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. . . . The 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

assu.

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. I, 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.

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 45. 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 £20 195. d., 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 13s. on the life of a man, and £47 35. 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),
more extended and complete comparisons will be given.
In 1846 Mr. Charles Rann Kennedy, Barrister-at-
Law, pub. A Treatise on Annu.
In the same year
Mr. Edward Scury pub. Life Assu. and Annu. Tables.

True Table. Dr. Price's T. 3 p.c.

3 p.c.

Age.

Years'
Purchase.

Years' Purchase.

17:08

12.27

23.39

20.66

20

21.41

18.63

30

19:08

16.92

40

16.29

14.84

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. Or annu. from £1 to £30 might be granted on condition of not being returnable. In cases of periodical payments, if payments were 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 :

The

In 1853 also the 12th Ann. Report of the Reg.-Gen. was pub., and contained the ENGLISH LIFE T. No. 2. This was constructed from the deaths during the years 1838-44; the pop. of 1841 serving for the basis in this as in No. 1. results of No. 2 T. were confined to Males only. The annu. values deduced therefrom are given at 3 rates of int. ; and are shown in the margin.

Years' Purchase.-Males.

Age.

3 p.c.

4 p.c.

5 p.c.

Birth.

19.2660

16.0764

13'7504

5

24'5587

20'5340

17'5733

1Ο

24'2042

20.3828

17.5339

15

23'2225

16.5663

18.3612

16.0955

In vol. iii. of Assu. Mag. pub. in 1853, will be found an important practical suggestion by Mr. Peter Hardy, viz., whether the approximate value of an annu. on 3 joint lives would be more accurate, if it were obtained by means of the curtate expectation of two joint lives, instead of being ascertained, "as at present, by means of the value of an annu. on the same joint lives, at the particular rate of int. involved in the calculation." The subject, however, is so technical as to be beyond our present range. In the same vol. Mr. C. W. Merrifield, of the Privy Council Office, communicated "a method for obtaining an expression of the rate of int. in immediate annu,," and Mr. Jas. Meikle, whose name will become familiar to the reader of these pages, communicated formulæ for obtaining the value of a L. annu. at one rate of int. from the value at another given rate.

In 1854, by 17 & 18 Vict., c. 90, all the Acts relating to the inrolment of annu. were repealed, in conjunction with the repeal of the Usury Laws. It is probable that the great majority of life annu. granted during some years previous were really void for the want of inrolment. Thus, after more than three centuries of restrictions from these Usury Laws, the dealing in life annu. became free and unfettered-with this general exception, that the Courts of Equity will always interfere to set aside an "unconscionable bargain," especially if made under any aspect of fraud, or with a minor, or person mentally incapacitate.

It may seem strange at first sight, but it is unquestionably true, that since dealings in life annu. have been freed from all restrictions, the number of such transactions has very greatly diminished. But we must look to the true reason of this, and undoubtedly it is due to the repeal of the Usury Laws, which had a direct tendency to encourage the very description of transactions they were supposed to suppress. The attempt to enforce one common rate of int. for loans on every varying description of security was an act of unmitigated folly. Any person attempting to borrow on a security demanding a higher rate of int. than the legal rate, as on a life int., a leasehold estate, or a rever., was compelled to obtain the advance under cover of a life annu. And these transactions, when reasonably conducted, were not without some special advantages. To the borrower on a redeemable annu. there was the great advantage of being certain not to have the money called in by the lender, combined with the equally great convenience of being able to pay off the principal whenever he pleased. He had to consider how much he could afford to pay for these advantages. To the lender there was the advantage of securing in general a permanent investment of his money at a higher rate of int. than he could obtain by way of mortgage, and without sinking his principal, unless he chose to waive the ins., in order to increase the amount of his annu. This mode of raising money has the further advantage, that, in the various ramifications of property incident to a highly civilized state of society, it frequently affords the only means by which a parent without cap., but with a good and certain yearly income, can raise a sufficient sum to secure the advancement of his children in the world.-Kelly.

It was right, therefore, that all restrictions should be removed (see 1855).

In the 4th vol. of Assu. Mag. (1854), there appears a paper by Prof. De Morgan: On the Demonstration of Formula connected with Int. and Annu. The paper is purely scientific. In the same vol. is a paper by Holmes Ivory, then one of the Vice-Presidents of the Inst. On the Method of approximating to the Values of Deferred and other Life Annu., when payable Half-yearly and Quarterly. The writer says:

The difference between the value of an immediate life annu. when payable yearly, and that of the same annu. when payable half-yearly or quarterly, has, as is well known, been variously estimated by our leading authorities. According to Dr. Price and Mr. Morgan, a fifth of a year's purchase will be generally more than a sufficient add. if the value of the annu. is desired payable half-yearly, and three

tenths of a year's purchase if the value of the annu. is desired payable quarterly (Price, vol. i., p. 246, 6th and 7th eds.). Mr. Baily again, following Simpson, lays it down as a rule, that the value of annu. payable yearly must be increased nearly one-fourth of a year's purchase, in order to show the value of the same annu, payable half-yearly; and that they must be increased nearly three-eighths of a year's purchase in order to show the value of the same annu. payable quarterly "(Francis Baily, c. x., sec. 355). The same rule is also given by Mr. Milne (ch. viii., sec. 485).

The writer, while explaining the cause of the difference of these estimates, adopted Mr. Baily's rule.

By 18 & 19 Vict., c. 15, secs. 12 and 14, 1855, it is provided-in order that it may be ascertained by search what life annu. or rent-charges may have been charged upon lands by their owners-that any annu. or rent-charge granted after the passing of that Act (and not given by marriage settlement or by will) for one or more life or lives, or for any term of years, or greater estate determinable on one or more life or lives, shall not affect any lands, tenements, or hereditaments, as to purchasers, mortgagees, or creditors, until a memorandum containing the name and the usual or last known place of abode, and the title, trade or profession of the person whose estate is intended to be affected thereby, and the date of the instrument whereby the annu. or rent-charge is granted, and the amount of the annual sum to be paid, shall be left with the senior Master of the Common Pleas at Westminster, who shall forthwith enter the particulars aforesaid in a book in alphabetical order by the name of the person whose estate is intended to be affected by the annu. or rent-charge, together with the year and the day of the month when every such memorandum or minute is so left with him.

In the 5th vol. of Assu. Mag. (1855), there are various papers on the subject of life annu. Mr. Edwin H. Galsworthy contributed a formula, to find the amount of an annu. increasing or decreasing by a constant quantity; also to find the present value of an annu. increasing or decreasing by a constant quantity. Mr. Charles Gabriel Shaw contributed another ingenious" formula, for a like purpose. Mr. James Meikle contributed a formula, to determine the rate of int. in a life annu., the tables of mort. and age being given. Mr. Charles Jellicoe a short formula in elucidation of these. Mr. Peter Hardy contributed an "elegant " formula for an approximate value of annu. at simple int.

In the same vol. there is a reprint from the Trans. of the Cambridge Phil. So. of a paper by Sir J. W. Lubbock, Bart., in 1828, On the Calculation of Annu., and on some questions in the Theory of Chance; and another paper from the same source, by the same author, read 1829: On the Comparison of Various T. of Annu.

In 1856 Mr. Wm. Orchard pub., Single and Ann. Prems, for Annu. In this same year also were pub. the remaining copies of Mr. Griffith Davies' Treatise on Annu., etc., (first pub. 1825,) in a more complete form than orig. Mr. William Braid made a communication to the Assu. Mag. (vol. vi. p. 109) On Annu. and Assu. Tables for 3 Lives.

In 1857 Mr. Charles M. Wallich, author of the well-known T. bearing his name, read before Sec. F. (Economic Science and Statistics) of the British Asso. a paper on Annu. for Lives. The author said:

The table of the values of annu. on lives, as hitherto constructed, only show the rate of int. which a purchaser may make on the money employed, and replace the cap., provided he can reinvest the surplus income, beyond the int. on the purchase-money, at the same rate of int. As it is often important to know the price which should be paid for such annu., in order that the purchaser may enjoy a certain higher rate of int. on the money invested, whilst the circumstances of the times only permit a much lower rate to be calculated upon for the future investments, I have constructed the following formula, which will show the purchase-money to be paid for an annu. under such circumstances.

Mr. Willich then furnishes the following

Table of Annu. according to the Carlisle T. of Mort. at 3 p.c.; also the price which should be paid for an annu. so that the purchaser may obtain 5 p.c. int. on the money invested, while the reinvestments to replace cap. are estimated to be made at only 3 p.c.: Tables of this character are of great value in monetary transactions.

Age.

Value of Annuity
at 3 p.c. Carlisle.

Value of an Annuity if 5 p.c. is to be enjoyed while the reinvestments are only to be made at 3 p.c.

In 1857 several papers appeared in the Assu. Mag., vol. vii., bearing upon life annu. Thus, in a paper upon the writings of the late Dr. Thomas Young: A Formula for expressing the Decrement of Human Life. The subject is treated of in a highly scientific manner. Mr. Peter Hardy gave a paper: An Investigation into the proper method of determining the amount of an Annu. forborne and improved at Int. during the existence of a given life. Mr. Thomas Carr offered some obs. on the first-named paper. Mr. Adler supplied a formula for an approximate value of annu. at simple int.

In 1857 Mr. F. G. P. Neison published the 3rd edition of his Contributions to Vital Statistics; and therein is contained Tables of Mort. deduced separately from (1) Rural Districts; (2) Town Districts; (3) City Districts, of England and Wales; and then (4) the preceding three combined; and (5) combined T. of Rural, Town, and City