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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