Mathematics of Finance

Contents

Preface   ix

1 Simple interest and simple discount   11.1 Simple interest    1
1.2 Interest paid on bank balances   5
1.3 Present values   8
1.4 Equations of value   12
1.5 Partial payments   17
1.6 Promissory notes   19
1.7 Review exercises   23

2 Compound interest   25
2.1 The compound interest formula   25
2.2 Equivalent rates   30
2.3 Present value at compound interest   34
2.4 Future or present value for a fractional time period   38
2.5 Finding the interest rate or the time period   42
2.6 Equations of value   46
2.7 Changing interest rates   51
2.8 Other applications of compound interest theory   55
2.9 Review exercises   59


3 Annuities   61
3.1 Definitions   61
3.2 Future value of an ordinary annuity   61
3.3 Present value of an ordinary annuity   72
3.4 Annuities due   80
3.5 Perpetuities   84
3.6 Deferred annuities   88
3.7 Summary of annuities   90
3.8 Review exercises   95


4 More annuity problems   97
4.1 Introduction   97
4.2 Finding the periodic payment   97
4.3 Finding the interest rate   101
4.4 Finding the term of an annuity   105
4.5 Changes in the interest rate   109
4.6 Annuities where payments vary   112
4.7 Review exercises   119


5 General annuities   121
5.1 Introduction   121
5.2 Change the interest rate to value general annuities   121
5.3 Finding the periodic payment   126
5.4 Two alternative methods   128
5.5 Review exercises   134


6 Housing and other personal loans   135
6.1 Introduction   135
6.2 Mortgages and other reducible rate loans   136
6.3 Loan outstanding   142
6.4 Changes in the loan interest rate   149
6.5 Comparing the cost of interest only loans   156
6.6 Flat rate loans and the Rule of 78   161
6.7 Review exercises   173


7 Bonds   175
7.1 Introduction and terminology   175
7.2 Calculating the price for a given yield at interest payment dates   176
7.3 Purchase price for a given yield between interest payment dates   183
7.4 Finding the yield for a given price   188
7.5 Taxation on bonds   194
7.6 Premium and discount   200
7.7 The bond market and other forms of securities   204
7.8 Sinking funds   212
7.9 Review exercises   217


8 Business decisions and compound interest   219
8.1 Net present value   219
8.2 Internal rate of return   224
8.3 Capitalised costs   231
8.4 Depreciation   235
8.5 Review exercises   243


9 Contingent payments   245
9.1 Introduction   245
9.2 Probability   245
9.3 Mathematical expectation   253
9.4 Contingent payments with compound interest   257
9.5 Review exercises   264


Appendix A Exponents and logarithms   266
Appendix B Progressions   276
Appendix C Linear interpolation   284
Appendix D Continuous compounding   289
Appendix E The number of each day of the year   296


Answers to even-numbered exercises   297


Glossary   303


Index   307

This customized resource has been designed for students of ACST202 Mathematics of Finance at Macquarie University