Page:Encyclopædia Britannica, Ninth Edition, v. 13.djvu/185

LIFE.] INSURANCE 173 ate both the hypothesis of payments being due at the end of the year and that of a uniform distribution of each year s deaths, neither of which is strictly admissible. The lives assured, instead of being regarded as subject to successive yearly decrements, are considered to be diminishing in number continuously ; and in like manner interest, instead of being payable annually, is supposed to be grow ing due from moment to moment. The methods referred to afford great facilities for the solution of various problems which can only be solved approximately, or with extreme labour, by the usual modes of computation, but they are not employed in the ordinary calcu lations of assurance offices. The premiums obtained by calculation from the funda mental data of interest and mortality are called " net " or "pure" premiums. In calculating the premiums to be charged by an assurance office, it is to be borne in mind that, while fluctuations will undoubtedly occur in the rates of mortality prevailing at different times among the lives assured, and in the rates of interest realized on the invested funds, the terms on which assurances are undertaken are not subject to variation at the will of the office in order to meet such fluctuations. The office must hold itself absolutely responsible for the fulfilment of its part of the contract, but the premiums cannot be increased beyond the amount fixed at the outset. Hence it is obviously neces sary that the premiums should be on such a scale as to. keep the office safe under all circumstances. Further, the premiums must contain a sufficient provision for the ex penses necessarily incurred in carrying on business. There fore the rates actually charged must be larger than those which would suffice if only a probable death-rate and a probable rate of interest had to be taken into account. In the earliest days of assurance it seems to have been the practice to make an addition for safety to the rates of premium deduced from the fundamental data, and certain payments were required as " entry-money " to help to meet expenses. Afterwards, when experience had shown that the tables of mortality then in use considerably overstated the death-rate likely to be experienced, the addition made to the premiums was removed, but the offices continued to use tables giving high death-rates in combination with a rate of interest well within that which might safely be expected. With the introduction, however, of mortality tables which approached more closely the death-rates among assured lives, there revived the practice of making an ad dition to the "pure" premiums, in order to provide for expenses, for fluctuations in the death-rate, and for other contingencies. This addition is called the "loading" or "margin," and the premiums which include it are called "office premiums," as being those which enter into the contract between the office and the assured. Few if any of the older assurance offices continue to base their estimates of liability on the tables which were originally employed in the construction of their scales of premium ; but many of them still charge the same rates as formerly, or at all events rates which have not been con structed from the tables of mortality now in use. Hence the terms " loading " and " margin " have come to bear a somewhat extended meaning. They are now used to designate the difference between the premiums payable by the assured and the net premiums deduced from any table that may be employed for the time. There have been various theories as to the proper method of loading premiums. The plan most commonly employed at first was that of adding a constant percentage of the net premiums at all ages. Some actuaries objected to this method, holding it to be inequitable as between old and young lives, and proposed in its stead the addition of an equal sum for every age (that is, in effect, a constant per centage of the sum assured) as more in accordance with the object in view. By others a combination of these two plans was preferred. The premiums were loaded by a per centage for " profit " and contingencies, and a constant addition was made to cover the expenses of management. More recently other methods have been proposed, and it has been specially insisted on that the "loading" should be adjusted so as to give due weight to the fact that by far the larger proportion of expense is usually connected with the first year s premium ; but most of the scales of pre miums now in use by assurance offices have been arrived at by one or other of the methods of loading mentioned above. The rates of the Northampton Table, at 3 per cent, interest, furnish an example of a scale of net rates used as office premiums, without any specific addition by way of " loading." These are shown in the following table. As an example of a scale of office premiums formed by loading with a constant percentage, we give that obtained by adding 25 per cent, to the net rates of the Carlisle table, reckoning interest at 3 per cent It will be seen that, owing to the lower death-rate shown by that table, the premiums even with the addition mentioned are lower than those of the Northampton Table up to age fifty. After that age the loaded Carlisle premiums are higher than the Northampton pure premiums, but still the Carlisle rates without loading are lower than the Northampton rates. For the sake of further illustration we give the net premiums deduced from the healthy males table (H M ) of the Institute of Actuaries at the same rate of interest ; and in a separate column is shown what percentage of " loading," on a com parison with those premiums, is contained in the Carlisle rates with their 25 per cent, addition. The premiums are those required for the assurance of 100 for the whole term of life. Age. Northampton 3 per cent, rates, net. Carlisle 3 per cent, rates, with 25 pel- cent, added. II M 3 per cent. rates, without loading. Percentage by which col. (;i) exceeds col. (4). 0) (2) (3) (4) ( ) 15 1 18 7 1 13 2 146 35-37 20 237 1 17 4 187 30-61 25 2 8 1 227 1 12 6 31-03 30 2 13 5 2 8 10 1 17 7 29-93 35 2 19 10 2 15 10 2 3 10 27-38 40 3 7 11 350 2 11 9 25-60 45 3 17 11 3 15 5 323 21-15 50 4 10 8 4 10 7 3 16 19-19 55 564 5 13 8 4 14 6 20-28 60 674 749 5 19 9 20-88 65 7 16 9 8 19 3 7 14 1 16-33 Constitution of Offices. The nature of life assurance is such as to render impracticable its successful prosecution as a matter of individual or private enterprise. To secure a sufficiently uniform operation of the laws of average, the transactions must be carried out on a scale quite incom patible with the sufficiency of private credit for their ful filment ; while the indefinite and lengthened periods over which the engagements extend also mark them out as beyond the reach of individual responsibility. Accordingly, with the limited exception of the insurance scheme of the Government, the business in the United Kingdom may be said to be entirely in the hands of public companies or societies. These bodies have been of three kinds (1) the purely mutual offices, in which the assured themselves constitute the society ; (2) proprietary offices, as they once existed, being joint-stock companies which carried on the business of assurance for the benefit of the shareholders, among whom were divided the whole "profits" or "surplus" arising from the contributions of the assured ; and (3) the mixed offices, possessed of a share capital, but dividing among their assured a proportion (generally from two-thirds to nine-tenths) of the "profits" realized. In the present day there are but two kinds of offices, mutual and mixed, the proprietary companies either having di.s- Assur- ance J1 Mutual. Proprie- tarv - Mixed.