A Basic Course in the Theory of Interest and Derivatives ...

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

March 24, 2017

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In memory of my parents August 1, 2008 January 7, 2009

Preface

This manuscript is designed for an introductory course in the theory of interest and annuity. This manuscript is suitablefor a junior level course in the mathematics of finance. A calculator, such as TI BA II Plus, either the solar or battery version, will be useful in solving many of the problems in this book. A recommended resource link for the use of this calculator can be found at

. 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: mfinan@atu.edu This project has been supported by a research grant from Arkansas Tech University.

Marcel B. Finan Russellville, Arkansas March 2009

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PREFACE

Contents

Preface

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The Basics of Interest Theory

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1 The Meaning of Interest . . . . . . . . . . . . . . . . . . . . . . . 10

2 Accumulation and Amount Functions . . . . . . . . . . . . . . . . 15

3 Effective Interest Rate (EIR) . . . . . . . . . . . . . . . . . . . . 25

4 Linear Accumulation Functions: Simple Interest . . . . . . . . . . 32

5 Date Conventions Under Simple Interest . . . . . . . . . . . . . . 40

6 Exponential Accumulation Functions: Compound Interest . . . . 46

7 Present Value and Discount Functions . . . . . . . . . . . . . . . 56

8 Interest in Advance: Effective Rate of Discount . . . . . . . . . . 63

9 Nominal Rates of Interest and Discount . . . . . . . . . . . . . . 75

10 Force of Interest: Continuous Compounding . . . . . . . . . . . 88

11 Time Varying Interest Rates . . . . . . . . . . . . . . . . . . . . 104

12 Equations of Value and Time Diagrams . . . . . . . . . . . . . . 111

13 Solving for the Unknown Interest Rate . . . . . . . . . . . . . . 118

14 Solving for Unknown Time . . . . . . . . . . . . . . . . . . . . . 127

The Basics of Annuity Theory

155

15 Present and Accumulated Values of an Annuity-Immediate . . . 156

16 Annuity in Advance: Annuity Due . . . . . . . . . . . . . . . . . 170

17 Annuity Values on Any Date: Deferred Annuity . . . . . . . . . 181

18 Annuities with Infinite Payments: Perpetuities . . . . . . . . . . 191

19 Solving for the Unknown Number of Payments of an Annuity . . 199

20 Solving for the Unknown Rate of Interest of an Annuity . . . . . 209

21 Varying Interest of an Annuity . . . . . . . . . . . . . . . . . . . 219

22 Annuities Payable at a Different Frequency than Interest is Con-

vertible . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224

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