shall not take place for a certain number of years. The number of years within which, according to the present law of France, a perpetual annuity (rente constitutuée en perpétuel) may be made irredeemable, is limited to ten. (Code Civil, art. 1911.)

An annuity for life or years is not redeemable in the same manner; but it may be agreed by the parties to the contract that it shall be redeemable on certain terms; or it may afterwards be redeemed by consent of both parties; and where the justice of the case requires it (where there has been fraud, for instance, or the bargain is unreasonable), a court of equity will decree a redemption. When such an annuity is granted in consideration of money advanced, the annual payments may be considered as composed of two portions, one being in the nature of interest, the other a return of a portion of the principal, so calculated, that when the annuity shall have determined, the whole of the principal will be repaid. Annuities for life or years, being the only security that can be given by persons who have themselves a limited interest in their property, are frequently made in consideration of a loan. Besides this advantage, annuities for life, inasmuch as they are attended with risk, are not within the reach of the usury laws, and are therefore often used in order to evade them; and the legislature has accordingly required that certain formalities should be observed in creating them. It is enacted (by stat. 53 Geo. III. c. 141) "That every instrument by which an annuity for life is granted shall be null and void, unless within thirty days after the execution thereof there shall be enrolled in the High Court of Chancery a memorial containing the date, the names of the parties and witnesses, and the conditions of the contract; and if the lender does not really and truly advance the whole of the consideration money, that is, if part of it is returned, or is paid in notes which are afterwards fraudulently cancelled, or is retained on pretence of answering future payments; or if, being expressed to be paid in money, it is in fact paid in goods, the person charged

Annuities may be, and very frequently are, created by will, and such a bequest is considered in law as a general legacy; and, in case of a deficiency in the estate of the testator, it will abate proportionably with the other legacies. The payment of an annuity may be charged either upon some particular fund (in which case if the fund fails the annuity ceases) or upon the whole personal estate of the grantor; which is usually effected by a deed of covenant, a bond, or a warrant of attorney. If the person charged with the payment of an annuity becomes bankrupt, the annuity may be proved as a debt before the commissioners, and its value ascertained, according to the provisions of the bankrupt act (6 Geo. IV. c. 16, § 54). The value thus ascertained be comes a debt charged upon the estate of the bankrupt; and hereby both the bankrupt and his surety are discharged from all subsequent payments.

If the person on whose life an annuity is granted dies between two days of payment, the grantee has no claim whatever in respect of the time elapsed since the last day of payment: from this rule, however, are excepted such annuities as are granted for the maintenance of the grantee; and the parties may in all cases, if they choose it, by an express agreement, provide that the grantee shall have a rateable portion of the annuity for the time between the last payment and the death of the person on whose life it is granted. On government annuities a quarter's annuity is paid to the executors of an annuitant, if they come in and prove the death. (Comyns, Digest, tit. "Annuity;" Lumley, On Annuities.)

ANNŬÍTY, a term derived from the

Latin, annus, a year; signifying, in its | most general sense, any fixed sum of money which is payable either yearly or in given portious at stated periods of the year. Thus, the lease of a house, which lets for 501. a year, and which has 17 years to run, is to the owner an annuity of 501. for 17 years. In an ordinary use of the term, it signifies a sum of money payable to an individual yearly, during life. In the former case, it is called, in technical language, an annuity certain; and in the latter, a life annuity.

It is evident that every beneficial interest, which is either to continue for ever, or to stop at the end of a given time, such as a freehold, a lease, a debt to be paid in yearly instalments, &c., is contained under the general head of an annuity certain, while every such interest which terminates with the lives of any one or more individuals, all that in law is called a life-estate, and all salaries, as well as what are most commonly known by the name of life annuities, fall under the latter term. Closely connected with this part of the subject are COPYHOLDS (which see), in which an estate is held during certain lives, but in which there is a power of renewing any life when it drops, that is, substituting another life in place of the former, on payment of a fine —REVERSIONS, or the interest which the next proprietor has in any estate, &c., after the death of the present-and lifeinsurance, in which the question is, what annuity must A. pay to B. during his life, in order that B may pay a given sum to A.'s executors at his death?

If money could not be improved at interest, the value of an annuity certain would simply be the yearly sum multiplied by the number of years it is to continue to be paid. Thus a lease for 3 years of a house which is worth 100l. a year, might either be bought by paying the rent yearly, or by paying 3007. at once. A life annuity, in such a case, will be worth an annuity certain, continued for the average number of years lived by individuals of the same age as the one to whom the annuity is granted. But if compound interest be supposed, which is always the case in real transactions of this kind, the laudlord, in the case of the

1000

annuity certain just alluded to, must only receive such a sum, as when put out to interest, with 1007. subtracted every year for rent, will just be exhausted at the end of 3 years. To exemplify this, let us suppose that money can be improved at 4 per cent. In Table I., in the column headed 4 p. c. (4 per cent.), we find 2.775 opposite to 3 in the first column, by which is meant that the present value of an annuity of one pound to last 3 years is 2.775l., or 275. The present value of an annuity of 100l. under the same circumstances is therefore 277.5l., or 2771. 10s. This is the value of a lease for three years corresponding to a yearly rent of 100l. The landlord who receives this, and puts it out at 4 per cent., will, at the end of one year, have 288/. 128. From this he subtracts 100l. for the rent which has become due, and puts out the remainder, 1887. 12s., again at 4 per cent. At the end of a year this has increased to 1967. 2s. 10d., from which 100l. is again subtracted for rent. The remainder, 961. 2s. 10d., again put out at interest, becomes at the end of the year 997. 19s. 9d., within three pence of the last year's rent. This little difference arises from the imperfection of the Table, which extends to three decimal places only.

TABLE I.-Present Value of an Annuity of One Pound.

In this Table we see what would be possessed by the receiver of an annuity at the end of his term, if he put each year's annuity out at interest so soon as he received it. For example, an annuity of 17., in 40 years, at 5 per cent., amounts to 120.87., which includes 407. received altogether at the end of the different years, and 80-81. the compound interest arising from the first year's annuity, which has been 39 years at interest, the second year's annuity, which has been 38 years at interest, and so on, down to the last year's annuity, which has only just been received. When the annuity is payable half-yearly or quarterly, its present value is somewhat greater than that given in the preceding Table. For the annuitant, receiving certain portions of his annuity sooner than in the case of yearly payments, gains an additional portion of interest. Since 4 per cent. is 2 per cent. half-yearly and 1 per cent. quarterly, and since every term contains twice as many half-years as years, and four times as many quarters, it is evident that an annuity of 10cl. a-year, payable half-yearly, at 4 per cent., for 10 years, is the same in present value as one of 5cl. per annum, payable yearly, at 2 per cent., for 20 years. Again, 100l. a-year, payable quarterly for 10 years, money being at 4 per cent., is equivalent to an annuity of 257., payable yearly for 40 years, money being at 1 per cent.

The principles on which the calculation

of life annuities depends will be more fully explained in the articles PROBABILITY and MORTALITY. Let us suppose 100 persons, all of the same age, buy a life annuity at the same office. Let us also suppose it has been found out, that of 100 persons at that age, 10 die in the first year, on the average, 10 more in the second year, and so on. If then it can be relied upon that 100 persons will die nearly in the same manner as the average of mankind, or at least that in such a number the longevity of some will be compensated by the unexpected death of others, the fair estimation of the value of a life annuity to be granted to each may be made as follows:-To make the question more distinct, let us suppose the bargain to be made on the 1st of January, 1844, so that payment of the annuities is due to the survivors on new-year's day of each year. Moreover let each year's annuity be made the subject of a separate contract. The first question is, what ought each individual to pay in order that he may receive the annuity of 11., if he survives in 1845. By the general law of mortality, we suppose that only 90 will remain to claim, who will, therefore, receive 90l. among them, the remaining 10 having died in the interval. It is sufficient, therefore, to meet the claims of 1845, that the whole 100 pay among them, January 1, 1844, such a sum as will, when put out at interest (suppose 4 per cent.) amount to 90l. on January 1, 1845. This sum is 86 654l., and its hundredth part is 86654/., which is, therefore, what each should pay to entitle himself to receive the annuity in 1845. There will be only 80 to claim in 1846, and, therefore, the whole 100 must among them pay as much as will, put out at 4 per cent. for 2 years, amount to 80l. This sum is 73.9681., and its hundreth part is 73968., which is, therefore, what each must pay, in order to receive the annuity, if he lives, in 1846. The remaining years are treated in the same way, and the sum of the shares of each individual for the different years, is the present value of an annuity for his life. must observe, that in the term value of an annuity it is always implied that the first annuity becomes payable at the expira

We

tion of a year after the payment of the purchase-money.

The value of a life annuity depends, therefore, upon the manner in which it is presumed a large number of persons, similarly situated with the buyer, would die off successively. Various Tables of these decrements of life, as they are called, have been constructed, from observations made among different classes of lives. Some make the mortality greater than others; and of course, Tables which give a large mortality, give the value o the annuity smaller than those which suppose men to live longer. Those who buy annuities would, therefore, be glad to be rated according to tables of high mortality or low expectation of life; while those who sell them would prefer receiving the price indicated by tables which give a lower rate of mortality. In insurances the reverse is the case: the shorter the time which a man is supposed to live, the more must he pay the office, that the latter may at his death have accumulated wherewithal to pay his executors. We now give in Table V. the values of annuities according to three of the most celebrated Tables.

TABLE V.—Present Value, or Purchasemoney, of a Life Annuity.

Northampton.

Carlisle. Gov.M. Gov.F. Age. 3 p.c. 4 p.c. 5p.c. 3p.c. 4p.c. 5p.c. 4p.c. 4p.c. 0 12.3 10.3 8.9 5 20 5 17 2 14.8

10 27 17 5 15 1

17.3 14.3 12.1

23.7 19.6 16.6 19.3 20.0

23.5 19 6 16.7 18.8

19.7

15 19 7 16 8 14 6 22.6 19.0 16 2 18.0 19.1

20 18 6 16 0 14 0

2 7 18 4 15-8

17.3 18.6

25 17.8 15.4 13.6 20.7 17.6 15 3 16.9 18.1 30 16.9 14.8 13.1 19.6 16.9 14 16 4 17 5 35 15 9 14.0 12.5 18.4 16 0 14 1 15.7 16.9 40 14-8 13.2 11.8 17.1 15.1 13.4 14.9 16.2 45 13.7 12.3 11.1 15.9 14.1 12.6 13.8 15:3 50 12-4 11 3 10.3 14.3 12.9 11.7 12.4 14.2 55 11.2 10 2 9.4 12.4 11.3 10.3 11.0 12.8 60 9.8 90 8.4 10.5 9.7 8.9 65 8.3 7.8 7.3 8.9 8.3 7.8 8.2 9.6 70 6.7 6.4 6.0 7.1 6.7 6.3 6.8 7.9 75 5.2 5.0 4.7 5.5 5.2 5.0 5.4 6.3 80.8 3.6 35 4.4 4.2 4.0 3.8 4.9 95 2.6 2.5 2.5 3.2 3.1 3.0 2.3 3.8 90 1.8 1.8 1.7 2.5 2.4 2.3 1.3 2.1 95 ⚫2 .2 .2 2.8 27 2.6 .6 1.0

high a mortality at all the younger and middle ages of life, and, consequently, too low a value of the annuity. The second is from the Carlisle Table, formed by Mr. Milne, froin observations made at Carlisle. It gives much less mortality than most other Tables, and, therefore, gives higher values of the annuities; but it has since been proved to represent the actual state of life among the middle classes, in the century now ending, with much greater accuracy than could have been supposed, considering the local character of the observations from which it was derived. The third table is that constructed by Mr. Finlaison, from the observation of the mortality in the govern ment tontines and among the holders of annuities granted by government in redemption of the national debt, and differs from the former two in distinguishing the lives of males from those of females. Most observations hitherto published unite in confirming the fact, that females, on the average, live longer than males, and in the annuities now granted by government, a distinction is made accordingly. The mean between the values of annuities on male and female lives,

according to the Government Tables, agrees pretty nearly with the Carlisle Tables, the rate of interest being the

same.

The first of these is calcnlated from the Northampton Table, formed by Dr. Price, from observations of burials, &c., at Northampton. As compared with all other Tables of authority, it gives too