An Introduction to the Mathematics of Money

1. Front Matter

   Pages i-xi

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2. Simple Interest

   Pages 1-11

3. Compound Interest

   Pages 13-43

4. Infiation and Taxes

   Pages 45-53

5. Annuities

   Pages 55-73

6. Loans and Risks

   Pages 75-81

7. Amortization

   Pages 83-100

8. Credit Cards

   Pages 101-112

9. Bonds

   Pages 113-147

10. Stocks and Stock Markets

    Pages 149-163

11. Stock Market Indexes, Pricing, and Risk

    Pages 165-190

12. Options

    Pages 191-244

13. Back Matter

    Pages 245-294

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Introduction 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.

• Arithmetic
• Calculation
• banking
• economics
• finance
• inflation
• mathematics
• pricing
• proof
• statistics
• stock market
• quantitative finance

From the reviews:

"This book is written for students without assuming a background or any experience in investing. A basic knowledge in real analysis is necessary. The student is introduced to elements of saving and investing that are of lifelong practical use. These includes saving, checking accounts, certificates of deposit, student loan, credit cards, mortgages, buying and selling bonds of stocks. The authors follow a systematic pattern with a variety of examples and exercises. … suitable for fundamental courses in mathematics, investing, banking, financial engineering, and related topics." (Klaus Ehemann, Zentralblatt MATH, Vol. 1114 (16), 2007)

"This book is designed to serve as an undergraduate text on the fundamentals of personal savings and investing. … The book includes an appendix that covers basic concepts and techniques in probability and mathematical statistics. … follows a different philosophy; it allows the results and examples to speak for themselves. … it serves as a valuable resource for attaining savings, investment, and retirement goals." (Joseph Cavanaugh, The American Statistician, Vol. 62 (2), May, 2008)

• Department of Mathematics, University of Arizona, Tucson, USA

  David Lovelock, Marilou Mendel, A. Larry Wright

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