Understanding the Mathematics of Personal Finance: An Introduction to Financial Literacy

✍ Scribed by Lawrence N. Dworsky

• Publisher: Wiley
• Year: 2009
• Tongue: English
• Leaves: 262
• Category: Library

✦ Synopsis

A user-friendly presentation of the essential concepts and tools for calculating real costs and profits in personal finance

Understanding the Mathematics of Personal Finance explains how mathematics, a simple calculator, and basic computer spreadsheets can be used to break down and understand even the most complex loan structures. In an easy-to-follow style, the book clearly explains the workings of basic financial calculations, captures the concepts behind loans and interest in a step-by-step manner, and details how these steps can be implemented for practical purposes. Rather than simply providing investment and borrowing strategies, the author successfully equips readers with the skills needed to make accurate and effective decisions in all aspects of personal finance ventures, including mortgages, annuities, life insurance, and credit card debt.

The book begins with a primer on mathematics, covering the basics of arithmetic operations and notations, and proceeds to explore the concepts of interest, simple interest, and compound interest. Subsequent chapters illustrate the application of these concepts to common types of personal finance exchanges, including:

• Loan amortization and savings

• Mortgages, reverse mortgages, and viatical settlements

• Prepayment penalties

• Credit cards

The book provides readers with the tools needed to calculate real costs and profits using various financial instruments. Mathematically inclined readers will enjoy the inclusion of mathematical derivations, but these sections are visually distinct from the text and can be skipped without the loss of content or complete understanding of the material. In addition, references to online calculators and instructions for building the calculations involved in a spreadsheet are provided. Furthermore, a related Web site features additional problem sets, the spreadsheet calculators that are referenced and used throughout the book, and links to various other financial calculators.

Understanding the Mathematics of Personal Finance is an excellent book for finance courses at the undergraduate level. It is also an essential reference for individuals who are interested in learning how to make effective financial decisions in their everyday lives.

✦ Table of Contents

Understanding the Mathematics of Personal Finance......Page 5
Contents......Page 9
Preface......Page 13
Acknowledgments......Page 17
List of Abbreviations......Page 19
1.1 Arithmetic, Notation, and Formulas......Page 21
1.2 Minus (Negative) Signs......Page 25
1.3 Lists and Subscripted Variables......Page 26
1.4 Changes......Page 29
1.5 Exponents......Page 31
1.6 Summations......Page 32
1.7 Graphs and Charts......Page 33
1.8 Approximations......Page 38
1.9 Rates—Average and Instantaneous......Page 39
1.10 Inequalities and Ranges of Numbers......Page 42
Problems......Page 43
2. Compound Interest......Page 46
2.1 Some Mathematics......Page 50
2.2 My Website Spreadsheet......Page 51
2.4 Scaling......Page 52
2.5 Proration—Working Inside a Compounding Interval......Page 53
2.6 Initial Charges and Effective Interest Rate......Page 54
2.7 In the Limit—Continuous Compounding......Page 55
Problems......Page 57
3.1 Loans......Page 58
3.2 Calculating the Payment Amount......Page 64
3.3 Paying off a Loan Very Slowly......Page 65
3.4 My Website Spreadsheet......Page 66
3.5 A Note About Total Interest for a Year......Page 67
3.7 Loans with First Payment Due Immediately......Page 68
3.8 Irregular Payments......Page 69
3.9 Regular Savings......Page 70
Problems......Page 72
4. Mortgages......Page 74
4.2 Fixed Rate Mortgages......Page 75
4.3 Adjustable Rate Mortgages (ARMs)......Page 77
4.5 Up-Front Costs......Page 79
Problems......Page 80
5. Prepayment Penalties......Page 81
5.1 Rule of 78......Page 83
5.2 Other Prepayment Penalties......Page 86
Problems......Page 88
6. Credit Cards......Page 89
6.1 Credit Card Statements......Page 90
6.2 Transfers......Page 93
6.3 Payment Allocation......Page 95
6.5 Some Calculation Examples......Page 96
6.8 A Bankruptcy Spiral......Page 101
6.11 Debit Cards—Something Completely Different......Page 103
Problems......Page 104
7. Present Value......Page 106
7.2 Doing It with My Spreadsheet......Page 108
7.3 The Effect of Interest Rates on Present Value Calculations......Page 110
7.5 A Very Involved Example: Writing Your Own Spreadsheet......Page 111
7.6 Future Value......Page 113
7.7 Present Value of Prepayment Penalties......Page 114
Problems......Page 115
8. Comparing Loans......Page 116
8.1 Up-Front Costs......Page 119
8.2 Adjustable Rate Mortgages (ARMs)......Page 120
8.3 A Few Last Words......Page 122
Problems......Page 123
9.1 Understanding Personal Federal Income Tax Rates......Page 125
9.3 Taxation of Earned Interest......Page 131
9.5 Deferred Taxation Savings......Page 132
9.7 Inflation......Page 135
Problems......Page 138
10.1 What Is an Insurance Policy?......Page 139
10.2 Probability......Page 140
10.3 Introduction to the Life Tables......Page 146
10.4 Expected Values......Page 148
10.5 Term Insurance......Page 150
10.6 Time Payments......Page 153
10.8 Insurance for the Rest of Your Life......Page 154
10.9 Whole Life Insurance......Page 156
10.10 Breaking Down the Year......Page 159
Problems......Page 162
11. Annuities......Page 164
11.2 Immediate Annuity with Period Certain......Page 165
11.3 Deferred Annuities......Page 168
11.4 Life Annuities......Page 170
11.5 Payments for Couples......Page 173
11.7 Variable Annuities......Page 176
Problems......Page 177
12.1 Reverse Mortgages......Page 178
12.2 Viatical Settlements......Page 182
Problems......Page 183
13. Investing: Risk versus Reward......Page 184
13.1 Stocks......Page 185
13.2 Portfolios......Page 187
13.3 Calculators......Page 191
13.4 Dollar Cost Averaging......Page 193
13.6 Stock Dividends......Page 194
13.8 Options......Page 195
13.9 Online Calculators and Listings......Page 199
13.10 Ponzi Schemes and Other Scams......Page 200
Problems......Page 205
Reference......Page 206
14.1 Probability and Odds......Page 207
14.2 Probability and Expected Return......Page 208
14.3 Pari-Mutuel Betting......Page 213
Problems......Page 217
15.1 Introduction to the Spreadsheets......Page 218
15.2 Some Programming Notes......Page 225
16.1 Chapter 1......Page 227
16.2 Chapter 2......Page 230
16.3 Chapter 3......Page 233
16.4 Chapter 4......Page 235
16.5 Chapter 5......Page 236
16.6 Chapter 6......Page 238
16.7 Chapter 7......Page 240
16.8 Chapter 8......Page 241
16.9 Chapter 9......Page 243
16.10 Chapter 10......Page 246
16.11 Chapter 11......Page 249
16.12 Chapter 12......Page 253
16.13 Chapter 13......Page 254
16.14 Chapter 14......Page 257
Index......Page 260

✦ Subjects

Финансово-экономические дисциплины;Финансовая математика;