Missing picture

Understanding the Mathematics of Personal Finance

John Wiley, New Jersey, 2009

Table of Contents

Chapter Section Title Page
Prefaceix
List of Abbreviations iv
- - - - - - - - - -
1 Background Mathematics 1
1.1Arithmetic Notation and Formulas1
1.2Minus (Negative) Signs 5
1.3Lists and Subscripted Variables 6
1.4Changes 9
1.5Exponents 11
1.6Summations 12
1.7Graphs and Charts 13
1.8Approximations 18
1.9Rates - Average and Instantaneous 19
1.10Inequalities and Ranges of Numbers 22
Problems 23
- - - - - - - - - -
2 Compound Interest 26
2.1Some Mathematics 30
2.2My Website Spreadsheet 31
2.3OnLine Calculators 32
2.4Scaling 32
2.5Proration - Working Inside a Compounding Interval 33
2.6Initial Charges and Effective Interest Rate 34
2.7In the Limit - Continuous Compounding 35
Problems 37
- - - - - - - - - -
3 Loan Amortization and Savings 38
3.1 Loans 38
3.2Calculating the Payment Amount 44
3.3Paying Off a Loan Very Slowly 45
3.4My Website Spreadsheet 46
3.5A Note About Total Interest For a Year 47
3.6OnLine Calculators 48
3.7Loans With First Payment Due Immediately 48
3.8Irregular Payments 49
3.9Regular Savings 50
Problems 52
- - - - - - - - - -
4 Mortgages 54
4.1OnLine Calculators 55
4.2Fixed Rate Mortgages 55
4.3Adjustable Rate Mortgages (ARMSS) 56
4.4Balloon Loans 59
4.5Upfront Costs 59
Problems 60
- - - - - - - - - -
5 Prepayment Penalties 61
5.1Rule of 78 63
5.2Other Prepayment Penalties 66
Problems 68
- - - - - - - - - -
6 Credit Cards 70
6.1Credit Card Statements 70
6.2Transfers 73
6.3Payment Allocation 75
6.4Daily Balance 76
6.5Some Calculation Examples 76
6.6Grace Period 81
6.7Changing Interest Rates 81
6.8A Bankruptcy Spiral 81
6.9Minimum Payment 83
6.10Other Interest Calculation Approaches 83
6.11Debit Cards - Something Completely Different 83
Problems 84
- - - - - - - - - -
7 Present Value 86
7.1Online Calculators 88
7.2Doing It With My Spreadsheet 88
7.3The Effect of Interest Rates 90
7.4Why This All Matters 91
7.5A Very Involved Example: Writing Your OwnSpreadsheet 91
7.6Future Value 93
7.7Present Value of Prepayment Penalties 94
Problems 95
- - - - - - - - - -
8 Comparing Loans 96
8.1Up Front Costs 99
8.2Adjustable Rate Mortgages (ARMs) 100
8.3A Few Last Words 102
Problems 103
- - - - - - - - - -
9 Taxation and Inflation 105
9.1Understanding Personal Federal Income Tax Rates 105
9.2OnLine Tax Calculators 111
9.3Taxation of Earned Interest 111
9.4Deductable Interest 112
9.5Deferred Taxation Savings 112
9.6OnLine Deferred Taxation Plan Calculators 115
9.7Inflation 115
Problems 118
- - - - - - - - - -
10 Life Insurance 119
10.1What Is An Insurance Policy? 119
10.2Probability 120
10.3Introduction To The Life Tables 120
10.4Expected Value 128
10.5Term Insurance 130
10.6Time Payments 133
10.7Deceasing Term Insurance 134
10.8Insurance For The Rest Of Your Life 134
10.9Whole Life Insurance 136
10.10Breaking Down The Year 139
Problems 142
- - - - - - - - - -
11 Annuities 144
11.1A Benchmark Savings Plan 145
11.2Immediate Annuity With Period Certain 145
11.3Deferred Annuities 148
11.4Life Annuities 150
11.5Payments For Couples 153
11.6OnLine Calculators 156
11.7Variable Annuities 156
Problems 157
- - - - - - - - - -
12 Reverse Mortgages and Viatical Settlements 158
12.1Reverse Mortgages 158
12.2Viatical Settlements 162
Problems 163
- - - - - - - - - -
13 Investing: Risk Versus Reward 164
13.1Stocks 165
13.2Portfolios 167
13.3Calculators 171
13.4Dollar Cost Averaging 173
13.5Short Sales 174
13.6Stock Dividends 174
13.7Bonds 175
13.8Options 175
13.9OnLine Calculators and Listings 179
13.10Ponzi Schemes and Other Scams 180
Problems 185
References 186
- - - - - - - - - -
14 Gambling 187
14.1Probability and Odds 187
14.2Probability and Expected Return 188
14.3Pari-Mutuel Betting 193
Problems 197
- - - - - - - - - -
15 Spreadsheet Calculators 198
15.1Introduction to the Spreadsheets 198
15.2Some Programming Notes 202
- - - - - - - - - -
16 Solutions 207
16.1Chapter 1 207
16.2Chapter 2 210
16.3Chapter 3 213
16.4Chapter 4 215
16.5Chapter 5 216
16.6Chapter 6 218
16.7Chapter 7 220
16.8Chapter 8 221
16.9Chapter 9 223
16.10Chapter 10 226
16.11Chapter 11 229
16.12Chapter 12 233
16.13Chapter 13 234
16.14Chapter 14 237
- - - - - - - - - -
16 Index 240