Understanding the Mathematics of Personal Finance von Lawrence N Dworsky

<b>A user-friendly presentation of the essential concepts and tools for calculating real costs and profits in personal finance</b><p><i>Understanding the Mathematics of Personal Finance</i> 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.</p><p>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:</p><ul><li><p>Loan amortization and savings</p></li><li><p>Mortgages, reverse mortgages, and viatical settlements</p></li><li><p>Prepayment penalties</p></li><li><p>Credit cards</p></li></ul><p>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.</p><p><i>Understanding the Mathematics of Personal Finance</i> 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.</p>

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 ofProbably Not: Future Prediction Using Probability and Statistical Inference, also published by Wiley.

Preface xiAcknowledgments xvList of Abbreviations xvii1. Background Mathematics 11.1 Arithmetic, Notation, and Formulas 11.2 Minus (Negative) Signs 51.3 Lists and Subscripted Variables 61.4 Changes 91.5 Exponents 111.6 Summations 121.7 Graphs and Charts 131.8 Approximations 181.9 RatesAverage and Instantaneous 191.10 Inequalities and Ranges of Numbers 22Problems 232. Compound Interest 262.1 Some Mathematics 302.2 My Website Spreadsheet 312.3 Online Calculators 322.4 Scaling 322.5 ProrationWorking Inside a Compounding Interval 332.6 Initial Charges and Effective Interest Rate 342.7 In the LimitContinuous Compounding 35Problems 373. Loan Amortization and Savings 383.1 Loans 383.2 Calculating the Payment Amount 443.3 Paying off a Loan Very Slowly 453.4 My Website Spreadsheet 463.5 A Note About Total Interest for a Year 473.6 Online Calculators 483.7 Loans with First Payment Due Immediately 483.8 Irregular Payments 493.9 Regular Savings 50Problems 524. Mortgages 544.1 Online Calculators 554.2 Fixed Rate Mortgages 554.3 Adjustable Rate Mortgages (ARMs) 574.4 Balloon Loans 594.5 Up-Front Costs 59Problems 605. Prepayment Penalties 615.1 Rule of 78 635.2 Other Prepayment Penalties 66Problems 686. Credit Cards 696.1 Credit Card Statements 706.2 Transfers 736.3 Payment Allocation 756.4 Daily Balance 766.5 Some Calculation Examples 766.6 Grace Period 816.7 Changing Interest Rates 816.8 A Bankruptcy Spiral 816.9 Minimum Payment 836.10 Other Interest Calculation Approaches 836.11 Debit CardsSomething Completely Different 83Problems 847. Present Value 867.1 Online Calculators 887.2 Doing It with My Spreadsheet 887.3 The Effect of Interest Rates on Present Value Calculations 907.4 Why This All Matters 917.5 A Very Involved Example: Writing Your Own Spreadsheet 917.6 Future Value 937.7 Present Value of Prepayment Penalties 94Problems 958. Comparing Loans 968.1 Up-Front Costs 998.2 Adjustable Rate Mortgages (ARMs) 1008.3 A Few Last Words 102Problems 1039. Taxation and Inflation 1059.1 Understanding Personal Federal Income Tax Rates 1059.2 Online Tax Calculators 1119.3 Taxation of Earned Interest 1119.4 Deductible Interest 1129.5 Deferred Taxation Savings 1129.6 Online Deferred Taxation Plan Calculators 1159.7 Inflation 115Problems 11810. Life Insurance 11910.1 What Is an Insurance Policy? 11910.2 Probability 12010.3 Introduction to the Life Tables 12610.4 Expected Values 12810.5 Term Insurance 13010.6 Time Payments 13310.7 Decreasing Term Insurance 13410.8 Insurance for the Rest of Your Life 13410.9 Whole Life Insurance 13610.10 Breaking Down the Year 139Problems 14211. Annuities 14411.1 A Benchmark Savings Plan 14511.2 Immediate Annuity with Period Certain 14511.3 Deferred Annuities 14811.4 Life Annuities 15011.5 Payments for Couples 15311.6 Online Calculators 15611.7 Variable Annuities 156Problems 15712. Reverse Mortgages and Viatical Settlements 15812.1 Reverse Mortgages 15812.2 Viatical Settlements 162Problems 16313. Investing: Risk versus Reward 16413.1 Stocks 16513.2 Portfolios 16713.3 Calculators 17113.4 Dollar Cost Averaging 17313.5 Short Sales 17413.6 Stock Dividends 17413.7 Bonds 17513.8 Options 17513.9 Online Calculators and Listings 17913.10 Ponzi Schemes and Other Scams 180Problems 185Reference 18614 Gambling 18714.1 Probability and Odds 18714.2 Probability and Expected Return 18814.3 Pari-Mutuel Betting 193Problems 19715 Spreadsheet Calculators 19815.1 Introduction to the Spreadsheets 19815.2 Some Programming Notes 20516 Solutions 20716.1 Chapter 1 20716.2 Chapter 2 21016.3 Chapter 3 21316.4 Chapter 4 21516.5 Chapter 5 21616.6 Chapter 6 21816.7 Chapter 7 22016.8 Chapter 8 22116.9 Chapter 9 22316.10 Chapter 10 22616.11 Chapter 11 22916.12 Chapter 12 23316.13 Chapter 13 23416.14 Chapter 14 237Index 240

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