ANNUITY, from the Latin annus, a year, is a. sum of money paid annually. The term, in its full meaning, expresses an obligation on one party to pay, and a right in another to receive the amount. The different kinds of annuities that may exist are as various as the conditions and fancies of those concerned in them; and it is impos posible to define them all. An A. may be for the life of any person, however long that may be, becoming extinguished only by his death. It may be perpetual, so that as each enjoyer of it dies, his heirs may succeed to it. It may be on the life of the survivor of any number of persons—for instance, a father may leave to his five daughters an A. of £500 a year from his estate, to be enjoyed by the latest survivor, so that while the five are alive, they have £100 each; after the first death among them, the lapsed share is dis tributed among the survivors, giving them £125, each; so on, the last survivor enjoying the whole £500. On the other han1, each might have a separate A. terminat lug at her death; and again, instead of either of these simple arrangements, there might be, and often is, a more complex adjustment, giving the survivors on each death a cer tain proportion only of the deceased's A. An A. may begin immediately, and stop on a contingency, such as the death of a person to whom the annuitant is heir. It may be "deferred," so as to begin to be payable only after the lapse of so many years; and then it may either be payable absolutely in perpetuity, or for a given number of years, or it may be payable to an annuitant only for the remaining years of his life, if lie survive the contingency.
It will thus be seen that here is infinite variety in the nature of annuities, and conse quently, in the calculations regarding them. The fixed elements of such calculations, independently of this variety, are in themselves double, being vital statistics, and the profit or interest of money. As to the former, they can only apply, of course, to the adjustment of annuities on a large scale. If a person should sell a single A.—that is to say, engage for a sum down to pay a certain person an A. for life—no study of vital sta
tistics could make his bargain other than a chance; and though he went on the most approved tables, it might occur either that the annuitant dies immediately, leaving the whole purchase-money as his profit, or that the annuitant lives to extreme old age, and renders him a great loser by the bargain. But on a large, and especially on a national the rate of mortality and the value of life may be so nicely rendered in statis tics, that a market may be opened for the purchase and sale of annuities at their exact value—that is to say, at such a rate that the sum paid in from time to time by persons purchasing annuities, shall just serve to pay each annuitant's annual claim. Such vital statistics, however, can only be obtained through a very accurate and long continued registration of births, deaths, and marriages (q.v.); and it is known that the government having adjusted the price of annuities by the celebrated Northampton tables, contracted a losing bargain with their annuitants as a body, and, without being conscious of it until afterwards, sacrificed a considerable amount of public money.
The second element, besides vital statistics, in the calculation of annuities, is the profit or interest of money. If this did not require to be considered, an A. of £1 a year for 10 years would just cost £10. But while paying the A., the person who has engaged for it is drawing the interest of the money. If lie sold an A. of £1 a year for 10 years for £10, he would be drawing the interest of £10 for the first year, £9 for the second, and so on; and the annuitant's bargain would be to a like extent disadvantageous. As the interest of money' may be various, so may this element of the calculation of an A.; and to calculate it with reference to future indefinite variations, is of course impossible. It will be seen at once that when the variety of kinds of A. have to be adjusted to differ ent rates of profit, an immense field is opened for calculation. It is, in fact, a province of algebraic science in which several men have achieved reputations.