Table of Contents
Preface to the First Edition ix
Preface to the Second Edition x
Part I Payments Certain 1
Chapter 1 Variations on the Theme An = P(1 + i)n: Some General Principles of Compound Interest 1
Preliminaries 1
Introduction to Compound Interest 5
Time Diagrams, Equations of Value, and Focal Dates 9
Depreciation 14
Summary of Formulas 18
Chapter 2 Mixing it Up: Nominal Rates of Interest, Multiple Deposits and Withdrawals, and More 21
Nominal Rates 21
Multiple Deposits/Withdrawals 25
A More General Look at Equations of Value and Focal Dates 29
Effective Rates; Equivalent Rates; Comparing Nominal Rates 32
Summary of Formulas 41
Chapter 3 Introduction to Annuities 43
Regular Annuities and Geometric Sums 43
A General Formula for Regular Annuities 48
An Important Application of Annuities-Bonds 64
Summary of Formulas 70
Chapter 4 More General Annuities 73
Non-Regular Annuities 73
Annuities Whose Payments Increase/Decrease by a Fixed Percentage 76
Perpetuities 82
Perpetuities Increasing or Decreasing by a Fixed Percentage 86
A Brief Look at Stocks 89
Summary of Formulas 93
Chapter 5 Amortization and Sinking Funds 95
Introduction 95
Amortization and Outstanding Principal 95
Amortization Schedules 102
Sinking Fund Schedules 106
Yield Rates 111
Summary of Formulas 115
Part II Life Contingencies 119
Chapter 6 Probability & The Mortality Table 119
What is Probability? 119
The Mortality Table 121
Probability Distributions for Ages at Death 126
Average Age at Death for a Life Aged x 128
The Force of Mortality 136
Summary of Formulas 138
Chapter 7 Life Annuities 141
Introduction 141
Pure Endowments 141
Life Annuities 145
Life Annuities with Payments Increasing/Decreasing by a Fixed Percentage 157
Summary of Formulas 164
Chapter 8 Life Insurance 167
Introduction 167
How Life Insurance Works 167
A General Formula for the Net Single Premium for Life Insurance 174
Policies with Benefits Increasing/Decreasing by a Fixed Percentage 181
Summary of Formulas 190
Chapter 9 Loose Ends: Reserves & Gross Premiums* 193
Introduction 193
Reserves 193
Gross Premiums 202
Summary of Formulas 212
Tables 215
Table I 216
Table II 217
Table III 218
Table IV 243
Solutions 269
Bibliography 369
Index 371
About the Author 377
