CONTENTS PAGE 'REFACB. ........ v CHAPTER I INTRODUCTION 1. Compound Interest .............. 1 2. Present Value .............. 2 3. Annuities. ............ 3 4. Amount of a Forborne Annuity ............. 4 5. Present Value of a Term Annuity ............ 5 6. Alternative Proofs. .................. 5 7. Present Value of an Annuity-due ............ 6 8. General Remark.................... 7 9. Factorials. .............. 7 10. Independent Events .................. 8 11. Arrangements or Permutations ............. 9 12. Combinations or Groups ................ 10 13. Binomial Coefficients ................. 11 CHAPTER II THEORY OF PROBABILITY 14. Fundamental Principle................. 13 15. Bernoulli's Theorem .................. 14 16. Compound Probability................. 16 17. Total Probability ................... 18 18. Repeated Trials. ............... 20 19. Expectation in n Trials................. 24 CHAPTER III THE MORTALITY TABLE 20. Definition. ............... 27 21. The Life Curve ................ 28 vii viiiCONTENTS
22.Probability of Living or Dying 23.Population ......... 24.Central Death Rate ..... 25.Expection of Life ...... 26.Probable Lifetime ...... 27.Mathematical Expectation . . 28.Biometric Functions .....
CHAPTER IV CONTINGENT FUNCTIONS ENDOWMENTS AND ANNUITIES
29. Pure Endowments................ 30. Commutation Symbols. ............. 31. Contingent Annuities. .............. 32. Intercepted Annuities .............. CHAPTER V CONTINGENT FUNCTIONS LITE INSURANCE POLICIES. NET PREMIUMS 33. Whole-life Insurance. Net Single Premium. .... 34. Intercepted Insurance. Net Single Premium .... 35. Sufficiency Test for Net Single Premium ...... 36. Whole-life Insurance. Net Annual Premium .... 37. Limited-payment Policies. ............ 38. Intercepted Insurance. Net Annual Premium.... 39. Sufficiency Test for Annual Premium........ 40. Endowment Insurance .............. 41. Annuities Payable Oftener than Once a Year .... 42. Premiums Payable Oftener than Once a Year .... CHAPTER VI VALUATION OF POLICIES 43. General Methods for Finding Policy Values..... 44. Prospective Method ............... 45. Retrospective Method .............. CONTENTS ix PAGE 3. Equivalence of Prospective and Retrospective Methods . 64 7. Accounting or Accumulation Method ....... 5^ ?. Fackler Valuation Symbols ......... 65 9. Cost of Insurance ........ 6f 0. Cost in Terms of Premium ........ °' 1. Valuation in Terms of Cost. ......... bo 2. Preliminary Term Valuation ......... 7U 3. Modified Preliminary Term Valuation ........- 71 CHAPTER VII POLICY OPTIONS. LOADING. SURPLUS 74 4. Options. ....'' „. 15. Surrender Value. ...... 16. Paid-up Insurance. ..... 17. Extension of Insurance ...... >8. Loading .......' i9. Surplus. ......'''' CHAPTER VIII INCREASING INSURANCES 81 30. Increasing Insurance. ..... Bl. Intercepted Increasing Insurance ..... ° 62. Return-premium Policies ........ CHAPTER IX JOINT CONTINGENT FUNCTIONS PART I. THEORETICAL DEVELOPMENT QQ 63. Joint Contingent Functions. ...... 0 64. Joint Endowments. '.",".",." 65. Each Person's Share of the Present Value of a Survivorship ^ Endowment. .......' 66. Joint Annuities ......' „ 67. Joint Annuities-due ..... 68. Joint Insurance ....... 69. Instalment Insurances ..... X CONTENTS PART II. NUMERICAL COMPUTATION PAGE 70. Joint Endowments................... 97 71. Commutation Symbols for Two or More Lives. ...... 98 72. Force of Mortality................... 99 73. Equal Age ...................... 100 74. Law of Uniform Seniority................ 101 75. A Makehamized Table of Mortality ........... 102 76. Probability of Living. ................. 103 77. Commutation Symbols Continued ............ 103 CONCLUSION 1. General Remarks ................... 106 2. Stirling's Formula ................... 106 3. Probability of Expectation ............... 107 4. Deviation. ...................... 107 5. Probability of Deviation ................ 108 6. Probability of Deviation Lying between Given Limits . . . 108 7. Probable Deviation .................. 109 8. Mean Deviation. ................... 109 9. Standard Deviation .................. 109 10. Recapitulation. ................'.... no TABLES I. Compound Amount of land Present Value of I at 3^% . .111 11. American Experience Table of Mortality. ........" 112 III. Commutation Columns and Valuation Symbols, American Experience Table at 3^%. ............. 114 IV. Hunter's Makehamized American Experience Table. Com- mutation Columns at 3^% ............. 116 INDEX. ....................... 119