## An Introduction to the Mathematics of Money: Saving and InvestingIntroduction Some people distinguish between savings and investments, where savings are monies placed in relatively risk-free accounts with modest rewards, and where investments involve more risk and the potential for greater rewards. In this book we do not distinguish between these ideas. We treat them both under the umbrella of investing. In general, income falls into two categories: earned income—which is the income derived from your everyday job—andunearnedincome—which is income derived from investing. You attend college to strengthen your prospects for earned income, so why do you need to worry about unearned income, namely, investment income? There are many reasons to invest and to learn about investing. Perhaps the primary one is to take charge of your own ?nancial future. You need money for short-term goals (such as living expenses, emergencies) and for long-term goals (such as buying a car, buying a house, educating children, paying catastrophic medical bills, funding retirement). Investing involvesborrowingandlending,andbuyingandselling. • borrowing and lending. When you put money into a bank savings account,youarelendingyourmoneyandthebankisborrowingit.Youcan lend money to a bank, a business, a government, or a person. In exchange forthis,theborrowerpromisestopayyouinterestandtoreturnyourinitial investment at a future date. Why would the borrower do this? Because the borrower anticipates using this money in a way that earns more than the interest promised to you. Examples of borrowing and lending are savings accounts, certi?cates of deposits, money-market accounts, and bonds. |

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### Contents

Simple Interest | 1 |

12 Ambiguities When Interest Period is Measured in Days | 8 |

13 Problems | 10 |

Compound Interest | 13 |

22 Time Diagrams and Cash Flows | 23 |

23 Internal Rate of Return | 26 |

24 The Rule of 72 | 36 |

25 Problems | 37 |

91 Buying and Selling Stock | 151 |

92 Reading The Wall Street Journal Stock Tables | 160 |

93 Problems | 161 |

Stock Market Indexes Pricing and Risk | 165 |

102 Rates of Return for Stocks and Stock Indexes | 172 |

103 Pricing and Risk | 175 |

104 Portfolio of Stocks | 186 |

105 Problems | 188 |

Inﬂation and Taxes | 44 |

32 Consumer Price Index CPI | 48 |

33 Personal Taxes | 50 |

34 Problems | 51 |

Annuities | 55 |

42 An Annuity Due | 66 |

43 Perpetuities | 70 |

44 Problems | 71 |

Loans and Risks | 74 |

51 Problems | 79 |

Amortization | 83 |

62 Periodic Payments | 88 |

63 Linear Interpolation | 94 |

64 Problems | 97 |

Credit Cards | 101 |

72 Credit Card Numbers | 108 |

73 Problems | 110 |

Bonds | 113 |

81 Noncallable Bonds | 114 |

82 Duration | 126 |

83 Modified Duration | 129 |

84 Convexity | 137 |

85 Treasury Bills | 139 |

86 Portfolio of Bonds | 141 |

87 Problems | 144 |

Stocks and Stock Markets | 148 |

Options | 191 |

111 Put and Call Options | 192 |

112 Adjusting for Stock Splits and Dividends | 196 |

113 Option Strategies | 198 |

114 PutCall Parity Theorem | 208 |

115 Hedging with Options | 211 |

116 Modeling Stock Market Prices | 215 |

117 Pricing of Options | 220 |

118 The BlackScholes Option Pricing Model | 225 |

119 Problems Walking | 238 |

Appendix Induction Recurrence Relations Inequalities | 245 |

A2 Recurrence Relations | 247 |

A3 Inequalities | 249 |

A4 Problems | 252 |

Appendix Statistics | 254 |

B2 Probability | 256 |

B4 Moments | 271 |

B5 Joint Distribution of Random Variables | 275 |

B6 Linear Regression | 277 |

B7 Estimates of Parameters of Random Variables | 280 |

B8 Problems | 281 |

Answers | 283 |

287 | |

289 | |

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