Page:Encyclopædia Britannica, Ninth Edition, v. 13.djvu/187

 LIFE,] INSURANCE 175 1869 the subject is considered at some length, and several interesting tables are devoted to its illustration. The fol lowing figures, extracted from one of those tables, show the rates of mortality at different quinquennial periods of life among the &quot; healthy lives, male and female,&quot; divid ing the lives into groups according to the duration of their assurances. Age. (1) Annual Mortality per cent, in periods of Assurance. Under five years. (2) Five years and Upwards. (3) Under ten years. (4) Ten years and Upwards. (5) Total. (6) 20 to 24 67 90 71 64 71 25 29 66 i-oo 73 92 73 30 34 76 97 83 1-00 85 35 39 83 1*10 93 1-17 97 40 44 91 1-19 1-00 1-28 1-09 45 49 117 1-44 1-25 1-52 1-36 50 54 1-28 1-85 1-52 1-90 172 55 59 1-81 2-47 2-10 2-52 2-35 60 64 271 3-50 3-05 3-55 3-38 65 69 3 63 5-06 4-35 5-11 4-90 70 74 5 51 7 35 6-51 7-40 7 23 A prominent feature of this table is the divergence of the figures in column 3 from those in column 2, and on the other hand the comparatively close agreement of the figures in column 3 with those in column 5. This seems to indicate that among lives which have been less than five years assured the rate of mortality is materially lower than that prevailing among lives of similar ages who have been assured for longer periods, but that after the first five years the causes which bring about this lessen ing of the rate of mortality have in great measure ceased to operate. It was this peculiarity of the statistics that led to the construction of the H M(5) table, the first five years of assurance being regarded as marking, although not in any strict or absolute sense, a distinct period in the value of assured life, after which &quot;for all practical purposes the benefit of selection may perhaps be said to be lost.&quot; Mr Sprague has since pointed out that this distinction is not altogether satisfactory, and he has sought by the con struction of a series of &quot;Select Mortality Tables&quot; for separate ages at entry (Ass. Mag. xx. 95 and xxi. 229) to supply a more exact basis of calculation than the H M and H M(5) tables afford. Besides its influence upon the rates of mortality, selec tion has also a very noticeable effect in regard to the causes of death among the assured. Diseases to which a predis position may be inferred from family or personal history, or which admit of detection in an early stage by careful medical scrutiny, are less frequent among this selected class of lives than among the general population, while, on the other hand, assured persons seem to be more liable than others to particular forms of disease. This interesting subject is dealt with by Mr Mcikle in his Observations, formerly referred to; and it is also illustrated in numerous reports on the experience of different assurance companies by their medical officers. Valuations. The business of life assurance being founded on well-ascertained natural laws, and on principles of finance which in their broad aspect are of the simplest description, there exists no necessity for frequent close scrutiny of the affairs of an assurance office, in so far as the maintenance of a mere standard of solvency is con cerned. We have seen that the premiums charged for assurances are based on certain assumptions in regard to (1) the rate of mortality to be experienced, (2) the rate of interest to be earned by the office on its funds, and (3) the proportion of the premiums to be absorbed in expenses and in providing against unforeseen contingencies. If these assumptions are reasonably safe, an assurance office pro ceeding upon them may be confidently regarded as solvent so long as there is no conspicuously unfavourable deviation from what has been anticipated and provided for, and so long as the funds are not impaired by imprudent invest ments or otherwise. The ascertainment and division of profits, however, require that the affairs should be looked into periodically ; but the fluctuations to which the surplus funds are liable within limited periods of time, from varia tions of the death-rate and other causes, are generally re garded as furnishing a sufficient reason why such investiga tions should not take place too frequently. Accordingly in most offices the division of profits takes place only at stated intervals of years, usually five or seven years, when a complete survey is taken of the whole engagements present and future, and of the funds available to meet these. The mode in which the liability of an office under its current policies is estimated requires explanation. All statistical observations on the duration of human life Nature point to the conclusion that, after the period of extreme f reserve youth is past, the death-rate among any given body O f values&amp;gt; persons increases gradually with advancing age. If, there fore, assurance premiums were annually adjusted accord ing to the chances of death corresponding to the current age of the assured, their amount would be at first smaller, but ultimately larger, than the uniform annual payment required to assure a given sum whenever death may occur. This is illustrated by the following figures, calculated from the H M mortality table at 3 per cent, interest. In column 2 is the uniform annual premium at age thirty for a whole-term assurance of 100. In column 3 are shown the premiums which would be required at the successive ages stated in column 1 to assure 100 in the event of death taking place within a year. Column 4 shows the differences between the figures in column 2 and those in column 3. Age, 30 +n. (1) P 3(, (2) UAjjo+ri. ( &amp;gt;) ^SO-l ^SO+n. (t) 30 1-880 750 + 1-130 31 1-880 769 + 1-111 32 1-880 787 + 1-093 53 1-880 1 -800 + &quot; 074 54 1-880 1-916 036 55 1-880 2-042 102 95 1-880 61-848 -59-9(58 96 1-880 79-265 -77-385 97 1-880 97-087 -95-207 From this table it appears that if a number of persons effect, at the age of thirty, whole-term assurances on their lives by annual premiums which are to remain of uniform amount during the subsistence of the assurances, each of them pays for the first year 1 130 more than is required for the risk of that year. The second year the premiums are each 1*111 in excess of that year s risk. The third year the excess is only 1*093, and so it diminishes from year to year. By the time the individuals who survive have reached the age of fifty-four, their uniform annual premiums are no longer sufficient for the risk of the follow ing year ; and this annual deficiency goes on increasing until at the extreme age in the table it amounts to 95-207, thedifference between the uniformannual premium(l -880) and the present value (97087) of 100 certain to be paid at the end of a year. Now, since the uniform annual premiums are just sufficient to provide for the ultimate