ANNUITY, in the simplest sense of the word, denotes a payment made yearly The term is also applied to any series of periodical payments which fulfil the essential condition that they are made at regular fixed intervals. Thus an annuity may he payable yearly, half-yearly, quarterly, monthly, or even more frequently. It is, however, the total sum payable in the year, sometimes called the annual rent, which is adopted for the pur pose of describing the magnitude of the annuity. Hence a person in receipt of a quarterly payment of £25 is said to possess an annuity of f r oo payable by quarterly instalments.
In technical terminology an annuity is said to be payable during a given status, this being a word equally appropriate when the annuity is payable for a definite term of years and when the du ration is dependent upon some contingency. The most general definition of an annuity is therefore a series of payments made at regular intervals during the continuance of a given status.
The word annuity is sometimes used to denote an individual payment of a series, particularly in such phrases as "the first year's annuity." This usage, which has come into prominence in connection with the settlement of obligations contracted during the World War, is inaccurate and should be avoided.
Within these two main classes there are various types of annui ties to which special technical designations have been allotted. Unless otherwise stated, the first payment of an annuity is as sumed to be made at the end of the first year in the case of a yearly annuity and at the end of the first interval in the case of an annuity payable by instalments. This form of annuity is called an immediate annuity. An annuity of which the first payment is made at the beginning of the first interval is called an annuity due; if the annuity is not to be entered upon until the lapse of a certain number of years it is called a deferred annuity; if the payments are to continue for ever, it is called a perpetuity.
A continuous annuity is one which is assumed to be paid momently by infinitely small instalments. It would be impossible in actual experience to discover a series of payments precisely conforming to these conditions, but it is obvious that the value of such a series would not differ appreciably from that of a series of payments made daily or even weekly. The conception of con tinuous payments has permitted the application of the processes of the differential and integral calculus to the computation of annuity values. It has, therefore, been of great practical utility in facilitating the calculations of bodies, e.g., industrial insurance companies, whose revenue and expenditure consist largely of numerous small daily or weekly payments.
The person to whom an annuity is payable is called the an nuitant, and the life involved is called the nominee. A person who purchases an annuity on his own life is himself at once both annuitant and nominee.
Annuities-certain.—In an annuity-certain the status is a definite term of years, and thus the value of a given series of payments is dependent only upon the operation of interest.
The value of an annuity may be regarded as a loan or invest ment of money whereby the lender or investor becomes entitled to receive a series of uniform payments consisting partly of interest and partly of repayment of capital. Such a transaction may be considered from two points of view. In the first instance the successive instalments of principal may be at once applied to diminish the amount outstanding at the end of each interval, which will thus be gradually reduced until with the final payment of the annuity the total capital invested is repaid. As the prin cipal is repaid the interest diminishes and, since the combined annual payment is uniform in amount, the liquidation of the debt proceeds at an accelerating pace. Alternatively a uniform portion of each annuity payment may be regarded each year as interest on the original capital and the balance must be set aside and in vested, together with all accumulations of interest on it, from time to time at the assumed rate in order that the proceeds may be available to replace the capital at the end of the period when the annuity expires. Such a sum, periodically applied to the re demption of capital, is called a sinking fund. If the sinking fund were invested at a rate lower than that assumed, its accumula tions at the end of the period would not be sufficient to replace the invested capital. The periodical payments of the annuity are therefore sometimes calculated on the basis that the investor will obtain a specified rate of interest on his capital but will be able to replace the capital only by investing the instalments of sinking fund at a lower rate. The latter rate is technically known as the reproductive rate, and the rate realized as the remunerative rate. In periods of high income tax the distinction is of impor tance. The investor must be careful in arranging the transaction to secure that the reproductive rate is the net rate on which he can rely after deduction of tax.
the product may be represented by the symbol and D=+1+Dz+2+ .... etc. _ By the in this notation — device of preparing columns of D and N, technically known as commutation columns, not only the derivation of the value of an annuity at one age, but also the construction of a complete table of annuity values is abbreviated and facilitated.
Investigations of Annuitants' Mortality Experience.— By the Life Annuity Act of 1808 the British Government through the National Debt Commissioners were empowered to grant life annuities. The duration of the lives of nominees of both sexes was assumed to be correctly measured by the Northampton Table of mortality. This table, apart from the fact that it was prac tically the only one available, had been found to yield substantial profits in the case of the Equitable and other companies which had adopted it for life assurance business, but this fact, so far from suggesting its unsuitability for granting annuities, only con firmed its reputation. John Finlaison, subsequently appointed actuary to the National Debt Commissioners, appears to have been the first to realize that the country was sustaining consider able loss by the use of the table for the grant of annuities and must inevitably incur further loss unless the mortality basis were altered. As a result of his representations the issue of annuities was suspended in 1828.
In 1829 a new scheme was introduced. The mortality tables adopted were those constructed by Finlaison from an observa tion up to the end of 1822 of the duration of the lives of Tontine and National Debt Office annuitants. This was the first investi gation of the mortality of Government annuitants. Two main facts emerged from this investigation, and have been confirmed by subsequent experience—(a) that annuitants as a class are remarkable for their longevity and (b) that the vitality of females is appreciably superior to that of males, so that separate mortal ity tables must be prepared for each sex.
The second investigation of the mortality of Government an nuitants was carried out by A. G. Finlaison and published in 1860. The variations between the old and the new tables were found to be so insignificant that the Treasury did not consider it necessary to alter the charges made for annuities.
The next investigation was made by A. J. Finlaison and published in 1883. The data consisted of the records relating to the annuities granted by the National Debt Commissioners from 1808 to 1875. This investigation is notable because of the fact that it was the first in which the effect of "selection" was taken into consideration in deducing the rate of mortality amongst annuitants. It may be assumed that an annuity will not be purchased on the life of a person known to be suffering from a disease likely to impair his vitality. This discrimination exercised by the purchaser must clearly influence the rate of mortality for several years after the date of purchase, in much the same way as the medical examination does in the case of as sured lives, and allowance should be made for this fact in settling the selling price of annuities. A. J. Finlaison found that the effects of selection were discernible for four years following the date of purchase, and recommended that revised tables based on the resulting select rates of mortality should be adopted.
With the approval of Thomas Bond Sprague, then president of the Institute of Actuaries, whom the Treasury had consulted before sanctioning rates based on what was then a novel theory, the new tables were introduced in 1884, in substitution for those which had been in force since 1829.
In 1893 the Institute of Actuaries and the Faculty of Actuaries resolved to undertake the compilation of a new collective mortali ty experience of assured lives, and separately of annuity nomi nees, in the United Kingdom during the period 1863-93. Forty three companies contributed to the experience of annuitants, and 9,700 contracts in .respect of male lives and 24,300 in respect of female lives were brought under review, the whole constituting a more detailed and authoritative investigation of annuitants' mor tality than any that had previously been attempted. The tables, officially designated Oam and Oaf for males and females respec tively, were published in 1902. In the construction of these tables the duration of selection was taken to be five years.
The fourth investigation of the experience of National Debt Office annuitants carried on the observations from 1875 to 1904, and was published in The methods adopted in the construc tion of the tables and the results of the investigation were very similar to those of the British Offices, Oam and Oaf tables. The vitality of both sexes was shown to have increased, the difference between the new and the previous tables being most marked in the case of females.
Shortly after the War investigations of the recent mortality experience, both of life office and Government annuitants, were undertaken. In each case the observations related to the years 1900-20, and the mortality of each of the three constituent periods 1900-7, 1907-14 and 1914-20 was also separately ex amined. The two investigations proceeded almost simultaneously, that of the life offices, however, being begun and completed several months in advance of the other.
The life office annuitants investigation was again carried out under the auspices of the Institute and Faculty. The numbers of contracts examined were 19,946 of males, and 51,892 of females. The first section of the report of Messrs. Elderton and Oakley, the actuaries in charge of the investigation, was published in 1923. This proved to be a document of first-class importance in the history of actuarial science. The authors discussed the question of selection in all its aspects and suggested, both on theoretical and on practical grounds, that its effects could be ignored after the first year following purchase. Even more notable was their recommendation that annuity values should be based not on the rates of mortality derived directly from the observed experience, but on these rates modified to allow for progressive future im provement in vitality. The principle of allowing for progressive decrease in the death-rate had been previously applied in special circumstances, such as the commutation of the life interests of incumbents under the Welsh Church act of 1914, but this was the first instance of its application to a general investigation the re sults of which were destined to be a recognized standard for many years. These recommendations were adopted by the Insti tute and Faculty, and the volume of tables which were officially designated a(m) and a(f) was published in 1925 and gave only "projected" rates of mortality and annuity values derived from them. These rates of mortality are naturally lighter than those recorded in any of the previous investigations and the values of annuities are correspondingly increased.
The examination of the mortality experience of Government life annuitants was carried out by Sir Alfred W. Watson, K.C.B., the Government actuary, and Mr. H. Weatherill, actuary to the National Debt Commissioners, whose report was published in 1924. On that occasion the scope of the investigation was ex tended to include not only the annuities granted directly by the National Debt Commissioners, but also those issued through the agency of Trustee Savings Banks and the Post Office Savings Bank. The number of contracts brought under observation was 23,230 in respect of males and 57,551 in respect of females. The mortality experienced during the period was found to be appreci ably lighter in the case of both sexes than that of the investigation, the decline being again more significant amongst women than amongst men. It was ascertained also that the mor tality experience of the Savings Bank annuitants was lower than that of the lives concerned in the National Debt Office annuities. The difference is presumably due to the fact that annuities pur chased under wills in circumstances in which there is no element of self selection are proportionately more numerous among trans actions with the National Debt Office than with the Savings Banks. In an appendix to the report several questions of theo retical and practical importance were discussed at length. It was concluded that the effects of selection were traceable for at least five years, but as a measure of practical convenience it was de cided to employ a select rate of mortality in respect of only the first year after the date of purchase, and to provide for the selec tion thus excluded by a subsequent adjustment of the annuity values. Progressive improvement in vitality was found to be ex hibited not only in the experience of annuitant lives but also in that of other special classes of lives and of the population gener ally. To provide for its persistence in the future the actuaries, as a result of extensive experiments, recommended that appropriate selling prices for annuities granted in the immediate future would be the values of select annuities derived directly from the 1900-20 experience increased by 3% in the case of male lives and by 4% in the case of female lives.
Government Life Annuity Business.—Government life an nuities were first granted in 1808. The scheme was revised in 1829 by the Act To Geo. iv., c. 24. The object of the scheme is the acceleration of the reduction of the National Debt (q.v.), by the substitution of terminable for perpetual annuities.
Annuity Values.—The following table gives specimen annui ty values according to successive investigations. The differences in the principles and methods adopted in the construction of the several tables are briefly indicated in the headings of the columns.
can companies.
In 1920 the writer of this article prepared an experience based on the material of 20 of the principal American companies under annuities issued in the United States. It is called the American Annuitants Table of Mortality and was used with various modifica tions as a basis of premiums by American companies until 1938. While the Combined Annuity Table was published in 1928 and the 1937 Standard Annuity Table in 1938, each of these was based on the American Annuitants Table, with allowances for decreases in mortality.
The rates of mortality of a British experience compiled for the years 1900-20, a(m) and a(f), are now compared with the Standard Annuity rates for quinquennial ages commencing with age 50, the average age at which annuities are issued in America being 63. The British rates are on an ultimate basis (excluding the experience of the first annuity year) and the American rates on an aggregate basis (including all annuity years).
The charges made by offices for the grant of annuities have generally been revised in conformity with the 190o-20 tables, and are consequently less favourable to purchasers than was formerly the case. The amount of business transacted has steadily increased. From 1906 to 1914 the average annual amount received by offices established within the United Kingdom for the purchase of immediate annuities did not greatly exceed £2,000,000. During the war period it fell, the minimum of £920,00o being reached in 1916. In 1919 the consideration money again exceeded £2,000, 000, and after a decline to 11,500,000 in 1921 it increased to £3,000,000 in 1923, and remained at about that figure in each of the two following years. It is noteworthy that a considerable share of the annuity business transacted within the United King dom has been obtained by DJminion and Foreign companies. From 1910 to 1922 the average amount received annually by these offices was more than £400,000, in 1923 it approached £65o,000, and has subsequently exceeded £1,000,00o a year. (P. G. B.) While annuities have generally been issued py life insurance companies in the United States, it is only in recent years that there has been a considerable demand for them. For example, in the year 1900 the considerations received for annuities by compa nies operating in New York State amounted to $6,600,000 which increased to $8,900,000 in 1920 and to $355,000,000 in 1937. Life annuities are not issued by the United States Government as they are by the British Government.
Until the publication of the McClintock table of mortality in 1899, the basis for the determination of premiums for annuities was a British experience. Emory McClintock, then actuary of the Mutual Life Insurance Company of New York, published the data on annuities issued throughout the world by the principal Ameri The 1937 Standard Mortality for women was taken as five years younger than for men since actual experiences gave such results approximately and as this artifice saved a great deal of labour in calculating premiums.
It must not be inferred from the above table that the rate of mortality among annuitants is higher in Great Britain than in America. As vitality has shown a tendency to increase with calen dar year the above tables represent an attempt to make allowance for this improvement. The British table is a forecast of the mortality to be experienced under issues of 1925 and the Ameri can table is an estimate of the improvement in mortality as of 1937. Most American companies made further allowance for a probably lower mortality by setting back the ages an additional year or two.
In order to develop annuitant mortality tables and keep in close touch with current experience, the Joint Committee on Mortality, consisting of representatives of the Actuarial Society of America and the Association of Life Insurance Medical Directors, com menced in 1936 to make a continuous mortality study, based on annuities issued in 1931 and subsequent years.
Twenty large companies are contributing their data to this study, which is published each year in the Transactions of the Actuarial Society of America.
The decreasing mortality among annuitants has led to a lower annuity in return for a given amount of purchase money. In addi tion the lowered yields on investments have accentuated this proc ess. As a result several American companies are issuing participat ing annuities under which the guaranteed return may be increased by annual dividends. The great majority of the companies have continued to issue non-participating annuities under which a fixed yield is specified.
In addition to the ordinary annuities which are payable through out life on an annual, semi-annual, quarterly or monthly basis and which cease at death, many American companies issue annui ties providing for a return of the excess of the consideration over annuity payments made, if any, or for guaranteed payments over a specified period whether the annuitant dies or survives. Deferred annuities with payments to begin at a specified age are also com monly issued, and in event of death during the period of defer ment a return of premiums with or without interest may be granted.
A variation of this form gives the annuitant the privilege of electing a smaller annuity before the specified age in accordance with a table inserted in the policy. Premium rates distinguish be tween men and women applicants according to age last birthday and are adjusted to completed quarter-years of age.
One of the outstanding features since 193o has been the develop ment of group annuities which cover an annuity payable at the retirement age. Reports of the life insurance companies transact ing business in New York State showed 53o group annuity con tracts on different employers or corporations on Dec. 31, 1937, cov ering more than 500,000 individual certificates and representing an annual income at maturity of more than $89,000,000.
The mortality is lower among annuitants than among holders of life insurance policies on account of the psychology which en ters into the transactions. A man buying an annuity hopes to live long enough to receive in payments from the company more than the single premium paid by him and he therefore would not pur chase the annuity if, in his own judgment, he were a poor risk. On the other hand, the applicant for a life insurance policy knows that his beneficiaries would have a larger return for the premiums if he died in the early rather than the later years of the policy. The lower experience among annuitants is largely the result of "self-selection" through the discrimination exercised by the pur chaser. The mortality is partly due to the attractiveness of annui ties compared with investments—the more remunerative the latter the greater the "self-selection" against the company—and partly due to the conditions in the various countries, such as that of leaving annuities to servants and to persons who are not able to look after their financial interests. The fact that the mortality among persons who take annuities ceasing at their death is dis tinctly lower than among those who apply for an annuity with a refund at death of the single premium less annuity payments is evidence of the power of "self-selection" among groups of indi viduals.
Under the 1936 regulations of the United States Internal Reve nue Department a sum equal to 3%of the consideration paid is tax able income from an annuity; the excess above such 3% is ex cluded from gross income until the aggregate amounts excluded equal the consideration paid. All payments received thereafter are taxable as income for the year in which they are received.
BIBLIOGRAPHY.—The standard text-books are: R. Todhunter, ComBibliography.—The standard text-books are: R. Todhunter, Com- pound Interest and Annuities-Certain (rev. by R. C. Simmonds and T. P. Thompson) and E. F. Spurgeon, Life Contingencies. There are numerous papers of historical, theoretical and practical interest in the volumes of the Journal of the Institute of Actuaries, which was first published in 185o as the Assurance Magazine, but has continued under the present name since 1866. The results of the British life offices annuitants investigations are contained in the volumes British Offices Annuity Tables 1893, Mortality and Monetary Tables, and Mortality of Annuitants 1900-20. The Report on the Mortality Experience of Government Life Annuitants, 1900-1920, appeared as a Stationary Office publication in 1924.
The following are among the more valuable papers on annuities published in the Transactions of the Actuarial Society of America:— R. W. Weeks, Mortality on Annuitants in American Life Insurance Companies (iv, 275) ; Emory McClintock, Tables for the Estimation of Mortality Among Annuitants (vi, 13) ; C. C. Ferguson, Participat ing Annuities (xv, 354) ; Arthur Hunter, Mortality Among American Annuitants and Premiums Based Thereon (xxi, 157) ; C. D. Ruther ford, An Annuity Table Complying with the Requirements of the New Canadian Valuation Standard (xxviii, p. 54) ; F. D. Kinecke, A New Annuity Mortality Table (xxxix, p. 8) ; Report of Joint Committee on Mortality Under Annuity Issues (xxxviii, 2 21 ; xxxix, III and xl, 238) .
These are to appear yearly. Other papers on annuities may be found through the Index to the Transactions. The Transactions of the Faculty of Actuaries, and the Record of the American Institute of Actuaries also contain important papers. (A. Hu.)