Annuity

Annuity is the term employed to describe a payment generally (but not necessarily) of uniform amount falling due in each year during a given term, such as a period of years or the life of an individual; and payable, either in one sum at the end of the year, or by half-yearly or other installments. Annuities differ from other investments in this, that the capital sum invested or 'sunk' in the purchase of the annuity is not returnable when the annuity ceases to be payable—a portion of it is, in fact, returned in each payment of the annuity. By thus sacrificing the capital, a larger income is obtained, and hence the purchase of a life annuity is resorted to by persons whose main object is to secure a competency for themselves. For example, a male aged 60, by paying £1000 to the government, can secure an annuity of £87, 1s. 8d. for the remainder of his life, while the same sum invested in consols at par would yield £30 only. Annuities are divisible into two classes: (1) Annuities certain—that is, for a fixed term of years, subject to no contingency whatever, and depending for their value simply upon the operation of compound interest; and (2) Annuities contingent—that is, annuities depending not merely upon the operation of compound interest, but also upon the continuance of some status, such as the life of a person, whose duration can only be estimated by the theory of probabilities, on the average of a large number of cases. The former class is dealt with under the article INTEREST; the theory of annuities certain being, in fact, a branch of the theory of compound interest.

The LIFE ANNUITY (which is generally meant when the simple term 'annuity' is employed) is the principal example of the latter class, and to it our remarks must be mainly directed. In scientific treatises on the subject, an annuity is always assumed, unless otherwise described, to consist of an annual income of £1, or more simply of 1, payable at the end of each year survived—the amount for any larger sum being easily derived therefrom. When, in addition, a proportion of the year's annuity is payable up to the day of death, the annuity is said to be complete—the ordinary annuity being sometimes, for distinction, referred to as a curtate annuity. By the Appointment Acts, however, annuities are held as accruing from day to day, and therefore as apportionable or complete unless otherwise specified—the legal and the scientific practice being thus at variance in this respect. When the first payment is due in advance, the annuity is known as an annuity due; and on the other hand, when the first payment is not to be made until the expiry of a certain number of years, it is called a deferred annuity.

The honour of having been the first to place the calculation of life annuities on a scientific basis, by applying the doctrines of probabilities and of compound interest to a mortality table deduced from the recorded statistics of an actual community (Breslau), belongs to the celebrated astronomer royal, Halley. His monograph on the subject is printed in the Philosophical Transactions for January 1693. When Halley wrote, the Revolution government was endeavouring to complete the raising of a sum of a million sterling, by the issue of life annuities, offering 14 per cent. during the lifetime of any nominee, without restriction of age; thus appraising selected life-interests at only a trifle more than seven years' purchase. Notwithstanding the fact that Halley's table showed the life-interests of young nominees to be worth upwards of thirteen years' purchase, or nearly double the amount charged, money found its way but slowly into the national treasury. Adam Smith attributes this to the supposed instability of the government; but it may doubtless also be traced to ignorance or distrust of Halley's conclusions on the part of his countrymen. Certain it is, that at a much later period (1746), an issue of exchequer life annuities—again on ruinous terms, and without restriction of age—was left to be taken up mainly by Dutchmen, who, being well informed on the subject of life contingencies through the writing of Kerseboom, nominated children, and mostly young females; while the English subscribers selected their nominees from either sex, and of any age, up to 50 or 60 indifferently.

In 1808 the National Debt Commissioners commenced the granting of life annuities, graduated according to age, on the basis of the Northampton table of mortality (see MORTALITY, TABLES OF). Previous annuity transactions had resulted in heavy loss, and it might have occurred to those responsible for the new departure, that that loss was not likely to be retrieved by adopting a table which had been proved to yield a large profit when used as a basis for life-assurance premiums! Not until 1828, however, and after Mr Finlaison, the government actuary, had pointed out that the loss from the annuity business was advancing at the rate of £8000 per week, was the Northampton table abandoned. Shortly thereafter, new tables of annuities, deduced from the past experience of the government, and distinguishing between male and female lives, were issued. Since then, the rate of mortality prevailing among government annuitants has been twice re-investigated, so as to embrace the additional data accumulated. The existing rates for government annuities are deduced from tables issued in 1884. These tables embrace the further feature of giving effect to the superior vitality found to prevail among the lives at the date of the purchase of the annuities, as compared with that of the general body of annuitants of corresponding ages. The same tables are doubtless the most appropriate basis upon which life-assurance companies, and other institutions granting annuities, can construct their scale of charges. But while the government rates are based upon the assumption that only $2\backslash frac\{1\}\{2\}$ per cent. interest will be realised on the investments, assurance companies can afford to assume a future rate of $3\backslash frac\{1\}\{2\}$ or $3\backslash frac\{3\}\{4\}$ per cent., while trusting, like the government, to the additional interest realised beyond the rate assumed proving sufficient to provide for the expenses of conducting the business. The following table gives examples of the rates of annuity, per £100 sunk, deduced from the new government annuity tables—the annuities being calculated as ‘complete,’ and payable by half-yearly instalments:

The rates in the column headed $2\backslash frac\{1\}\{2\}$ per cent. are those actually allowed by the government; while those in the column headed $3\backslash frac\{1\}\{2\}$ per cent. may be taken as affording an approximation to the more favourable terms which may be obtained from various life-assurance offices in this country. A comparison of the two will show that at least past errors are not being perpetuated by the government.

The total sum paid by the government, in respect of annuities, in an average year considerably exceeds £1,000,000 sterling, while the corresponding sum paid by the assurance offices may amount to about £650,000. These two sums, however, represent only a very small proportion of the total annuity interest of the country; for, not to speak of the various widows' funds and annuity societies, it has to be borne in mind that a very large amount both of real and of personal property in this country is held in life-rent.

There is another important practical aspect in which the subject of life annuities may be viewed. While the government and corporate bodies granting annuities rely upon the principle of averages for the satisfactory working out of their transactions, a purchaser of an isolated annuity must proceed differently. He requires to protect himself against the loss of his capital, through the early death of the annuitant, and this can only be done by effecting an assurance on the life of the latter, without which, the transaction becomes a speculation and not an investment. Suppose a complete life annuity of £50 to be offered for sale, and an individual to be willing to purchase it at such a price as will yield him 5 per cent. on his outlay; then the first thing he would require to ascertain would be the rate of premium at which the life of the annuitant could be assured. This being found to be, say, 3 per cent. per annum, the intending purchaser would next proceed to calculate the sum, X, the interest upon which, together with the premium to assure its return at the death of the annuitant, would amount to £50. Thus:

The premium to assure £625 is £18, 15s., and the interest on £625 at 5 per cent. is £31, 5s., together making up the annuity of £50. It should be borne in mind, however, that the £625 being the total outlay, the sum that can be paid to the seller is only £606, 5s., being the former sum, less £18, 15s., the amount of the first premium which requires to be paid in advance to the assurance office.

Of other forms of contingent annuities, a single example may be given. With many widows' funds it is a rule that the widow ceases to draw her annuity if she marries again. The calculation of an annuity ceasing either at death or upon re-marriage leads to no theoretical difficulties; but in order to obtain satisfactory results, it is necessary to have carefully compiled statistics of the ratio of re-marriage among widows of various ages.

In the law of England, an annuity is the right to the yearly payment of a certain sum of money, which is charged upon the person or personal estate of the individual bound to pay it. If it is charged upon real estate, the burden is called a rent or rent-charge, and not an annuity. An annuity may be created for a term of years, or for the life or lives of any persons named, or in perpetuity; and in the last case, if granted to a person and his heirs, the annuity is reckoned among incorporeal hereditaments; because, although the security is personal only, the annuity will descend in the same manner as real estate. In 1854 the old statutes relating to annuities were repealed, and enrolment in Chancery of annuity deeds is no longer necessary to give them validity. But registration is necessary in the case of annuities charged on land.

In Scots law, an annuity, as such, may be charged on real estate as well as on personality. In that system it has been simply defined to be a right to a yearly payment in money; and it may be created either by the payment of the sum of money in the form of a purchase, or it may be secured over land. In the latter case the creditor, in default of his annuity, may attach the land charged, claiming a capital sum out of the land sufficient to produce an annual interest equal to the annuity, until the expiration of the same. A like rule holds for the claim upon an annuity in bankruptcy. The instrument by which, in Scotland, the annuity is constituted in either of the above forms is called a Bond of Annuity. The right to an annuity on the life of another descends to the heir of the creditor. The annuitant under a trust is entitled to have the trust kept up for security.