## 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

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 |

Joint Distribution of Random Variables | 275 |

Linear Regression | 277 |

Estimates of Parameters of Random Variables | 280 |

Stocks and Stock Markets 149 | 148 |

Stock Market Indexes Pricing and Risk | 165 |

Options | 191 |

Induction Recurrence Relations Inequalities | 245 |

Recurrence Relations | 247 |

Problems | 281 |

Answers | 283 |

287 | |

289 | |

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amortization amount annual interest rate assume Black-Scholes formula borrow calculate call option cash flows compounded annually computed concave coupon payment coupon rate credit card decimal decrease deposit diagram digits dividends DJIA dollar cost averaging earn equation estimate example exercise price expiration face value function future value geometric gives Hugh Kendrick ieff iinf iirr increase inequality inflation initial interest periods investment investor loan Luhn algorithm market value mathematical induction modified duration month monthly payment nominal rate noncallable bond number of days number of shares ordinary annuity paid payment period portfolio present value price per share principal Problem Profit per share purchase put option Put-Call Parity rate of return recurrence relations repay risk Rule of 72 sell short selling Show simple interest Solution spreadsheet stock price stock split Table Value Line variance Year’s yield to maturity zero zero coupon bond