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Home > Health, Relationships and Personal development > Self-help, personal development and practical advice > Personal finance > Understanding the Mathematics of Personal Finance: An Introduction to Financial Literacy
Understanding the Mathematics of Personal Finance: An Introduction to Financial Literacy

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


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About the Book

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:
Preface xi Acknowledgments xv List of Abbreviations xvii 1. Background Mathematics 1 1.1 Arithmetic, Notation, and Formulas 1 1.2 Minus (Negative) Signs 5 1.3 Lists and Subscripted Variables 6 1.4 Changes 9 1.5 Exponents 11 1.6 Summations 12 1.7 Graphs and Charts 13 1.8 Approximations 18 1.9 Rates—Average and Instantaneous 19 1.10 Inequalities and Ranges of Numbers 22 Problems 23 2. Compound Interest 26 2.1 Some Mathematics 30 2.2 My Website Spreadsheet 31 2.3 Online Calculators 32 2.4 Scaling 32 2.5 Proration—Working Inside a Compounding Interval 33 2.6 Initial Charges and Effective Interest Rate 34 2.7 In the Limit—Continuous Compounding 35 Problems 37 3. Loan Amortization and Savings 38 3.1 Loans 38 3.2 Calculating the Payment Amount 44 3.3 Paying off a Loan Very Slowly 45 3.4 My Website Spreadsheet 46 3.5 A Note About Total Interest for a Year 47 3.6 Online Calculators 48 3.7 Loans with First Payment Due Immediately 48 3.8 Irregular Payments 49 3.9 Regular Savings 50 Problems 52 4. Mortgages 54 4.1 Online Calculators 55 4.2 Fixed Rate Mortgages 55 4.3 Adjustable Rate Mortgages (ARMs) 57 4.4 Balloon Loans 59 4.5 Up-Front Costs 59 Problems 60 5. Prepayment Penalties 61 5.1 Rule of 78 63 5.2 Other Prepayment Penalties 66 Problems 68 6. Credit Cards 69 6.1 Credit Card Statements 70 6.2 Transfers 73 6.3 Payment Allocation 75 6.4 Daily Balance 76 6.5 Some Calculation Examples 76 6.6 Grace Period 81 6.7 Changing Interest Rates 81 6.8 A Bankruptcy Spiral 81 6.9 Minimum Payment 83 6.10 Other Interest Calculation Approaches 83 6.11 Debit Cards—Something Completely Different 83 Problems 84 7. Present Value 86 7.1 Online Calculators 88 7.2 Doing It with My Spreadsheet 88 7.3 The Effect of Interest Rates on Present Value Calculations 90 7.4 Why This All Matters 91 7.5 A Very Involved Example: Writing Your Own Spreadsheet 91 7.6 Future Value 93 7.7 Present Value of Prepayment Penalties 94 Problems 95 8. Comparing Loans 96 8.1 Up-Front Costs 99 8.2 Adjustable Rate Mortgages (ARMs) 100 8.3 A Few Last Words 102 Problems 103 9. Taxation and Inflation 105 9.1 Understanding Personal Federal Income Tax Rates 105 9.2 Online Tax Calculators 111 9.3 Taxation of Earned Interest 111 9.4 Deductible Interest 112 9.5 Deferred Taxation Savings 112 9.6 Online Deferred Taxation Plan Calculators 115 9.7 Inflation 115 Problems 118 10. Life Insurance 119 10.1 What Is an Insurance Policy? 119 10.2 Probability 120 10.3 Introduction to the Life Tables 126 10.4 Expected Values 128 10.5 Term Insurance 130 10.6 Time Payments 133 10.7 Decreasing Term Insurance 134 10.8 Insurance for the Rest of Your Life 134 10.9 Whole Life Insurance 136 10.10 Breaking Down the Year 139 Problems 142 11. Annuities 144 11.1 A Benchmark Savings Plan 145 11.2 Immediate Annuity with Period Certain 145 11.3 Deferred Annuities 148 11.4 Life Annuities 150 11.5 Payments for Couples 153 11.6 Online Calculators 156 11.7 Variable Annuities 156 Problems 157 12. Reverse Mortgages and Viatical Settlements 158 12.1 Reverse Mortgages 158 12.2 Viatical Settlements 162 Problems 163 13. Investing: Risk versus Reward 164 13.1 Stocks 165 13.2 Portfolios 167 13.3 Calculators 171 13.4 Dollar Cost Averaging 173 13.5 Short Sales 174 13.6 Stock Dividends 174 13.7 Bonds 175 13.8 Options 175 13.9 Online Calculators and Listings 179 13.10 Ponzi Schemes and Other Scams 180 Problems 185 Reference 186 14 Gambling 187 14.1 Probability and Odds 187 14.2 Probability and Expected Return 188 14.3 Pari-Mutuel Betting 193 Problems 197 15 Spreadsheet Calculators 198 15.1 Introduction to the Spreadsheets 198 15.2 Some Programming Notes 205 16 Solutions 207 16.1 Chapter 1 207 16.2 Chapter 2 210 16.3 Chapter 3 213 16.4 Chapter 4 215 16.5 Chapter 5 216 16.6 Chapter 6 218 16.7 Chapter 7 220 16.8 Chapter 8 221 16.9 Chapter 9 223 16.10 Chapter 10 226 16.11 Chapter 11 229 16.12 Chapter 12 233 16.13 Chapter 13 234 16.14 Chapter 14 237 Index 240

About the Author :
LAWRENCE N. DWORSKY, PhD, has previously served as a consultant for the Defense Advanced Research Projects Agency (DARPA), Littelfuse Corporation, HRL Laboratories, and Motorola, Inc., where he was a member of the Motorola Science Advisory Board. A Fellow of the Institute of Electrical and Electronic Engineers, Dr. Dworsky has written numerous journal articles and is the author of Probably Not: Future Prediction Using Probability and Statistical Inference, also published by Wiley.


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Product Details
  • ISBN-13: 9780470497807
  • Publisher: John Wiley & Sons Inc
  • Publisher Imprint: John Wiley & Sons Inc
  • Height: 237 mm
  • No of Pages: 264
  • Returnable: N
  • Sub Title: An Introduction to Financial Literacy
  • Width: 159 mm
  • ISBN-10: 0470497807
  • Publisher Date: 23 Oct 2009
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Spine Width: 12 mm
  • Weight: 466 gr


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