182 



ANNUITIES. 



mated, tin- rate of interest l>ein- ;i\rn. Hut annui- 

 i i - lor uncertain periods, and particularly lifoannui- 

 tii, 'ire more trc<|Hent, aiul tin- \aluc of the aiiniiily 

 liOQMpatodaOOOraing to the proluhlc diinilion of the 

 lifu by which it is limited. Many such annuities are 

 granted tor public -m in ; ; and, as Uiese do not 

 arise from a specific contract, and are not usually 

 subjects of purcliase, their precise \alue is not often 

 :i subject of investigation. But life annuities are 

 often 'created by contract, whereby the government 

 >r a private annuity office, agrees, for a certain sum 

 advanced by tlie purchaser, to pay a ceriain sum an- 

 nually, in yearly, quarterly, or other periodical pay- 

 ments, to the person advancing the money, or some 

 other annuitants named by him, during the life of the 

 annuitant ; or the annuity is granted to the an- 

 nuitant, his heirs, and assigns, during the life of 

 some other person, or during two or more joint 

 li\cs, or during the life of the longest liver or 

 survivor among a number of persons named in the 

 act or agreement whereby the annuity is raised. 

 Such aimuiiies are usually made transferable, and 

 are sold and purchased in the market as a species of 

 public stocks. When granted by a government, they 

 are generally one mode of raising loans ; when 

 created by a contract with a private corporation or 

 company, their object usually is, to give the annui- 

 tant tlie use, during his life, not only of the income 

 of his capital, but of the capital itself. If a person, 

 having a certain capital, and intending to spend this 

 capital and the income of it during his own life, and 

 leave no part to his heirs, could know precisely how 

 long he should live, he might loan this capital at a 

 certain rate during his life, and, by taking every year, 

 besides the interest, a certain amount of the capital, 

 he might secure the same annual amount for his sup- 

 port during his life, in such manner t hat he should 

 have the same sum to spend every year, and consume 

 precisely his whole capital during his life. But, 

 since he does not know how long he is to live, he 

 agrees with the government, or a"n annuity office, to 

 take the risk of the duration of his life, and agree to 

 pay him a certain annuity during his life, in exchange 

 for tlie capital which he proposes to invest in this 

 way. The probable duration of his life, therefore, 

 becomes a subject of computation ; and, for the pur- 

 pose of making this calculation, tables of longe- 

 vity are made, ny noting the proportions of deaths, 

 at certain ages, in the same country or district. 

 The celebrated mathematician, Dr Halley, was the 

 first who calculated a talile of mortality, which he 

 deduced from observations made at Breslaw, in Silesia. 

 In 1724, Mr De Moivre published the first edition of 

 his tract on Annuities on Lives. In order to facilitate 

 the calculation of their values, Mr De Moivre assum- 

 ed the annual decrements of life to be equal ; that is, 

 lie supposed that out of 86 (the utmost limit of life on 

 his hypothesis) persons born together, one would die 

 every year till the whole were extinct. This assump- 

 tion agreed pretty well with the true values between 

 thirty and seventy years of age, as given in Dr Hal- 

 ley's table ; but was very remote from the truth in the 

 earlier and later periods. Mr Thomas Simson, in his 

 work on Annuities and Reversions, originally pub- 

 lished in 1745J, gave a table of mortality deduced from 

 the London bills, and tables founded upon it of the 

 values of annuities. But at the period when this 

 table was calculated, the mortality in London was so 

 much higher than in the rest of the country, that the 

 values of the annuities given in it were far too small 



for general use. In I TJ(>, M. Deparcictix published, 

 in his Essui aur /<-. I'mlml^liti-a <{> In Duree de la 

 I if llmiiiiinr n work distinguished by its perspicui- 

 ty and neatness tallies of mortality deduced from 

 observations maile on the mortuary resist ers of several 

 religions house*, and on lists or the nominees in 

 several tontines. In this work, separate tables were 

 firstconstriicled ttir males and females, and the greater 

 longevity of the latter rendered apparent. M. De 

 parcicux's tables were a very great acquisition to the 

 science ; and are deeiilcdly superior to some that are 

 still extensively used. Dr Price's famous work on 

 Annuities, the first edition of which was published in 

 1770, contributed powerfully to direct the public at- 

 tention to inquiries of this sort ; and was, in this re- 

 spect, of very great utility. Of the more recent works, 

 the best are those of MrBaily,and Mr Milne, which, 

 indeed, are both excellent. The latter, U-sidcs all 

 that was previously known as to the history, theory, 

 or practice of the science, contains much new and 

 valuable matter ; and to it we beg to refer such of 

 our readers as wish to enter fully into the subject. 

 The table on which Dr Price laid the greatest stress, 

 was calculated from the burial registers kept at Nor- 

 thampton and some adjoining parishes. There can 

 be no doubt, however, as well from original defects in 

 the construction of the table, as from the improve- 

 ment that has since taken place in the healthiness of 

 the public, that the mortality represented in the 

 Nortliampton table is, and has long been, decidedly 

 above the average rate of mortality in England. Mr 

 Morgan, indeed, the learned actuary of the Equitable 

 Society, contends that this is not the case, and that the 

 Society's experience shows that the Northampton 

 table is still remarkably accurate. But the facts Mr 

 Morgan has disclosed in his View of the Rise and 

 Progress of the Equitable Society (p. 42), published in 

 1828, are quite at variance with this opinion : for he 

 there states, that the deaths of persons insured in the 

 Equitable Society, from fifty to sixty years of age, 

 during the twelve years previously to 1828, were 

 339 ; whereas, according to the Northampton table, 

 they should have been 545 ! And Mr Milne has en- 

 deavoured to show (Art. Annuities new edition of 

 Ency. Brit.) that the discrepancy is really much 

 greater. The only other table used to any extent in 

 England for the calculation of life annuities, is that 

 framed by Mr Milne from observations made by Dr 

 Heysham on the rate of mortality at Carlisle. It 

 gives a decidedly lower rate of mortality than tlie 

 Northampton table ; and there are good grounds for 

 thinking that the mortality which it represents is not 

 very different from the actual rate throughout most parts 

 of England ; though it cannot be supposed that a table 

 founded on so narrow a basis should give a perfectly 

 fair view of the average mortality of the entire king- 

 dom. In order to exhibit the foundations on which 

 tables of life annuities and insurance have been found- 

 ed in this and other countries, we give in the follow- 

 ing table, the rate of mortality that has been observed 

 to take place among 1,000 children born together, or 

 the numbers alive at the end of each year, till the 

 whole become extinct, in England, France, Sweden, 

 &C., according to the most celebrated authorities. 

 The rate of mortality at Carlisle, represented in this 

 table, is less than that observed any where else : the 

 rates which approach nearest to it are those deduced 

 from the observations already referred to, of M. De- 

 parcieux, and those of M. Kerseboom, on the holders 

 of life annuities in Holland : 



