Description
Book SynopsisA 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 pro
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
