An Introduction to the Mathematics of Money: Saving and Investing

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Springer Science & Business Media, Oct 24, 2006 - 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
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
References
287
Index
289
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