## 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 |

Compound Interest | 13 |

Inﬂation and Taxes 45 | 44 |

Annuities | 55 |

Loans and Risks 75 | 74 |

Amortization | 83 |

Credit Cards | 101 |

Bonds | 113 |

Inequalities | 249 |

Problems | 252 |

Statistics 255 | 254 |

Probability | 256 |

Moments | 271 |

JointDistributionofRandomVariables | 275 |

Linear Regression | 277 |

EstimatesofParametersofRandomVariables | 280 |

Stocks and Stock Markets 149 | 148 |

Stock Market Indexes Pricing and Risk | 165 |

Options | 191 |

Induction Recurrence Relations Inequalities | 245 |

RecurrenceRelations | 247 |

Problems | 281 |

Answers | 283 |

287 | |

289 | |

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amount annual annual interest rate annuity approximately asked assume average balance binomial bond borrow calculate call option cash cash ﬂows closes compounded computed consider constant continuously cost credit card decrease deposit diagram diﬀerent distribution dividends duration earn equal equation equity estimate example exercise price expected expiration expressed ﬁnd ﬁrst formula function future value geometric given gives increase induction inequality inﬂation initial interest investment investor Kendrick less loan maintenance maturity mean measure method month monthly namely NASDAQ nominal Note Notice paid payment period portfolio positive present value principal probability Problem proﬁt proof prove purchase random variable rate of return receive relations remaining result risk savings sell share short Show simple Solution standard stock price Suppose Table Theorem true variance yield zero