 SECTION11 Interest Rate Swaps511 11a Spot Rates and Forward Rates511 Summary of Concepts and Formulas in Section 11a520 Practice Questions on Section 11a521 11b What is an Interest Rate Swap?525 Summary of Concepts and Formulas in Section 11b530 PARTIISIX ORIGINAL PRACTICE EXAMS531 Practice Exam 1533 Questions for Practice Exam 1533 Solutions to Practice Exam 1539 Practice Exam 2547 Questions for Practice Exam 2547 Solutions to Practice Exam 2553 Practice Exam 3561 Questions for Practice Exam 3561 Solutions to Practice Exam 3567 Practice Exam 4579 Questions for Practice Exam 4579 Solutions to Practice Exam 4585 Practice Exam 5597 Questions for Practice Exam 5597 Solutions to Practice Exam 5603 Practice Exam 6613 Questions for Practice Exam 6613 Solutions to Practice Exam 6619 Copyright 2017 ASM, 12th editionviiIntroductionTo the student: Please read this Introduction.

10 It contains 12thedition of this manual has been revised and updated for the new syllabus in effect for theJune 2017 and later exams . The major changes in the syllabus were:.The topic of derivatives (except for interest rate swaps) was new study note on interest rate swaps was new study note on duration and convexity was new study note on determinants of interest rates was 12thedition consists of 11 sections covering all of the material on the syllabus (Part I of themanual), followed by six original practice exams (Part II of the manual). Following each sectionor subsection in Part I, there are illustrative examples called Stepping Stones (see below). Theseexamples are followed by a summary of the key concepts and formulas in the section, then byproblems and solutions from actual past SOA/CAS of this explain the concepts of financial mathematics in a way that appeals to your intuition andcommon point out shortcuts and tricks that can get you to the answer more warn you about common traps that students fall into and help you to avoid provide you with hundreds of problems from past exams , with provide you with original practice exams that will help prepare you for the real highlight the concepts, tricks, shortcuts, and traps, you will see special symbols such as thefollowing throughout the manual:!