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Unformatted text preview: A Basic Course in the Theory of Interest and Derivatives Markets: A Preparation for the Actuarial Exam FM/2 Marcel B. Finan Arkansas Tech University c All Rights Reserved Preliminary Draft Last updated 08/12/09 2 In memory of my parents August 1, 2008 January 7, 2009 Preface The purpose of this manuscript is to prepare the reader for the second actuarial exam, referred to as Exam 2 by the Casualty Actuarial Society and Exam FM by the Society of Actuaries. A calculator, such as the one allowed on the Society of Actuaries examinations (TI BA II Plus, either the solar or battery version), will be useful in solving many of the problems in this book. Familiarity with this calculator and its capabilities is an essential part of preparation for the examination. A recommended resource link is http://www.scribd.com/doc/517593/TI-BA-II-PLUS-MANUAL . The flow of topics in the book follows very closely that of Kellison’s The Theory of Interest and McDonald’s Derivatives Markets . The book covers designated sections from these textbooks as suggested by the SOA. The recommended approach for using this book is to read each section, work on the embedded examples, and then try the problems. Answer keys are provided so that you check your numerical answers against the correct ones. Problems taken from previous exams will be indicated by the symbol ‡ . This manuscript can be used for personal use or class use, but not for commercial purposes. If you find any errors, I would appreciate hearing from you: mfi[email protected] This project has been supported by a research grant from Arkansas Tech University. Marcel B. Finan Russellville, Arkansas March 2009 3 4 PREFACE Contents Preface 3 The Basics of Interest Theory 9 1 The Meaning of Interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2 Accumulation and Amount Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3 Effective Interest Rate (EIR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4 Linear Accumulation Functions: Simple Interest . . . . . . . . . . . . . . . . . . . . . . 28 5 Date Conventions Under Simple Interest . . . . . . . . . . . . . . . . . . . . . . . . . . 35 6 Exponential Accumulation Functions: Compound Interest . . . . . . . . . . . . . . . . 41 7 Present Value and Discount Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 8 Interest in Advance: Effective Rate of Discount . . . . . . . . . . . . . . . . . . . . . . 56 9 Nominal Rates of Interest and Discount . . . . . . . . . . . . . . . . . . . . . . . . . . 66 10 Force of Interest: Continuous Compounding . . . . . . . . . . . . . . . . . . . . . . . 78 11 Time Varying Interest Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 12 Equations of Value and Time Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . 100 13 Solving for the Unknown Interest Rate . . . . . . . . . . . . . . . . . . . . . . . . . . 107 14 Solving for Unknown Time . 14 Solving for Unknown Time ....
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This note was uploaded on 03/29/2010 for the course STATISTICS 50 taught by Professor Diaz during the Spring '10 term at California State University , Monterey Bay.

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book - A Basic Course in the Theory of Interest and...

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