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

ISBN: 978-0-470-49780-7
264 pages
October 2009
Understanding the Mathematics of Personal Finance: An Introduction to Financial Literacy  (0470497807) cover image
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.

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Preface.

Acknowledgments.

List of Abbreviations.

1. Background Mathematics.

1.1 Arithmetic, Notation, and Formulas.

1.2 Minus (Negative) Signs.

1.3 Lists and Subscripted Variables.

1.4 Changes.

1.5 Exponents.

1.6 Summations.

1.7 Graphs and Charts.

1.8 Approximations.

1.9 Rates—Average and Instantaneous.

1.10 Inequalities and Ranges of Numbers.

Problems.

2. Compound Interest.

2.1 Some Mathematics.

2.2 My Website Spreadsheet.

2.3 Online Calculators.

2.4 Scaling.

2.5 Proration—Working Inside a Compounding Interval.

2.6 Initial Charges and Effective Interest Rate.

2.7 In the Limit—Continuous Compounding.

Problems.

3. Loan Amortization and Savings.

3.1 Loans.

3.2 Calculating the Payment Amount.

3.3 Paying off a Loan Very Slowly.

3.4 My Website Spreadsheet.

3.5 A Note About Total Interest for a Year.

3.6 Online Calculators.

3.7 Loans with First Payment Due Immediately.

3.8 Irregular Payments.

3.9 Regular Savings.

Problems.

4. Mortgages.

4.1 Online Calculators.

4.2 Fixed Rate Mortgages.

4.3 Adjustable Rate Mortgages (ARMs).

4.4 Balloon Loans.

4.5 Up-Front Costs.

Problems.

5. Prepayment Penalties.

5.1 Rule of 78.

5.2 Other Prepayment Penalties.

Problems.

6. Credit Cards.

6.1 Credit Card Statements.

6.2 Transfers.

6.3 Payment Allocation.

6.4 Daily Balance.

6.5 Some Calculation Examples.

6.6 Grace Period.

6.7 Changing Interest Rates.

6.8 A Bankruptcy Spiral.

6.9 Minimum Payment.

6.10 Other Interest Calculation Approaches.

6.11 Debit Cards—Something Completely Different.

Problems.

7. Present Value.

7.1 Online Calculators.

7.2 Doing It with My Spreadsheet.

7.3 The Effect of Interest Rates on Present Value Calculations.

7.4 Why This All Matters.

7.5 A Very Involved Example: Writing Your Own Spreadsheet.

7.6 Future Value.

7.7 Present Value of Prepayment Penalties.

Problems.

8. Comparing Loans.

8.1 Up-Front Costs.

8.2 Adjustable Rate Mortgages (ARMs).

8.3 A Few Last Words.

Problems.

9. Taxation and Inflation.

9.1 Understanding Personal Federal Income Tax Rates.

9.2 Online Tax Calculators.

9.3 Taxation of Earned Interest.

9.4 Deductible Interest.

9.5 Deferred Taxation Savings.

9.6 Online Deferred Taxation Plan Calculators.

9.7 Inflation.

Problems.

10. Life Insurance.

10.1 What Is an Insurance Policy?

10.2 Probability.

10.3 Introduction to the Life Tables.

10.4 Expected Values.

10.5 Term Insurance.

10.6 Time Payments.

10.7 Decreasing Term Insurance.

10.8 Insurance for the Rest of Your Life.

10.9 Whole Life Insurance.

10.10 Breaking Down the Year.

Problems.

11. Annuities.

11.1 A Benchmark Savings Plan.

11.2 Immediate Annuity with Period Certain.

11.3 Deferred Annuities.

11.4 Life Annuities.

11.5 Payments for Couples.

11.6 Online Calculators.

11.7 Variable Annuities.

Problems.

12. Reverse Mortgages and Viatical Settlements.

12.1 Reverse Mortgages.

12.2 Viatical Settlements.

Problems.

13. Investing: Risk versus Reward.

13.1 Stocks.

13.2 Portfolios.

13.3 Calculators.

13.4 Dollar Cost Averaging.

13.5 Short Sales.

13.6 Stock Dividends.

13.7 Bonds.

13.8 Options.

13.9 Online Calculators and Listings.

13.10 Ponzi Schemes and Other Scams.

Problems.

Reference.

14 Gambling.

14.1 Probability and Odds.

14.2 Probability and Expected Return.

14.3 Pari-Mutuel Betting.

Problems.

15 Spreadsheet Calculators.

15.1 Introduction to the Spreadsheets.

15.2 Some Programming Notes.

16 Solutions.

16.1 Chapter 1.

16.2 Chapter 2.

16.3 Chapter 3.

16.4 Chapter 4.

16.5 Chapter 5.

16.6 Chapter 6.

16.7 Chapter 7.

16.8 Chapter 8.

16.9 Chapter 9.

16.10 Chapter 10.

16.11 Chapter 11.

16.12 Chapter 12.

16.13 Chapter 13.

16.14 Chapter 14.

Index.

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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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