Preface     ix

List of Abbreviations     iv

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

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

70

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 Value     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     202

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