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The following Table shows the values of annu. as deduced from the mort. of the whole of the Male and Female Lives in the preceding 7 Tables, taken separately; int. 4 p.c.
The superior value of female lives had been shown by previous writers, as, for instance, by Dr. Price in his T. for Sweden and Finland; but not in the same degree as is shown here, and some of the individual tables of Mr. Finlaison show even greater differences than these shown by the combined tables.
It would be interesting to compare the actual mort. under No. I obs. with the estimated mort. of the Table we have given under date 1692. There were but 1002 lives exposed to risk instead of the 10,000 contemplated. That Table predicted that the last life would drop in 1792, surviving 99 years from the date of nomination. As a matter of fact,
the last life (of the smaller number) died in 1783, having lived 90 years after nomination. On the 30th March, 1829, Mr. J. W. Lubbock (now Sir J. W. Lubbock, Bart.) read before the Cambridge Philosophical So. a paper On the Comparison of Various T. of Annuities; and the same was pub. in the Trans. of that So. shortly afterwards. abridgment of this paper was pub. in Assu. Mag. v., p. 277.
In this same year, 1829, Mr. Higham, the then Comptroller of the National Debt Office, proposed a plan for granting life, deferred, and term annuities, in connexion with Savings Banks, very similar to that adopted in 1833. Indeed, there cannot be much doubt that the Act of that year was based upon his recommendations.
In 1829 also Mr. James J. Duncan pub. in Glasgow Tables on the Prob. and Expectation of Male and Female Life in Glasgow; and of the Value of Annu. on Single Lives at all Ages, distinguishing the Sexes, at the several Rates of Int. of 3, 4, 5, and 6 p.c., deduced from the Glasgow Pop. and Mort. Bills, on an average of 6 years, from 1821 to 1827. The author says:
I have used a little liberty with the prob. in ascertaining the value of the annu. This was done to avoid the apparent inconsistency of, for example, age go of males showing a lower value than age 91: which a strict adherence to the prob., as shown in the T., would bring out. As this liberty, however, has only been taken in one or two of these extreme ages, it can lead to no practical error. He, in fact, adjusted the T. for these extreme ages. The following is an abstract of his Annu. T.; int. 4 p.c. :
There was also pub. in Edin., the same year, Principles of Life Annu. and Assu. Practically Illustrated, by an Accountant (see again 1834). In 1830 Mr. Robert Rankin pub., A Familiar Treatise on Life Assu. and Annu., etc., etc., to which was appended orig. tables of the Prob. and Expectation of Life in the City of Bristol. [BRISTOL MORT. T.] No annu. values were deduced. In the same year Mr. J. B. Benwell pub., New Formula in the Valuation of Annu. on Lives, etc.
In 1832 Mr. T. R. Edmonds propounded his theory of mort. founded upon the discovery of a numerical law regulating the existence of every human being. He pub. a series of annu. tables deduced from this theory graduated in the most beautiful manner. Although derived from theoretic computation only, they differ but very slightly from many other tables in use, as will be seen by the annexed example:
In the same year Mr. Charles Ellis pub., The Law of Fire and Life Ins. and Annu., with Practical Obs.
In 1833, by 3 & 4 William IV., c. 14, power was given to trustees and managers of savings banks to grant annu. to depositors for life, deferred, or for terms of years, such persons being not under 15 years of age, and for annu. not exceeding £20 on any one life. Tables to be used to be approved by Commissioners of Treasury. The provisions of the Act were numerous. They were amended in 1844, and are now repealed. In the same year Mr. John Tidd Pratt pub., The Law Relating to the Purchase of Gov. Annu., through the medium of the Savings Banks and Parochial Sos., comprising the stat. 3 Wm. IV., c. 14, with notes and references. Mr. W. G. Lumley also pub., Law of Annu. and Rent-charges. This became a standard work, worthy of its learned author. In 1833 there was also pub., Instructions for the Estab. of Parochial Sos. for Granting Gov. Annu., immediate or deferred, pursuant to 3 Wm. IV., c. 14.
In 1834 an equitable measure was passed regarding life annu., viz., that in the absence of any express stipulation against apportionment, all annu. should be apportioned so that, on the decease of an annuitant, the personal representatives should take the proportion accruing from the then last payment up to date of death. There was an exception as to annu. granted by ins. asso. This practice of apportionment had prevailed since 1738 as to annu. arising out of land (see ANNU. APPORTIONMENT ACT).
In 1834 Mr. Cleghorn pub. a small vol. on the subject of Widows' Funds, in which he gave such information as he had been enabled to deduce from an investigation of the Widows' Fund of the Ministers of Scotland, of the frequency of marriages and remarriages amongst that body; and other information calculated to throw light upon the probable claims on the annu. funds of that and similarly constituted asso.
In 1834 also was pub. in Edin., Principles of Life Annu. and Assu., etc., Practically Illustrated; showing the method of calculating the value of annu., rev., assu. on lives, policies, etc., with a large collection of useful tables, comprising the value of annu., deduced from the Carlisle and Northampton T. of Mort., with an appendix containing a comparative table of the rates of prem. demanded by all the assu. offices in Britain. By an Accountant.
In 1835 Mr. Thomas Birch Kelly pub., A Practical Treatise on the Law of Life Annu. with the Statutes and Precedents, etc., etc. Mr. Kelly attributes the rise of life annu. to the existence of the Usury Laws: a circumstance which he was one of the first to discover; but he was of opinion that life annu. were comparatively little known until the 18th century: an error from which further investigation might have freed him.
In the same year Mr. J. N. Mahon pub. a work on the duties and liabilities of executors and administrators under the Stamp Act; and a Table of Annu. and their Values.
In 1835 Mr. Charles Ansell's Treatise on Friendly Sos. was pub., and therein was contained a Mort. T. formed from the experience of F. Sos. for the ages 13 to 70 inclusive; and from the Northampton T. for the ages above 70. From this T. annu, values were given at the following rates of int.: 3, 34, 31, 4, and 5 p. c., and extended to 4 decimal places. We give an abstract of the T. at 3 rates:
It was in 1836 that the Independent West Middlesex scheme was concocted. Its hist., which is very remarkable, will be given pretty fully under its alphabetical title. The chief feature was the granting of annu. on terms which had not been heard of in modern times. They were indeed as much as 30 p.c. lower than the prices ordinarily charged. Thus a person aged 30 might secure [the promise of an] annu. of £80 for £1000 down. A writer in the Quarterly Review pointed out that a person securing such an annu. might insure his life so as to secure a return of his cap., and at the same time enjoy a handsome income. Large sums of money were obtained from the British public before the bubble burst.
In the appendix of official documents attached to the 3rd ann. Report of the Poor Law Commissioners (1837), we find the following in a letter addressed by the Sec. to the Boards of Guardians of Gt. Brit. :
But the Commissioners trust that you will, each in his own neighbourhood, do all in your power to promote the formation of such habits of forethought, of frugality, and self-dependence, as will keep them from falling back into pauperism, by aiding the estab. of sick-clubs, savings banks, and annu. sos.; and by inculcating on your labourers and servants the importance of thus guarding against loss of work, sickness, and old age.
Again, "The attention of the labouring classes should be directed to the annu. sos. sanctioned by the Gov., whereby they may obtain support in old age or infirmity.”
In 1837 Mr. Alex. McKean pub. Exposition of the Practical Life Tables, with a digest of the most approved rules and formulæ (illustrated by numerous examples), for the solution of all cases occurring in the actual daily bus. of life assu, annu., revs., etc., etc.
In 1839 Mr. Peter Hardy pub. The Doctrine of Simple and Compound Int., Annu., and Revs. Analytically and Practically Explained, with New and Extensive Tables. The work is clearly and comprehensively written.
During the year 1840-1 there was pub. by the So. for the Diffusion of Useful Knowledge, the well-known work of Mr. David Jones: On the Value of Annu. and Rev. Payments, with numerous Tables. These comprise annu. and ins. for single and for two joint lives and survivorships severally, according to the Northampton and Carlisle Tables of Mort., and at different rates of int.; and are generally and widely known as Jones' Tables. The author says in the preface:
The numerous transactions which take place connected with the sale of annu. and rev. render a knowledge of the principles on which their values are calculated extremely desirable. This treatise is intended to give the student an opportunity of acquiring a knowledge by no means superficial of the method of calculating annu, and rev., whether dependent on a fixed number of years, or the uncertain tenure of human life. The first part refers to annu. and reversions not dependent on life. . . 2nd part contains the method of finding the values of annu, and rev. dependent on the existence of one or more lives. A variety of tables will be found at the end of the 1st and 2nd parts. In the part which treats of life contin. resort has been had to Mr. Griffith Davies' method of constructing tables of the values of annu. pub. by him in a small tract in 1825; and a variety of formulæ have been deduced therefrom of considerable utility in working numerous cases connected with life annu. and
It affords the author great pleasure to acknowledge here the liberality of Messrs. Davies and Milne in giving permission to use their respective works to assist in the objects of this pub. From Mr. Milne's work have been taken the values of annu. by the Carlisle table for single lives, and at 5 and 6 p.c. for joint lives. Mr. Davies' work has furnished the rates of prem. for two lives.
These vols. are well known, and we need not pause to dwell further upon their contents. In 1841 Mr. Thomas H. Millar pub. A Practical Intro. to Life and Fire Assu.; showing the Method of Calculating the Value of Annu., Revs., Assu. Pols., Bons., etc., with numerous useful Tables, etc., etc. And in the same year there appeared in Chambers' Edin. Journal a paper entitled Cautions respecting L. Assu. and Annu.
In 1842 Mr. J. C. Hudson, of the Legacy Duty Office, Lond., pub. Tables for Valuing Annu. on Single Lives.
The year 1843 affords another land-mark in the hist. of L. annu.—again a double one. In this year were pub. (1.) The EXPERIENCE T., deduced from the mort. of 17 L. Offices, who contributed their entire mort. experience for obs.-sometimes called the Actuaries T., at others the Actuaries Experience, but which we propose in these pages to call EXPERIENCE T. No. 1. (2.) The 5th Ann. Report of the Registrar-General containing the ENGLISH MORT. T. No. 1, as compiled by Dr. Farr from the general mort. of the kingdom.
As we shall give a full hist. of each of these T. under its proper alphabetical head, we need not dwell upon them here: the less so, as in neither case were any money values deduced from these T. pub. in connexion with them.
The Reg.-Gen. in his Report, referring to the English T. and its prob. uses, said :
The sale of life annu. has been a frequent financial resource in recent times, and it possesses one advantage over other methods of raising money by involving the principle of extinction, and by spreading the repayment over the generations for whose advantage the debt is contracted. A series of life tables for the whole and for different parts of the pop., as well as a more comprehensive knowledge of the subject, will prevent the possibility of a recurrence of the frequent heavy losses which the Treasury has sustained in these transactions.
In 1844 was pub. the 6th R. of the Reg.-Gen. ;
Mr. Jenkin Jones in this same year pub. a series of tables of annu. and assu. calculated from the new rate of mort., viz., Experience T. No. 1, with examples. This is the only set of actuarial tables which has been deduced from the EXPERIENCE MORT. TABLE No. I. annexed is an abstract of the Annu. T. ::
and therein was contained a Table of Annu. Values, deduced from the English T. No. 1, the sexes being distinguished. We give only an abstract of the T., as in other cases (see next page);
The preceding table must be read in the light of the following explanation : By the English Life Table (No. 1), the present value of a life annu. of £1 at the age of 21 is £20 195. 9d. on the life of a male; £21 4s. 3d, on the life of a female. The present value of an annu. of £1000 a year on the life of a man would be 1000 times £20 19s. 9d., or nearly £20,986; and in the same way the value of an annu. of £10, £20, £35, or any other number of pounds, may be found. £100 will purchase an annu. of £4 155. 4d. on the life of a man aged 21, and £4 145. 3d. on the life of a woman at that age. £1000, which is 10 times £100, will purchase an annu. of 10 times the amount, or £47 135. on the life of a man, and £47 3s. on the life of a woman. The parties who granted annu. at these rates would gain nothing, as the values in the tables are the nett values: they might lose if the lives were well selected. Upon these accounts a certain arbitary per-centage must be put on the "present values," and taken off the "annuities."
In this year also, by 7 & 8 Victoria, c. 83, the Act of 1833, for enabling trustees of Savings Banks to grant annu., was amended to the extent that an annu. of 30 (instead of £20) might be granted upon any one life. Husband and wife might each have an annu. This, and the Act of 1833, were repealed in 1853.
Up to 1850 the annu. granted under the two Acts just named, were 5648, and of these 3385, or three-fifths of the whole number, came in after 1844.
In 1845 Dr. Farr pub., in 8th Report of R. G., what he termed the New Northampton Table. It was based upon the same data as Dr. Price employed in the orig. table; but that data was "corrected" in the light of the more exact information we now possess as to the circumstances of the pop. of Northampton at the period embraced in the registers upon which Dr. Price relied; and it therefore purports to be not only a new but a true Table of the Mort. of Northampton. It is instructive to note the annu. values deduced from this new and true table as contrasted with that which came to be so extensively employed for the purposes of annuity valuation at a former period.
Under the head of NORTHAMPTON Table (New),
True Table. Dr. Price's T. 3 p.c.
3 p. c.
In 1847 Mr. W. E. Hillman pub. a little book on the Theory and Practice of Assu., and therein he suggested, that as it was shown that the duration of life was affected by various diseases, whether persons suffering from such diseases should not have the benefit of the consequent reduced value of annu. on their lives. The subject will be further discussed under DISEASED LIVES, INS. OF.
Mr. Charles Ansell said before a House of Lords Committee in 1848 that most of the ins. offices had discontinued granting annu. at all: they had been found unprofitable. Many of the offices referred parties to the Gov. Mr. Finlaison said before the same Committee that there was nearly one million p.a. paid by the National Debt Office for annu.; but he thought the number of annuitants had reached its maximum-it had been going on for 40 years-the old ones died off about as fast as the new ones came on.
There are various sos. regis. under the Friendly Sos. Acts which grant annu., and which are not popularly known as annu. sos. Thus in the returns made by Friendly Sos. for the five years ending 31st Dec., 1850, there were included as being in the City of Lond. 6 sos., the oldest being founded in 1835, having an aggregate of 10,876 members, (the members of the 2nd largest of the 6 were not returned,) and total assets of £717,441 145.; while in other parts of Lond. 9 other sos. were returned, being, however, nearly all small ones.
In 1850 Mr. Thomas Weddle contributed to the Phil. Mag. a paper On Annu. and Assu. on Successive Lives. In vol. ii. of Assu. Mag., Mr. Peter Gray says, "The subject is treated with that gentleman's usual ability and elegance."
In the same year Mr. Samuel Brown read before the Inst. of Act. a paper On the General Method of Approximation to the Values of Annu. and Assu. for long terms of years, depending on one or two Lives. The paper is one of considerable interest, but of too scientific a character to be quoted in these pages. It will be found in Assu. Mag. i., p. 20. In the same vol. will be found a paper by the late Mr. Peter Hardy: On the Values of Annu., which are to pay certain given Rates of Int. on the Purchase-money during the whole term of their continuance, and to replace their Orig. Values, on their expiration at certain other given Rates. The writer says:
Notwithstanding the very large amount of leasehold property which in the course of every year is bought and sold in this country, and notwithstanding the extensive transactions-of almost hourly occurrence in the public market, in Gov. and other temporary annu., the subject of the rate of int. which any given purchase will yield the buyer is very imperfectly understood, even by the most deeply interested in the inquiry, unless they happen to be at the same time well versed in actuarial computations. It is not unfrequently imagined by a buyer, that if he purchase a leasehold property or a temporary annu. at a price corresponding with the value of an annu. at a given rate of int. (say 5 p.c.), he has made a purchase which will pay him 5 p.c., or which, in other words, will enable him to spend 5 p.c. p.a. on his outlay, and at the same time replace his cap. undiminished at the expiration of the term. This is a grave error, and very frequently leads to serious inconvenience. If a purchaser buys an annu. for a term of years, according to a 5 p.c. table, it is absolutely essential that the surplus of the annu. over and above the int. on the purchase-money should be ann. reinvested in some fund which will also yield a clear 5 p.c.; otherwise, the buyer's expectation to replace his cap. at the expiration of the term will not be realized.
This proposition is then fairly demonstrated; and a TABLE is furnished showing the present value of an annu. of £1 p.a. for a given number of years certain, supposing the purchaser thereof to take out of the annu. 5 p.c., 6 p. c., or 7 p.c. p.a., as an available int. on his purchase-money or cap. advanced, while he is only enabled to re-invest the surplus of the annu. beyond the available int. so as to make 3 p.c., 34 p.c., 4 p.c., and 5 p.c. thereof. In the same vol. will be found a paper compiled from materials supplied by Mr. W. T. Thomson: Mort. amongst Lives selected at the ages 75 to 81 for Gov. Annu. We have already referred to this subject in the present art. under date 1829. We shall speak of it more at large under Gov. Annuitants.
In the same vol. will be found some important correspondence on points involved in the preceding articles.
In 1851 there was pub., as the joint production of Mr. Peter Gray, Mr. Henry Ambrose Smith, and Mr. William Orchard: Assu. and Annu. Tables according to the Carlisle Rate of Mort. at 3 p.c. The editors of the Assu. Mag. say, "This work is of much greater value to actuaries than its mere title would seem to imply " (vol. ii. p. 194). In the same vol. there is a communication from Prof. De Morgan: On a Method of checking Annu. Tables at different Rates of Int. by help of one another. In this year Mr. J. H. James pub. A Treatise on Fire and Life Assu, Annu., and Rev. Payments, etc., etc. In 1853 an Act, 16 & 17 Vict., c. 45, To consolidate and amend the laws, and to grant add. facilities in relation to the purchase of Gov. annu. through the medium of Savings Banks, and to make other provisions in respect thereof, was passed. The former Acts were repealed in order that they might be consolidated and amended. Nearly all the provisions of the former Acts were reintroduced, and there were a few new ones. The age at which life annu. might be granted was reduced to 10; the amount of annu. to be not less than £4 or more than £30; husband and wife might each have an annu. Deferred annu. might be granted upon the condition of money paid for same being returnable in event of death before annu. has commenced. on condition of not being returnable. In cases of periodical payments, if payments were Or annu. from £1 to £30 might be granted not continued, a smaller annu. might be granted. Deferred might be converted into immediate annu. Commissioners might decline to grant annu. on "sufficient grounds." The Treasury should direct what tables to be used. Quarter's payment in add. to arrears to be paid at death. Annu. not assignable, except in case of bankruptcy. Annu. to be free of taxes, and to be deemed personal estate.
Mr. J. W. Stephenson pointed out in vol. x. of Assu. Mag., p. 44, that the tables pub. in conformity with this Act "were not computed in the usual way, but apparently on some principle wholly different from it." Of this he gives examples. We do not remember to have seen any explanation.
In the same year was passed the Succession Duty Act-16 & 17 Vict., c. 51-which contains elaborate schedules of the values of single and joint annu. for lives and for years, based upon Finlaison's T., males, 4 p.c. This Act supersedes the Tables given in the Legacy Duty Act, 36 Geo. III., c. 52 (see SUCCESSION DUTY ACT). The difference between the two T. in the value of annu. is very remarkable. Take the case of a £100 annu. on one life :
Table, 1853. £1892 8 6
1926 19 6
1729 9 6
O O O O O