An Introduction to the Mathematics of Money: Saving and Investing

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Springer Science & Business Media, Apr 5, 2007 - Mathematics - 300 pages
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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.
 

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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
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
References
287
Index
289
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