CONTENTS

1 Introduction—Who this Book is for and What it Hopes to

Accomplish

Historical Background—The Big Change in Investment, Loan,

and Money Management 1

What this Book Hopes to Accomplish 3

What Sort of Problems Might this Book Help You to Solve? 4

Who this Book is Meant to Address 4

The Mathematical Knowledge Required for this Book 5

The Role of Examples and Problems in this Book 6

2 Interest, Its Calculation, and Return on Investment

A General Introduction to Interest 7

How to Compute Interest 8

Notation 9

Percentage Rate and Time Period 10

Return on Investment 11

Analysis of Investments or Returns without Explicit Money Values,

and Intangible Investments and Returns 14

Chapter Summary 16

3 Compound Interest

What is Compound Interest? 20

Using Compound Interest Tables 21

Looking at the Compound Interest Tables 23

Compounding within a Period 23

The Equations for Compound Interest–Compounding within

a Period 24

v

Continuous Compounding: How it Works and When it

Applies 25

The Derivation of the Equations for Continuous Compounding 26

What is a Mathematical Model? 28

Some Famous Mathematical Models 29

Reasons for Using Continuous Functions in Financial Models 30

A Business Example of Use of Continuous Functions 30

Further Reﬂections on Approach 3 31

Computing i, Given S, S

NT

, T, and N 31

Accuracy Requirements 36

Legal Requirements for Accuracy 36

An Example from Compound Interest 36

Using Tables and Interpolating between Values 37

The Rule of 72 37

A Zero Interest Rate? 37

Negative Interest Rates? 38

Real and Nominal Rates 38

Chapter Summary 39

Suggestions for Further Study 41

4 Present Values

What is Present Value? 52

The Equation for Present Value 52

The General Equation for Present Value 53

The Present Value Tables 54

Using Present Values to Make Project Decisions 54

Example of Project Analysis 55

Using Different Interest Rates in the Analysis 57

The Equations for Flow of Funds Analysis 57

The Various Number Systems and What They Mean 58

Solving Polynomial Equations 61

Practical Considerations in Using Calculators and Computers to Solve

Polynomial Equations 62

Using the Bisection Method to Find Real Solutions 63

What if the Exponents are not Integers? 64

Chapter Summary 64

Suggestions for Further Study 67

5 Annuities Certain

What is an Annuity Certain? 77

Examples of Annuities Certain 78

Why Annuities Certain are Important 78

vi Contents

The Equation for the Present Value of an Annuity Certain 79

A Look at the Tables for an Annuity Certain 80

Solving for the Interest Rate, Given the Annuity Certain and

Its Cost 80

The Perpetuity 80

The Annuity Due 81

Further Comments 82

Analysis and Calculation of Some Combination Annuities Certain 83

Chapter Summary 83

6 Bond Price Calculation

What is a Bond? 104

How Bonds are Described 105

How to Read a Bond Market Report 105

What is a Call Feature? 106

What is a Put Option? 108

Discount Securities 108

The General Equation for Computing a Bond Price,

Given the Yield 108

A Note on Yield 110

A Note on Accrued Days in the Settlement Period

(A in Equation 6.1) and Dated Date 111

Analysis of the Equation 111

Standards of Accuracy 114

Pricing Zero Coupon Bonds 115

Pricing to a Call Feature 115

Examples of Bond Price Calculations 116

Amortization of Premium and Accrual of Discount 117

Accrual of Discount 117

Amortization of Premium 119

A Portfolio Management Interlude 120

Pricing a Bond to a Call 121

A Look at a Basis Book 123

Basic Rules for Prices and Yields 123

The Shape of the Price-Yield Curve 124

Dirty Price and Clean Price 125

Chapter Summary 126

Suggestion for Further Study 128

7 The Future Value (or Amount) of an Annuity

Uses of the Future Value of an Annuity 131

The Equation for the Future Value of an Annuity 132

Contents vii

The Tables for Amount of Annuity 133

Some Investment Policy Implications 133

Chapter Summary 133

8 Accrued Interest

What is Accrued Interest? 143

Bonds that Accrue Interest 144

The Equation for Accrued Interest 144

Chapter Summary 146

9 Discount Yield

Discount Yield 150

Calculation of the Discount and Price for Discount Securities 150

What is a Treasury Bill? 150

The Day-Count Conventions for T-Bills 151

Price Calculations for Discount Municipal Securities 152

Bond Equivalent Yield (BEY): What It Means and How to

Compute It 152

Derivation of the Bond Equivalent Yield Equations 153

Why We Care about Bond Equivalent Yield (BEY) 154

A Historical Note 155

Taxation of Income from Treasury Bills 155

Chapter Summary 155

10 Calculations for Other Securities

Certiﬁcates of Deposit 159

Repurchase Agreements 160

Uses of Repos and Reverse Repos 161

Pricing Repos 161

Chapter Summary 161

Class Project 161

11 Quotations and Bond Market Reports

Long-Term Instruments 163

Discount Instruments 165

Chapter Summary 166

12 Types of Yields

Nominal (or Coupon) Yield 168

Discount Yield 168

Current Yield 168

True (or Bond) Yield 169

viii Contents

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