Understanding the Mathematics of Personal Finance An Introduction to Financial Literacy

by Dworsky, Lawrence N.

• ISBN13: 9780470497807
• ISBN10: 0470497807
• Edition: 1st
• Format: Paperback
• Copyright: 2009-10-05
• Publisher: Wiley

Summary

This book explains how the calculations of various financial instruments work and also reviews various analysis tools (primarily the computer spreadsheet) to prepare readers to tackle new situations for effective and accurate decision making. This author details how even the most involved loan scenarios can be understood just by repeated application of the fundamental concept of compound interest, which is discussed early on in the book. Additional topical coverage includes loan amortization and amortization tables; mortgages (cost of points and up-front fees); prepayment penalties; credit card interest calculations; loan comparisons; life insurance; fixed and variable annuities; and the basics of investing. Essentially, everything involved with loans can be calculated using both a simple financial calculator and a computer spreadsheet program. While this book does not provide investment or borrowing strategies or tips for retirement planning, it does provide the tools needed to be able to calculate the real costs and/or profits involved in using these various financial instruments and allows readers to see for themselves what the "best deals" are. Performing the necessary calculations needed to understand a complex many year, many payment, loan structure can be very difficult - if it has to be done by hand. Fortunately, living in the era of inexpensive integrated circuit electronics changes everything. Pocket calculators are inexpensive and amazingly capable, and the author has chosen the Texas Instruments BA II Plus to describe how to perform the calculations discussed throughout the book. Other calculators are similar enough that it should not prove difficult for readers to translate the step-by-step instructions for use on other models. Similarly, there are many computer spreadsheet programs available, and the author utilizes the Microsoft Works spreadsheet; however, its operation is generic enough that the spreadsheets developed in the book can be set up almost identically using other spreadsheet programs.

Author Biography

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.

Table of Contents

Preface	p. xi
Acknowledgments	p. xv
List of Abbreviations	p. xvii
Background Mathematics	p. 1
Arithmetic, Notation, and Formulas	p. 1
Minus (Negative) Signs	p. 5
Lists and Subscripted Variables	p. 6
Changes	p. 9
Exponents	p. 11
Summations	p. 12
Graphs and Charts	p. 13
Approximations	p. 18
Rates-Average and Instantaneous	p. 19
Inequalities and Ranges of Numbers	p. 22
Problems	p. 23
Compound Interest	p. 26
Some Mathematics	p. 30
My Website Spreadsheet	p. 31
Online Calculators	p. 32
Scaling	p. 32
Proration-Working Inside a Compounding Interval	p. 33
Initial Charges and Effective Interest Rate	p. 34
In the Limit-Continuous Compounding	p. 35
Problems	p. 37
Loan Amortization and Savings	p. 38
Loans	p. 38
Calculating the Payment Amount	p. 44
Paying off a Loan Very Slowly	p. 45
My Website Spreadsheet	p. 46
A Note About Total Interest for a Year	p. 47
Online Calculators	p. 48
Loans with First Payment Due Immediately	p. 48
Irregular Payments	p. 49
Regular Savings	p. 50
Problems	p. 52
Mortgages	p. 54
Online Calculators	p. 55
Fixed Rate Mortgages	p. 55
Adjustable Rate Mortgages (ARMs)	p. 57
Balloon Loans	p. 59
Up-Front Costs	p. 59
Problems	p. 60
Prepayment Penalties	p. 61
Rule of 78	p. 63
Other Prepayment Penalties	p. 66
Problems	p. 68
Credit Cards	p. 69
Credit Card Statements	p. 70
Transfers	p. 73
Payment Allocation	p. 75
Daily Balance	p. 76
Some Calculation Examples	p. 76
Grace Period	p. 81
Changing Interest Rates	p. 81
A Bankruptcy Spiral	p. 81
Minimum Payment	p. 83
Other Interest Calculation Approaches	p. 83
Debit Cards-Something Completely Different	p. 83
Problems	p. 84
Present Value	p. 86
Online Calculators	p. 88
Doing It with My Spreadsheet	p. 88
The Effect of Interest Rates on Present Value Calculations	p. 90
Why This All Matters	p. 91
A Very Involved Example: Writing Your Own Spreadsheet	p. 91
Future Value	p. 93
Present Value of Prepayment Penalties	p. 94
Problems	p. 95
Comparing Loans	p. 96
Up-Front Costs	p. 99
Adjustable Rate Mortgages (ARMs)	p. 100
A Few Last Words	p. 102
Problems	p. 103
Taxation and Inflation	p. 105
Understanding Personal Federal Income Tax Rates	p. 105
Online Tax Calculators	p. 111
Taxation of Earned Interest	p. 111
Deductible Interest	p. 112
Deferred Taxation Savings	p. 112
Online Deferred Taxation Plan Calculators	p. 115
Inflation	p. 115
Problems	p. 118
Life Insurance	p. 119
What Is an Insurance Policy?	p. 119
Probability	p. 120
Introduction to the Life Tables	p. 126
Expected Values	p. 128
Term Insurance	p. 130
Time Payments	p. 133
Decreasing Term Insurance	p. 134
Insurance for the Rest of Your Life	p. 134
Whole Life Insurance	p. 136
Breaking Down the Year	p. 139
Problems	p. 142
Annuities	p. 144
A Benchmark Savings Plan	p. 145
Immediate Annuity with Period Certain	p. 145
Deferred Annuities	p. 148
Life Annuities	p. 150
Payments for Couples	p. 153
Online Calculators	p. 156
Variable Annuities	p. 156
Problems	p. 157
Reverse Mortgages and Viatical Settlements	p. 158
Reverse Mortgages	p. 158
Viatical Settlements	p. 162
Problems	p. 163
Investing: Risk versus Reward	p. 164
Stocks	p. 165
Portfolios	p. 167
Calculators	p. 171
Dollar Cost Averaging	p. 173
Short Sales	p. 174
Stock Dividends	p. 174
Bonds	p. 175
Options	p. 175
Online Calculators and Listings	p. 179
Ponzi Schemes and Other Scams	p. 180
Problems	p. 185
Reference	p. 186
Gambling	p. 187
Probability and Odds	p. 187
Probability and Expected Return	p. 188
Pari-Mutuel Betting	p. 193
Problems	p. 197
Spreadsheet Calculators
Introduction to the Spreadsheets	p. 198
Some Programming Notes	p. 205
Solutions	p. 207
Chapter 1	p. 207
Chapter 2	p. 210
Chapter 3	p. 213
Chapter 4	p. 215
Chapter 5	p. 216
Chapter 6	p. 218
Chapter 7	p. 220
Chapter 8	p. 221
Chapter 9	p. 223
Chapter 10	p. 226
Chapter 11	p. 229
Chapter 12	p. 233
Chapter 13	p. 234
Chapter 14	p. 237
Index	p. 240
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