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

<p>Preface xi</p>
<p>Acknowledgments xv</p>
<p>List of Abbreviations xvii</p>
<p>1. Background Mathematics 1</p>
<p>1.1 Arithmetic, Notation, and Formulas 1</p>
<p>1.2 Minus (Negative) Signs 5</p>
<p>1.3 Lists and Subscripted Variables 6</p>
<p>1.4 Changes 9</p>
<p>1.5 Exponents 11</p>
<p>1.6 Summations 12</p>
<p>1.7 Graphs and Charts 13</p>
<p>1.8 Approximations 18</p>
<p>1.9 Rates Average and Instantaneous 19</p>
<p>1.10 Inequalities and Ranges of Numbers 22</p>
<p>Problems 23</p>
<p>2. Compound Interest 26</p>
<p>2.1 Some Mathematics 30</p>
<p>2.2 My Website Spreadsheet 31</p>
<p>2.3 Online Calculators 32</p>
<p>2.4 Scaling 32</p>
<p>2.5 Proration Working Inside a Compounding Interval 33</p>
<p>2.6 Initial Charges and Effective Interest Rate 34</p>
<p>2.7 In the Limit Continuous Compounding 35</p>
<p>Problems 37</p>
<p>3. Loan Amortization and Savings 38</p>
<p>3.1 Loans 38</p>
<p>3.2 Calculating the Payment Amount 44</p>
<p>3.3 Paying off a Loan Very Slowly 45</p>
<p>3.4 My Website Spreadsheet 46</p>
<p>3.5 A Note About Total Interest for a Year 47</p>
<p>3.6 Online Calculators 48</p>
<p>3.7 Loans with First Payment Due Immediately 48</p>
<p>3.8 Irregular Payments 49</p>
<p>3.9 Regular Savings 50</p>
<p>Problems 52</p>
<p>4. Mortgages 54</p>
<p>4.1 Online Calculators 55</p>
<p>4.2 Fixed Rate Mortgages 55</p>
<p>4.3 Adjustable Rate Mortgages (ARMs) 57</p>
<p>4.4 Balloon Loans 59</p>
<p>4.5 Up–Front Costs 59</p>
<p>Problems 60</p>
<p>5. Prepayment Penalties 61</p>
<p>5.1 Rule of 78 63</p>
<p>5.2 Other Prepayment Penalties 66</p>
<p>Problems 68</p>
<p>6. Credit Cards 69</p>
<p>6.1 Credit Card Statements 70</p>
<p>6.2 Transfers 73</p>
<p>6.3 Payment Allocation 75</p>
<p>6.4 Daily Balance 76</p>
<p>6.5 Some Calculation Examples 76</p>
<p>6.6 Grace Period 81</p>
<p>6.7 Changing Interest Rates 81</p>
<p>6.8 A Bankruptcy Spiral 81</p>
<p>6.9 Minimum Payment 83</p>
<p>6.10 Other Interest Calculation Approaches 83</p>
<p>6.11 Debit Cards Something Completely Different 83</p>
<p>Problems 84</p>
<p>7. Present Value 86</p>
<p>7.1 Online Calculators 88</p>
<p>7.2 Doing It with My Spreadsheet 88</p>
<p>7.3 The Effect of Interest Rates on Present Value Calculations 90</p>
<p>7.4 Why This All Matters 91</p>
<p>7.5 A Very Involved Example: Writing Your Own Spreadsheet 91</p>
<p>7.6 Future Value 93</p>
<p>7.7 Present Value of Prepayment Penalties 94</p>
<p>Problems 95</p>
<p>8. Comparing Loans 96</p>
<p>8.1 Up–Front Costs 99</p>
<p>8.2 Adjustable Rate Mortgages (ARMs) 100</p>
<p>8.3 A Few Last Words 102</p>
<p>Problems 103</p>
<p>9. Taxation and Inflation 105</p>
<p>9.1 Understanding Personal Federal Income Tax Rates 105</p>
<p>9.2 Online Tax Calculators 111</p>
<p>9.3 Taxation of Earned Interest 111</p>
<p>9.4 Deductible Interest 112</p>
<p>9.5 Deferred Taxation Savings 112</p>
<p>9.6 Online Deferred Taxation Plan Calculators 115</p>
<p>9.7 Inflation 115</p>
<p>Problems 118</p>
<p>10. Life Insurance 119</p>
<p>10.1 What Is an Insurance Policy? 119</p>
<p>10.2 Probability 120</p>
<p>10.3 Introduction to the Life Tables 126</p>
<p>10.4 Expected Values 128</p>
<p>10.5 Term Insurance 130</p>
<p>10.6 Time Payments 133</p>
<p>10.7 Decreasing Term Insurance 134</p>
<p>10.8 Insurance for the Rest of Your Life 134</p>
<p>10.9 Whole Life Insurance 136</p>
<p>10.10 Breaking Down the Year 139</p>
<p>Problems 142</p>
<p>11. Annuities 144</p>
<p>11.1 A Benchmark Savings Plan 145</p>
<p>11.2 Immediate Annuity with Period Certain 145</p>
<p>11.3 Deferred Annuities 148</p>
<p>11.4 Life Annuities 150</p>
<p>11.5 Payments for Couples 153</p>
<p>11.6 Online Calculators 156</p>
<p>11.7 Variable Annuities 156</p>
<p>Problems 157</p>
<p>12. Reverse Mortgages and Viatical Settlements 158</p>
<p>12.1 Reverse Mortgages 158</p>
<p>12.2 Viatical Settlements 162</p>
<p>Problems 163</p>
<p>13. Investing: Risk versus Reward 164</p>
<p>13.1 Stocks 165</p>
<p>13.2 Portfolios 167</p>
<p>13.3 Calculators 171</p>
<p>13.4 Dollar Cost Averaging 173</p>
<p>13.5 Short Sales 174</p>
<p>13.6 Stock Dividends 174</p>
<p>13.7 Bonds 175</p>
<p>13.8 Options 175</p>
<p>13.9 Online Calculators and Listings 179</p>
<p>13.10 Ponzi Schemes and Other Scams 180</p>
<p>Problems 185</p>
<p>Reference 186</p>
<p>14 Gambling 187</p>
<p>14.1 Probability and Odds 187</p>
<p>14.2 Probability and Expected Return 188</p>
<p>14.3 Pari–Mutuel Betting 193</p>
<p>Problems 197</p>
<p>15 Spreadsheet Calculators 198</p>
<p>15.1 Introduction to the Spreadsheets 198</p>
<p>15.2 Some Programming Notes 205</p>
<p>16 Solutions 207</p>
<p>16.1 Chapter 1 207</p>
<p>16.2 Chapter 2 210</p>
<p>16.3 Chapter 3 213</p>
<p>16.4 Chapter 4 215</p>
<p>16.5 Chapter 5 216</p>
<p>16.6 Chapter 6 218</p>
<p>16.7 Chapter 7 220</p>
<p>16.8 Chapter 8 221</p>
<p>16.9 Chapter 9 223</p>
<p>16.10 Chapter 10 226</p>
<p>16.11 Chapter 11 229</p>
<p>16.12 Chapter 12 233</p>
<p>16.13 Chapter 13 234</p>
<p>16.14 Chapter 14 237</p>
<p>Index 240</p>