INSEAD Library

Includes bibliographical references and index

Digitized

An Introduction to the Mathematics of Money Saving and Investing Contents Preface .................................................................................................................... v 1 Simple Interest ............................................................................................. 1.1 The Simple Interest Theorem ........................................................... 1.2 Ambiguities When Interest Period is Measured in Days .................. 1.3 Problems............................................................................................ 2 Compound Interest ........................................................................................ 2.1 The Compound Interest Theorem ..................................................... 2.2 Time Diagrams and Cash Flows........................................................ 2.3 Internal Rate of Return .................................................................... 2.4 The Rule of 72 .................................................................................... 2.5 Problems............................................................................................ 3 Inflation and Taxes ........................................................................................ 3.1 Inflation........................................................................................... 3.2 Consumer Price Index (CPI)................................................................. 3.3 Personal Taxes................................................................................... 3.4 Problems............................................................................................ 4 Annuities ....................................................................................................... 4.1 An Ordinary Annuity ......................................................................... 4.2 An Annuity Due ................................................................................. 4.3 Perpetuities .................................................................................. 4.4 Problems............................................................................................ 1 1 8 10 13 13 23 26 36 37 45 45 48 50 51 55 55 66 70 71 5 Loans and Risks ............................................................................................... 75 5.1 Problems......................................................................................... 79 6 Amortization ................................................................................................ 6.1 Amortization Tables .......................................................................... 6.2 Periodic Payments............................................................................ 6.3 Linear Interpolation ................................................................... 6.4 Problems........................................................................................... 83 83 88 94 97 7 Credit Cards ......................................................................................................101 7.1 Credit Card Payments .................................................................... 101 7.2 Credit Card Numbers......................................................................108 7.3 Problems.......................................................................................... 110 8 Bonds ............................................................................................................. 113 8.1 Noncallable Bonds.......................................................................114 8.2 Duration .................................................................................. 126 8.3 Modified Duration............................................................................ 129 8.4 Convexity .......................................................................................... 137 8.5 Treasury Bills............................................................................ 139 8.6 Portfolio of Bonds ......................................................................... 141 8.7 Problems.......................................................................................... 144 9 Stocks and Stock Markets ........................................................................ 149 9.1 Buying and Selling Stock.......................................................... 151 9.2 Reading The Wall Street Journal Stock Tables ..............................160 9.3 Problems.......................................................................................... 161 10 Stock Market Indexes, Pricing, and Risk .............................................. 165 10.1 Stock Market Indexes ................................................................... 165 10.2 Rates of Return for Stocks and Stock Indexes ............................ 172 10.3 Pricing and Risk .......................................................................... 175 10.4 Portfolio of Stocks............................................................................186 10.5 Problems....................................................................................... 188 11 Options..................................................................................................... 191 11.1 Put and Call Options .................................................................. 192 11.2 Adjusting for Stock Splits and Dividends ................................... 196 11.3 Option Strategies......................................................................... 198 11.4 Put-Call Parity Theorem................................................................ 208 11.5 Hedging with Options.................................................................... 211 11.6 Modeling Stock Market Prices ....................................................... 215 11.7 Pricing of Options.......................................................................... 220 11.8 The Black-Scholes Option Pricing Model ..................................... 225 11.9 Problems....................................................................................... 238 A Appendix: Induction, Recurrence Relations, Inequalities .................... 245 A.1 Mathematical Induction................................................................. 245 A.2 Recurrence Relations ...................................................................... 247 A.3 Inequalities ...................................................................................... 249 A.4 Problems............................................................................................ 252 B Appendix: Statistics .................................................................................. 255 B.1 Set Theory ....................................................................................... 255 B.2 Probability ....................................................................................... 256 B.3 Random Variables .......................................................................... 256 B.4 Moments..........................................................................................271 B.5 Joint Distribution of Random Variables ........................................275 B.6 Linear Regression ............................................................................277 B.7 Estimates of Parameters of Random Variables .............................280 B.8 Problems..........................................................................................281 Answers ............................................................................................................... 283 References.......................................................................................................287 Index................................................................................................................................... 289