See also:

• ANNUITY (from Lat. annus, a year)

ANNUITY (from See also:

• LAT

Lat. annus, a See also:

• YEAR

year)  , a periodical See also:

• PAYMENT (Fr. paiement, from payer, to pay; Lat. pacare, to appease, pax, peace)

payment, made annually, or at more frequent intervals, either for a fixed See also:

• TERM

term of years, or during the continuance of a given See also:

• LIFE

life, or a See also:

• COMBINATION (Lat. combinare, to combine)

combination of lives . In technical See also:

• LANGUAGE (adapted from the Fr. langage, from langue, tongue, Lat. lingua)

language an See also:

• ANNUITY (from Lat. annus, a year)

annuity is said to be payable for an assigned status, this being a See also:

• GENERAL
• GENERAL (Lat. generalis, of or relating to a genus, kind or class)

general word chosen in preference to such words as " See also:

• TIME (0. Eng. Lima, cf. Icel. timi, Swed. timme, hour, Dan. time; from the root also seen in " tide," properly the time of between the flow and ebb of the sea, cf. O. Eng. getidan, to happen, " even-tide," &c.; it is not directly related to Lat. tempus)
• TIME, MEASUREMENT OF
• TIME, STANDARD

time," " term " or " See also:

• PERIOD
• PERIOD (Gr. irepioSos, a going or way round, circuit, aepi, round, and &Sis, way, road)

period," because it may include more readily either a term of years certain, or a life or combination of lives . The magnitude of the annuity is the sum to be paid (and received) in the course of each See also:

• YEAR

year . Thus, if £roo is to be received each year by a See also:

• PERSON, OFFENCES AGAINST THE

person, he is said to have " an annuity of See also:

• FLOOD (in O. Eng. flod, a word common to Teutonic languages, cf. Ger. Flut, Dutch vloed, from the same root as is seen in " flow," " float ")
• FLOOD, HENRY (1732-1791)

flood' If the payments are made See also:

• HALF

half-yearly, it is sometimes said that he has " a half-yearly annuity of Itoo "; but to avoid See also:

• AMBIGUITY (Fr. ambiguite, med. Lat. ambiguitas, from Lat. ambiguus, doubtful; ambi, both ways, agere, to drive)

ambiguity, it is more commonly said he has an annuity of ;See also:

• LOO (formerly called " Lanterloo," Fr. lanturlu, the refrain of a popular 17th-century song)

loo, payable by half-yearly instalments . The former expression, if clearly understood, is prefer-able on See also:

• ACCOUNT
• ACCOUNT (through O. Fr. acont, Late Lat. comptum, cornputare, to calculate)

account of its brevity . So we may have quarterly, monthly, weekly, daily annuities, when the annuity is payable by quarterly, monthly, weekly or daily instalments . An annuity ANNUITY 75 is considered as accruing during each instant of the status for which it is enjoyed, although it is only payable at fixed intervals . If the enjoyment of an annuity is postponed until after the See also:

• LAPSE (Lat. lapses, a slip or departure)

lapse of a certain number of years, the annuity is said to be deferred . If an annuity, instead of being payable at the end of each year, half-year, &c., is payable in advance, it is called an annuity-due . If an annuity is payable for a term of years See also:

• INDEPENDENT

independent of any contingency, it is called an annuity certain; if it is to continue for ever, it is called a See also:

• PERPETUITY (Lat. perpetuus, continuous)

perpetuity; and if in the latter See also:

• CASE
• CASE, JOHN (d. 1600)

case it is not to commence until after a term of years, it is called a deferred perpetuity . An annuity depending on the continuance of an assigned life or lives, is sometimes called a life annuity; but more commonly the See also:

• SIMPLE

simple term " annuity " is understood to mean a life annuity, unless the. contrary is stated . A life annuity, to cease in any event after a certain term of years, is called a temporary annuity .

The holder of an annuity is called an annuitant, and the person on whose life the annuity depends is called the nominee . If not otherwise stated, it is always understood that an annuity is payable yearly, and that the See also:

• ANNUAL

annual payment (or See also:

• RENT

rent, as it is sometimes called) is £r . It is, however, customary to consider the annual payment to be, not £r, but simply r, the reader supplying whatever monetary unit he pleases, whether See also:

• POUND
• POUND (2)—(a)

pound, See also:

• DOLLAR

dollar, See also:

• FRANC

franc, Thaler, &c . The annuity is the totality of the payments to be made (and received), and is so understood by all writers on the subject; but some have also used the word to denote an individual payment (or rent), speaking, for instance, of the first or second year's annuity,—a practice which is calculated to introduce confusion and should therefore be carefully avoided . Instances of perpetuities are the dividends upon the public See also:

• STOCKS

stocks in See also:

• ENGLAND
• ENGLAND, THE CHURCH OF

England, See also:

• FRANCE
• FRANCE, ANATOLE (1844– )

France and some other countries . Thus, although it is usual to speak of £loo See also:

• CONSOLS

consols, the reality is the yearly See also:

• DIVIDEND (Lat. dividendum, a thing to be divided)

dividend which the See also:

• GOVERNMENT
• GOVERNMENT (0. Fr. governement, mod. gouvernement, O. Fr. governer, mod. gouverner, from Lat. gubernare, to steer a ship, guide, rule; cf. Gr. xv(3epvav)

government pays by quarterly instalments . The practice of the See also:

• FRENCH
• FRENCH, DANIEL CHESTER (1850– )
• FRENCH, NICHOLAS (1604-1678)

French in this, as in many other matters, is more logical . In speaking of their public funds (rentes) they do not mention the ideal See also:

• CAPITAL (i.e. capital stock or fund)
• CAPITAL (Lat. caput, head)

capital sum, but speak of the annuity or annual payment that is received by the public creditor . Other instances of perpetuities are the incomes derived from the debenture stocks of railway companies, also the See also:

• FEU

feu-duties commonly payable on See also:

• HOUSE
• HOUSE (O. Eng. hiss, a word common to Teutonic languages, cf. Dut. huis, Ger. Haus; in Gothic it is only found in gudhiss, a temple; it may be ultimately connected with the root of " hide," conceal)

house See also:

• PROPERTY

property in See also:

• SCOTLAND
• SCOTLAND, CHURCH OF
• SCOTLAND, EPISCOPAL CHURCH OF

Scotland . The number of years' See also:

• PURCHASE

purchase which the perpetual annuities granted by a government or a railway See also:

• COMPANY

company realize in the open See also:

• MARKET (Lat. mercatus, trade or place of trade)

market, forms a very simple test of the See also:

• CREDIT (Lat. credere, to believe)

credit of the various governments or See also:

• RAILWAYS

railways . Terminable Annuities are employed in the See also:

• SYSTEM

system of See also:

• BRITISH

British public See also:

• FINANCE

finance as a means of reducing the See also:

• NATIONAL

National See also:

• DEBT (Lat. debitum, a thing owed)

Debt (q.v.) . This result is attained by substituting for a perpetual annual See also:

• CHARGE
• CHARGE (through the Fr. from the Late Lat. carricare, to load in a carrus or wagon; cf. " cargo ")

charge (or one lasting until the capital which it represents can be paid off en bloc), an annual charge of a larger amount, but lasting for a See also:

• SHORT, FRANCIS JOB (1857– )

short term .

The latter is so calculated as to pay off, during its existence, the capital which it replaces, with See also:

• INTEREST

interest at an assumed or agreed See also:

• RATE

rate, and under specified conditions . The See also:

• PRACTICAL

practical effect of the substitution of a terminable annuity for an See also:

• OBLIGATION

obligation of longer currency is to bind the See also:

• PRESENT

present See also:

• GENERATION (from Lat. generare, to beget, procreate; genus, stock, race)

generation of citizens to increase its own obligations in the present and near future in See also:

• ORDER
• ORDER (through Fr. ordre, for earlier ordene, from Lat. ordo, ordinis, rank, service, arrangement; the ultimate source is generally taken to be the root seen in Lat. oriri, rise, arise, begin; cf. " origin ")
• ORDER, HOLY

order to diminish those of its successors . This end might be attained in other ways; for instance,.by setting aside out of See also:

• REVENUE
• REVENUE (0. Fr. revenu, from revenir, to return)

revenue a fixed annual sum for the purchase and cancellation of debt (See also:

• PITT, THOMAS (1653-1726)
• PITT, WILLIAM (1759-1806)

Pitt's method, in intention), or by fixing the annual debt charge at a figure sufficient to provide a margin for reduction of the See also:

• PRINCIPAL

principal of the debt beyond the amount required for interest (See also:

• SIR

Sir See also:

• STAFFORD
• STAFFORD, EARLS AND MARQUESSES OF

Stafford . See also:

• NORTHCOTE, JAMES (1746-1831)

Northcote's method), or by providing an annual surplus of revenue over See also:

• EXPENDITURE

expenditure (the " Old Sinking Fund "), available for the same purpose . All these methods have been tried in the course of British See also:

• FINANCIAL

financial See also:

• HISTORY

history, and the second and third of them are still employed; but on the whole the method of terminable annuities has been the one preferred by chancellors of. the See also:

• EXCHEQUER

exchequer and by See also:

• PARLIAMENT (Anglo-Lat. parliamentum, Fr. parlement, from parler, to speak)

parliament . Terminable annuities, as employed by the British government, fall under two heads:—(a) Those issued to, or held by private persons; (b) those held by government departments or by funds under government See also:

• CONTROL (Fr. contrdle, older form contre rolle, from Med. Lat. contra-rotulus, a counter roll or copy of a document used to check the original; there is no instance in English of the use of " control " in this, its literal, meaning)

control . The important difference between these two classes is that an annuity under (a), once created, cannot be modified except with the holder's consent, i.e. is practically unalterable without a See also:

• BREACH (Mid. Eng. breche, derived from the common Teutonic root brec, which appears in " break," Ger. brechen, &c.)

breach of public faith; whereas an annuity under (b) can, if necessary, be altered by inter-departmental arrangement under the authority of parliament . Thus annuities of class (a) fulfil most perfectly the See also:

• OBJECT

object of the system as explained above; while those of class (b) have the See also:

• ADVANTAGE

advantage that in times of emergency their operation can be suspended without any inconvenience or breach of faith, with the result that the resources of government can on such occasions be materially increased, apart from any additional See also:

• TAXATION
• TAXATION (from " tax," derived, through the French, from Lat. taxare, to appraise, which again is connected with the same root as tangere, to touch)

taxation . For this purpose it is only necessary to retain as a charge on the income of the year a sum equal to the (smaller) perpetual charge which was originally, replaced by the (larger) terminable charge, whereupon the difference between the two amounts is temporarily released, while ultimately the increased charge is extended for a period equal to that for which it is suspended . Annuities of class (a) were first instituted in 18o8, but are at present mainly regulated by an See also:

• ACT (Lat. actus, actum)

act of 1829 . They may be granted either for a specified life, or two lives, or for an arbitrary term of years; and the See also:

• CONSIDERATION (from Lat. considerare, to look at closely, examine, generally taken to be from con-, and the base seen in sidus, sideris, a star, the word being supposed to be originally an astrological or astronomical term)

consideration for them may take the See also:

• FORM (Lat. forma)

form either of See also:

• CASH

cash or of government stock, the latter being cancelled when the annuity is set up . Annuities (b) held by government departments date from 1863 .

They have been created in See also:

• EXCHANGE

exchange for permanent debt surrendered for cancellation, the principal operations having been effected in 1863, 1867, 187o, 1874, 1883 and 1899 . Annuities of this class do not affect the public at all, except of course in their effect on the market for government securities . They are merely financial operations between the government, in its capacity as the banker of savings See also:

• BANKS, GEORGE LINNAEUS (1821-1881)
• BANKS, NATHANIEL PRENTISS (1816–1894)
• BANKS, SIR JOSEPH
• BANKS, THOMAS (1735-1805)

banks and other funds, and itself, in the capacity of custodian of the national finances . Savings See also:

• BANK

bank depositors are not concerned with the manner in which government invests their See also:

• MONEY

money, their rights being confined to the See also:

• RECEIPT (M.E. receite, derived through Fr. from Lat. recepta, participle of recipere, to receive)

receipt of interest and the repayment of deposits upon specified conditions . The case is, however, different as regards See also:

• FORTY

forty millions of consols (included in the above figures), belonging to suitors in See also:

• CHANCERY

chancery, which were cancelled and replaced by a terminable annuity in 1883 . As the liability to the suitors in that case was for a specified amount of stock, See also:

• SPECIAL

special arrangements were made to ensure the ultimate replacement of the precise amount of stock cancelled . Annuity Calculations.-The mathematical theory of life annuities is based upon a knowledge of the rate of mortality among mankind in general, or among the particular class of persons on whose lives the annuities depend . It involves a mathematical treatment too complicated to be dealt with fully in this See also:

• PLACE (through Fr. from Lat. platea, street; Gr. IrAar6s, wide)

place, and in practice it has been reduced to the form of tables, which vary in different places, but which are easily accessible . The history of the subject may, however, be sketched . See also:

• ABRAHAM, or ABRAM (Hebrew for " father is high ")

Abraham See also:

• DEMOIVRE, ABRAHAM (1667-1754)

Demoivre, in his Annuities on Lives, propounded a very simple See also:

• LAW
• LAW (0. Eng. lagu, M. Eng. lawe; from an old Teutonic root lag, " lie," what lies fixed or evenly; cf. Lat. lex, Fr. loi)
• LAW, JOHN (1671—1729)
• LAW, WILLIAM (1686-1761)

law of mortality which is to the effect that, out of 86 See also:

• CHILDREN, LAW RELATING TO

children See also:

• BORN, IGNAZ, EDLER VON (1742–1791)

born alive, r will See also:

• DIE
• DIE (Fr. de, from Lat. datum, given)

die every year until the last See also:

• DIES, CHRISTOPH ALBERT (1755-1822)

dies between the ages of 85 and 86 . This law agreed sufficiently well at the See also:

• MIDDLE

middle ages of life with the mortality deduced from the best observations of his time; but, as observations became more exact, the approximation was found to be not sufficiently See also:

• CLOSE
• CLOSE (from Lat. clausum, shut)
• CLOSE, MAXWELL HENRY (1822-1903)

close . This was particularly the case when it was desired to obtain the value of See also:

• JOINT (through Fr. from Lat. junctum, jungere, to join)

joint life, contingent or other complicated benefits .

Therefore Demoivre's law is entirely devoid of practical utility . No simple See also:

• FORMULA
• FORMULA (Lat. diminutive of forma, shape, pattern, &c., especially used of rules of judicial procedure)

formula has yet been discovered that will represent the rate of mortality with sufficient accuracy . The rate of mortality at each See also:

• AGE (Fr. age, through late Lat. aetaticum, from aetas)

age is, therefore, in practice usually determined by a See also:

• SERIES (a Latin word from serere, to join)

series of figures deduced from observation; and the value of an annuity at any age is found from these See also:

• NUMBERS, BOOK OF
• NUMBERS, PARTITION OF

numbers by means of a series of arithmetical calculations . The mortality table here given is an example of See also:

• MODERN

modern use . The first writer who is known to have attempted to obtain, on correct mathematical principles, the value of a life annuity, was See also:

• JAN

Jan De Witt, See also:

• GRAND

grand See also:

• PENSIONARY

pensionary of See also:

• HOLLAND
• HOLLAND, CHARLES (1733–1769)
• HOLLAND, COUNTY AND PROVINCE OF
• HOLLAND, HENRY FOX, 1ST BARON (1705–1774)
• HOLLAND, HENRY RICH, 1ST EARL OF (1S9o-,649)
• HOLLAND, HENRY RICHARD VASSALL FOX, 3RD
• HOLLAND, JOSIAH GILBERT (1819-1881)
• HOLLAND, PHILEMON (1552-1637)
• HOLLAND, RICHARD, or RICHARD DE HOLANDE (fl. 1450)
• HOLLAND, SIR HENRY, BART

Holland and See also:

• WEST
• WEST, BENJAMIN (1738-1820)
• WEST, NICHOLAS (1461-1533)

West See also:

• FRIESLAND, or VRIESLAND

Friesland . Our knowledge of his writings on the subject is derived from twopapers contributed by See also:

• FREDERICK
• FREDERICK (Mod. Ger. Friedrich; Ital. Federigo; Fr. Frederic and Federic; M.H.G. Friderich; O.H.G. Fridurih, " king or lord of peace," from O.H.G. fridu, A.S. frith, " peace," and rfh " rich," " a ruler," for derivation of which see HENRY)

Frederick Hendriks to the Assurance See also:

• MAGAZINE

Magazine, vol. ii. p . 222, and vol. iii. p . 93 . The former of these contains a See also:

• TRANSLATION

translation of De Witt's See also:

• REPORT (O.Fr. report or raport, modern rapport, from O.Fr. reporter, mod. rap porter, Lat. reportare, to bring back, in poetical use only, of bringing back an account, news, &c.)

report upon the value of life annuities, which was prepared in consequence of the See also:

• RESOLUTION

resolution passed by the states-general, on the 25th of See also:

• APRIL

April 1671, to negotiate funds by life annuities, and which was distributed to the members on the 3oth of See also:

• JULY

July 1671 . . The latter contains the translation of a number of letters addressed by De Witt to Burgomaster Johan Hudde, bearing See also:

• DATES

dates from See also:

• SEPTEMBER (Lat. septem, seven)

September 167o to See also:

• OCTOBER

October 1671 . The existence of De Witt's report was well known among his contemporaries, and Hendriks collected a number of extracts from various authors referring to it; but the Number Living and Dying at each Age, out of ro,000 entering at Age 10 . Age .

Living . Dying . Age . Living . Dying . 10 ro,000 79 54 6791 129 11 9,921 0 55 6662 153 12 9,921 40 56 65o9 150 13 9,881 35 57 6359 152 14 9,846 40 58 6207 156 15 9,806 22 59 605 1 153 16 9,784 0 6o 5898 184 i 17 9,784 41 61 5714 186 r8 9,743 59 62 5528 191 19 9,684 68 63 5337 200 20 9,616 56 64 5137 206 21 9,560 67 65 4931 215 22 9,493 59 66 4716 220 23 9,434 73 67 4496 220 24 9,361 64 68 4276 237 25 9,297 48 69 4039 246 26 9,249 64 70 3793 213 27 9,185 6o 71 358o 222 28 9,125 71 72 3358 268 29 9,054 67 73 3090 243 30 8,987 74 74 2847 300 31 8,913 65 75 2547 241 32 8,848 74 76 2306 245 33 8,774 73 77 2061 224 34 8,701 . 76 78 1837 226 35 8,625 71 79 1611 219 36 8,554 75 8o 1392 196 37 8,479 81 81 1196 191 38 8,398 87 82 1005 173 39 8,311 88 83 832 172 40 8,223 81 84 66o 119 41 8,142 85 85 541 117 42 8,057 87 86 424 92 43 7,970 84 87 332 72 44 7,886 93 88 260 74 45 7,793 97 89 186 36 46 7,696 96 90 15o 34 47 7,600 107 91 116 36 48 7,493 Io6 92 8o 36 49 7,387 113 93 44 29 50 7,274 120 94 15 0 51 7,154 124 95 15 5 52 7,030 120 96 10 10 53 6,910 119 report is not contained in any collection of his See also:

• WORKS

works extant, and had been entirely lost for 18o years, until Hendriks discovered it among the See also:

• STATE
• STATE, GREAT OFFICERS OF

state archives of Holland in company with the letters to Hudde . It is a document of extreme interest, and (notwithstanding some inaccuracies in the reasoning) of very See also:

• GREAT

great merit, more especially considering that it was the very first document on the subject that was ever written . It appears that it had See also:

• LONG, GEORGE (1800-1879)
• LONG, JOHN DAVIS (1838– )

long been the practice in Holland for life annuities to be granted to nominees of any age, in the See also:

• CONSTANT, BENJAMIN (1845-1902)

constant proportion of See also:

• DOUBLE
• DOUBLE (from the Mid. Eng. duble, the form which gives the present pronunciation, through the Old Er. duble, from Lat. duplus, twice as much)

double the rate of interest allowed on stock; that is to say, if the towns were borrowing money at 6 %, they would be willing to See also:

• GRANT (from A.-Fr. graunter, O. Fr. greanter for creanter, popular Lat. creantare, for credentare, to entrust, Lat. credere, to believe, trust)
• GRANT, ANNE (1755-1838)
• GRANT, CHARLES (1746-1823)
• GRANT, GEORGE MONRO (1835–1902)
• GRANT, JAMES (1822–1887)
• GRANT, JAMES AUGUSTUS (1827–1892)
• GRANT, ROBERT (1814-1892)
• GRANT, SIR ALEXANDER
• GRANT, SIR FRANCIS (1803-1878)
• GRANT, SIR JAMES HOPE (1808–1895)
• GRANT, SIR PATRICK (1804-1895)
• GRANT, U
• GRANT, ULYSSES SIMPSON (1822-1885)

grant a life annuity at 12 %, and so on . De Witt states that " annuities have been sold, even in the present See also:

• CENTURY (from Lat. centuria, a division of a hundred men)

century, first at six years' purchase, then at seven and eight; and that the See also:

• MAJORITY (Fr. majorite; Med. Lat. majoritas; Lat. major, greater)

majority of all life annuities now current at the See also:

• COUNTRY (from the Mid. Eng. contre or contrie, and O. Fr. cuntree; Late Lat. contrata, showing the derivation from contra, opposite, over against, thus the tract of land which fronts the sight, cf. Ger. Gegend, neighbourhood)

country's expense were obtained at nine years' purchase "; but that the See also:

• PRICE
• PRICE, BARTHOLOMEW (1818–1898)
• PRICE, BONAMY (1807-1888)
• PRICE, RICHARD (1723-1791)

price had been increased in the course of a few years from eleven years' purchase to twelve, and from twelve to fourteen . He also states that the rate of interest had been successively reduced from 6; to 5 %, and then to 4 % . The principal object of his report is to prove that, taking interest at 4 %, a life annuity was See also:

• WORTH
• WORTH, CHARLES FREDERICK (1825-1895)

worth at least sixteen years' purchase; and, in fact, that an annuitant purchasing an annuity for the life of a See also:

• YOUNG
• YOUNG, A
• YOUNG, ARTHUR (1741-1820)
• YOUNG, BRIGHAM (1801-1877)
• YOUNG, CHARLES MAYNE (1777–1856)
• YOUNG, EDWARD (1683–1765)
• YOUNG, JAMES (1811-1883)
• YOUNG, THOMAS (1773-1829)

young and healthy nominee at sixteen years' purchase, made an excellent bargain .

It may be mentioned that he argues that it is more to the advantage, both of the country and of the private investor, that the public loans should be raised by way of grant of life annuities rather than perpetual annuities . It appears conclusively from De Witt's See also:

• CORRESPONDENCE
• CORRESPONDENCE (from med. scholastic Lat. correspondentia, corrcspondere, compounded of Lat. cum, with, and respond ere, to answer; cf. Fr. correspondance)

correspondence with Hudde, that the rate of mortality assumed as the basis of his calculations was deduced from careful examination of the mortality that had actually prevailed among the nominees on whose lives annuities had been granted in former years . De Witt appears to have come to the conclusion that the See also:

• PROBABILITY (Lat. probabilis, probable or credible)

probability of See also:

• DEATH

death is the same in any half-year from the age of 3 to 53 inclusive; that in the next ten years, from 53 to 63, the probability is greater in the ratio of 3 to 2; that in the next ten years, from 63 to 73, it is greater in. the ratio of 2 to 1; and in the next seven years, from 73 to 8o, it is greater in the ratio of 3 to I; and he places the limit of human life at 80 . If a mortality table of the usual form is deduced from these suppositions, out of 212 persons alive at the age of 3, 2 will die every year up to 53, 3 in each of the ten years from 53 to 63, 4 in each of the next ten years from 63 to 73, and 6 in each of the next seven years from 73 to 8o, when all will be dead . De Witt calculates the value of an annuity in the following way . Assume that annuities on Io,000 lives each ten years of age, which satisfy the Hm mortality table, have been See also:

• PURCHASED

purchased . Of these nominees 79 will die before attaining the age of r1, and no annuity payment will be made in respect of them; none will die between the ages of 11 and 12, so that annuities will be paid for one year on 9921 lives; 40 attain the age of 12 and die before 13, so that two payments will be made with respect to these lives . Reasoning in this way we see that the annuities on 35 of the nominees will be payable for three years; on 40 for four years, and so on . Proceeding thus to the end of the table, 15 nominees attain the age of 95, 5 of whom die before the age of 96, so that 85 payments will be paid in respect of these 5 lives . Of the survivors all die before attaining the age of 97, so that the annuities on these lives will be payable for 86 years . Having previously calculated a table of the values of annuities certain for every number of years up to 86, the value of all the annuities on the 10,000 nominees will be found by taking 40 times the value of an annuity for 2 years, 35 times the value of an annuity for 3 years, and so on—the last term being the value of to annuities for 86 years—and adding them together; and the value of an annuity on one of the nominees will then be found by dividing by ro,000 . Before leaving the subject of De Witt, we may mention that we find in the correspondence a distinct See also:

• SUGGESTION

suggestion of the law of mortality that bears the name of Demoivre .

In De Witt's See also:

• LETTER (through Fr. lettre from Lat. littera or litera, letter of the alphabet; the origin of the Latin word is obscure; it has probably no connexion with the root of linere, to smear, i.e. with wax, for an inscription with a stilus)

letter, dated the 27th of October 1671 (See also:

• ASS (O.E. assa; Lat. asinus)
• ASS, FEAST OF THE

Ass . Mag. vol. iii. p . 107), he speaks of a " provisional See also:

• HYPOTHESIS (from Gr. inrorcOivat, to put under; cf. Lat. suppositio, from sub-ponere)

hypothesis " suggested by Hudde, that out of 8o young lives (who, from the context, may be taken as of the age 6) about r dies annually . In strictness, therefore, the law in question might be more correctly termed Hudde's than Demoivre's . De Witt's report being thus of the nature of an unpublished state See also:

• PAPER
• PAPER (Fr. papier, from Lat. papyrus)

paper, although it contributed to its author's reputation, did not contribute to advance the exact knowledge of the subject; and the author to whom the credit must be given of first showing how to calculate the value of an annuity on correct principles is See also:

• EDMUND
• EDMUND, or EADMUND (c. 980-1016)
• EDMUND, SAINT [EDMUND RICE] (d. 1240)

Edmund See also:

• HALLEY, EDMUND (1656–1742)

Halley . He gave the first approximately correct mortality table (deduced from the records of the numbers of deaths and baptisms in the See also:

• CITY (through Fr. cite, from Lat. civitas)

city of See also:

• BRESLAU (Polish Wraclaw)

Breslau), and showed how it might be employed to calculate the value of an annuity on the life of a nominee of any age (see Phil . Trans . 1693; Ass . Mag. vol. xviii.) . Previously to Halley's time, and apparently for many years subsequently, all dealings with life annuities were based uponmere conjectural estimates . The earliest known reference to any estimate of the value of life annuities See also:

• ROSE
• ROSE (Rosa)
• ROSE, GEORGE (1744-1818)
• ROSE, HUGH JAMES (1795—1838)
• ROSE, WILLIAM STEWART (1775-1843)

rose out of the requirements of the Falcidian law, which (40 B.c.) was adopted in the See also:

• ROMAN

Roman See also:

• EMPIRE

empire, and which declared that a testator should not give more than three-fourths of his property in legacies, so that at least one-See also:

• FOURTH

fourth must go to his legal representatives . It is easy to see how it would occasionally become necessary, while this law was in force, to value life annuities charged upon a testator's See also:

• ESTATE (through O. Fr. estat, mod. flat, from Lat. status, state, condition, position, stare, to stand)

estate .

See also:

• AEMILIUS, PAULUS (PAOLO Ea111.io) (d. 1529)

Aemilius See also:

• MACER, AEMILIUS

Macer (A.D . 230) states that the method which had been in See also:

• COMMON

common use at that time was as follows:—From the earliest age until 30 take 30 years' purchase, and for each age after 30 deduct i year . It is obvious that no consideration of See also:

• COMPOUND
• COMPOUND (from Lat. componere, to combine or put together)

compound interest can have entered into this estimate; and it is easy to see that it is See also:

• EQUIVALENT

equivalent to assuming that all persons who attain the age of 30 will certainly live to the age of 6o, and then certainly die . Compared with this estimate, that which was propounded by the praetorian See also:

• PREFECT (prefet)

prefect See also:

• ULPIAN (DoMrrIus ULPIANUS)

Ulpian was a great improvement . His table is as follows:-- Age . Years' Age . Years' Purchase . Purchase . See also:

• BIRTH (a word common in various forms to Teutonic languages from the root of the verb " to bear ")

Birth to 20 , 30 45 to 46 14 20 „ 25 28 46 ,, 47 13 25 „ 30 25 47 ,, 48 12 30 ,, 35 22 48 ,, 49 II 35 ,, 40 20 49 ,, 50 to 40 „ 41 19 50 „ 55 9 41 „ 42 18 55 „ 60 7 42 ,, 43 17 6o and c 43 ,, 44 16 upwards 1 44 „ 45 15 Here also we have no See also:

• REASON (Lat. ratio, through French raison)

reason to suppose that the See also:

• ELEMENT (Lat. elementum)

element of interest was taken into consideration; and the See also:

• ASSUMPTION, FEAST OF

assumption, that between the ages of 40 and 50 each addition of a year to the nominee's age diminishes the value of the annuity by one year's purchase, is equivalent to assuming that there is no probability of the nominee dying between the ages of 40 and 50 . Considered, however, simply as a table of the See also:

• AVERAGE

average duration of life, the values are fairly accurate . At all events, no more correct estimate appears to have been arrived at until the close of the 17th century . The See also:

• MATHEMATICS (Gr. /saBnµar1Kil, Sc. vOcvn or E7rlQTt'µn; from p iN.La, "learning" or "science ")

mathematics of annuities has been very fully treated in Demoivre's See also:

• TREATISE

Treatise on Annuities (1725); See also:

• SIMPSON, MATTHEW (1811-1884)
• SIMPSON, SIR JAMES YOUNG (1811-1870)
• SIMPSON, THOMAS (1710-1761)

Simpson's See also:

• DOCTRINE

Doctrine of Annuities and Reversions (1742); P .

See also:

• GRAY
• GRAY (or GREY), WALTER DE (d. 1255)
• GRAY, ASA (1810-1888)
• GRAY, DAVID (1838-1861)
• GRAY, ELISHA (1835-1901)
• GRAY, HENRY PETERS (1819-18/7)
• GRAY, HORACE (1828–1902)
• GRAY, JOHN DE (d. 1214)
• GRAY, JOHN EDWARD (1800–1875)
• GRAY, PATRICK GRAY, 6TH BARON (d. 1612)
• GRAY, ROBERT (1809-1872)
• GRAY, SIR THOMAS (d. c. 1369)
• GRAY, THOMAS (1716-1771)

Gray, Tables and Formulae; See also:

• BAILY, EDWARD HODGES (1788-1867)
• BAILY, FRANCIS (1774-1844)
• BAILY, WILLIAM HELLIER (1819-1888)

Baily's Doctrine of Life Annuities; there are also innumerable compilations of Valuation Tables and Interest Tables, by means of which the value of an annuity at any age and any rate of interest may be found .