CHAPTER I PROGRESSIONS SECTION PAGB 1. Definitions ................... 1 2. Derivation and use of formulas ............ 2 3. Geometrical progressions in which the number of terms increases indefinitely .................. 6 CHAPTER II LIMITS AND SERIES 4. Variables and sequences ... ........... 10 5. Infinite series with constant terms ........... 14 6. The direct-comparison test ............. 16 7. The test-ratio test ................ 19 8. Power series .................. 23 9. The binomial series ................ 24 10. The exponential series ............... 26 11. The logarithmic series ................ 28 CHAPTER III LOGARITHMS 12. Definitions and preliminary notions .......... 30 13. The characteristic and the mantissa for a system of logarithms with base 10 ................. 32 14. Computation by logarithms ............. 34 15. Exponential equations ............... 36 16. The transformation of logarithms of one system into logarithms of another system ................ 38 v vi MATHEMATICAL THEORY OF INVESTMENT CHAPTER IV GRAPHICAL REPRESENTATION SBCTION 17. Definitions and first principles ........... 18. Some important graphs ..............
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PART II. INTEREST AND ANNUITIES
CHAPTER V INTEREST 19. Simple interest ................. 51 20. Ordinary and exact interest ............. 52 21. Computation of simple interest ............ 53 22. Compound interest ................ 54 28. Nominal and effective rates of interest ......... 59 24. Instantaneous compound interest. Force of interest ..... 61 25. Computation of compound interest ........... fi4 26. Discount .................... 67 27. The rate of discount ................ 70 28. The equation of value ............... 73 29. Equation of payments ............... 74 CHAPTER VI ANNUITIES 30. Definitions and notation .............. 77 31. The amount of an annuity ............. 79 32. The present value of an annuity ........... 82 33. Annuities due and deferred annuities .......... 84 34. Perpetuities and capitalization ............ 86 35. Continuous annuities ............... 92 36. The annuity that will amount to 1 ........... 93 37. The annuity that 1 will purchase ........... 95 38. Fundamental relation between — and — ........ 96 s-i a-, n| n| 39. The term of an annuity certain ............ 97 40. Computation of annuities; the use of annuity tables ..... 101 41. The rate of interest borne by an annuity ......... 109 CONTENTS vii CHAPTER VII THE EXTINCTION OF INTEREST-BEARING DEBTS BY PERIODICAL PAYMENTS—AMORTIZATION SECTION PAGE 42. The amortization of an interest-bearing debt by equal annual installments .................. 114: 43. The amount remaining due after the rth payment has been made 117 44. The amount remaining due when both the payments and the time intervals are unequal ............... 121 45. The amortization schedule ............. 121 46. The amortization schedule in general terms ........ 123 47. The amortization schedule when the debt is expressed in bonds of a given denomination ............. 125 CHAPTER VIII THE VALUATION OF BONDS 48. Bonds bought to yield a certain rate of interest ...... 127 49. The computation of the premium ........... 130 50. The amortization of the premium on a bond bought above par . 133 51. The accumulation of the discount on a bond bought below par . 134 52. Schedule for the amortization of the premium in general terms when the interest interval and the conversion interval coincide 136 53. Bonds bought between two interest dates ........ 138 54. Installment bonds ................ 140 CHAPTER IX SINKING FUNDS AND DEPRECIATION 55. Sinking funds .................. 142 56. Depreciation .................. 149 57. The composite life of a plant ............. 154 58. The wearing value of a single asset whose probable life is given 156 59. The valuation of mining properties .......... 160 CHAPTER X BUILDING AND LOAN ASSOCIATIONS 60. Definitions and first principles ............ 164 61. The effective rate of interest realized by the investor .... 167 62. The time required for stock to mature ......... 168 63. The rate of interest paid by the borrowing shareholder .... 170 viii MATHEMATICAL THEORY OF INVESTMENT PAET III. PEOBABILITY AND ITS APPLICATIONS TO FINANCIAL PROBLEMS CHAPTER XI THE THEORY OF PROBABILITY SECTION PAGE 64. Definitions and first principles ............ 175 65. Simple problems in probability ............ 177 66. Total and partial probability ............. 179 67. Compound probability ............... 180 68. Probability of an event when several trials are made .... 183 69. Mathematical expectation .............. 185 70. The mortality table ................ 186 CHAPTER XII LIFE ANNUITIES 71. Endowments and life annuities ............ 192 72. The computation of life annuities; commutation columns . . . 195 73. Deferred and temporary life annuities .......... 197 CHAPTER XIII SOME PROBLEMS IN LIFE INSURANCE 74. Definitions ................... 200 75. Whole life insurance ............... 202 76. Term insurance ....'............. 205 77. Endowment insurance ............... 207 78. Reserves; valuation of policies ............ 209 79. Loading; gross premiums .............. 212 80. Concluding note on life insurance ........... 214 PART IV. TABLES TABLE NO. L The number of each day of the year from January 1 ... 218 II. Exact interest at 5% for times from 1 to 365 days ..... 219 III. The compound amount on 1 ............ 220 IV. The present value of 1 .............. 224 CONTENTS ix TABI.E NO. PAGB V. The amount of 1 per annum ............ 228 VI. The present value of 1 per annum .......... 232 VII. The annuity that 1 will purchase .......... 236 VIII. Compound amounts for times less than a year ...... 240 IX. The value of 7(p) ................. 240 X. The value of — ............ .... 240 Jw XI. American Experience Table of Mortality ........ 241 XII. Commutation columns ........... 242 INDEX ..................... 243