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The first consideration which strikes us in reference to this Table is, upon what data was it founded? the next, who supplied it? Was it Halley? It comes suspiciously near to the advent of his Table, as we shall presently see. If not, it can no longer be maintained that he invented the first life table. Or is the preceding Table purely conjectural? Its application was certainly conjectural, inasmuch as the ages of the nominees not being restricted in any manner, could not be known. But then, as we have shown ages had not at this period been taken into account. Halley, however, knew the necessity and the value of the element of age!
We have seen that the entire million was not sub. under the Act of 1692; accordingly in 1693 another Act was passed - 5 Wm. & Mary c. 5-for granting life annuities also at the rate of 14 p.c. p.a. on the sum of £118,506 5s. 10d. required to make up the orig. amount. This granting of life annu. at 14 p.c. was virtually estimating the value of an annu. on a single life at 7 years' purchase. But the actual experience of this batch of annu. has been tested by means of the investigations of Mr. John Finlaison [see 1829], and was found to have ranged from 17 years' purchase at age 10, down to 4 years' purchase at age 75.
In 1693 we reach the name of Dr. Halley, who (subject to the preceding query) constructed the first mort. Table, and thus placed the valuation of life annuities upon a scientific basis. He read a paper before the Royal Society: An estimate of the degrees of mort. of mankind, drawn from curious tables of the births and funerals at the city of Breslaw, with an attempt to ascertain the price of annuities upon lives; wherein he showed how the prob. of life and death, and the values of annu. and assu. on lives, might be determined by the aid of Mort. Tables. He states that till then all such matters had been dealt in by imaginary valuation!
Dr. Halley having defined the chances of life, proceeds to illustrate the application of the table to the determination of the value of life annu., and apparently selected 6 p.c. int. as the rate most current in his own day.
He first indirectly advances that the worth of an annuity not dependent upon life would be represented by adding together the several discounted values of the successive payments. But in a life annuity, as each payment would only be claimable upon the persons living to the respective dates, so each payment would prospectively be worth such a proportion only of the discounted value as there was a proportionate chance of the persons living to the date in question. Now the chances of a person of any particular age living to the respective dates of payment were easily determinable, as already mentioned, by considering the relative number of yearly survivors, indicated by the table of mort.
The value of the life annuity was therefore dependent: firstly, upon deriving from int. tables or calculations, the discounted value of each yearly payment; and, secondly, upon taking such a proportion only of each discounted value as there might be a proportionate chance of the payment being respectively claimed. Such separately reduced values being added together, would then constitute the total value of the life annuity.
This method of valuing life annuities by ascertaining the value of each future payment separately is obviously and demonstrably true in the present day, as in Dr. Halley's own time; but inasmuch as the labour of such subdivision for every age would be necessarily very great, the reader will not be surprised to learn that less elaborate methods have since been discovered. Dr. Halley himself remarked upon the operose requirements of his formula, but very frankly owned that after several trials he had not succeeded in devising any less laborious method. He had, however, the perseverance to calculate the results for every fifth age as embodied in the accompanying table, which, from its constituting the
first annuity table for different ages, seems no less interesting as the primary step in the art of life-finance, than the preceding table was in that of life-measurement.
Dr. Halley, in connexion with this Table, observes :
This shows the great advantage of putting money into the present fund lately granted to their Majesties, giving 14 p.c. p.a., or at the rate of 7 years' purchase for a life; when young lives, at the usual rate of int., are worth above 13 years, purchase. It shows likewise the advantage of young lives over those in years; a life of ten years being almost worth 13 years' purchase, whereas one of 35 is worth but 11.
This appears to us to lead to the inference that Halley may have been concerned in the preparation of the preceding scheme.
Dr. Halley then considers the chances appertaining to two or more lives, and shows that the same principle of investigation already applied to single lives should be extended to the more compound cases; for the separate yearly values being ascertained and added together, would similarly constitute the total value of such annuities; care, however, being taken that each yearly value was previously compounded of the chances of the different lives under consideration, according to the terms of the particular case to be solved. -Farren.
In 1693 Leybourn's Panarithmologia was pub., and it contained tables of annuity values, and of compound int., with much other interesting information concerning marine ins., usury, leases, etc., but no mention is made of life annu.
Some money was borrowed in 1694 on annu. for lives, under the authority of 5 Wm. & Mary, c. 20. The terms were 14 p.c. for one life, 12 p.c. for two lives, and 10 p.c. for three. "Natives or foreigners" might contribute. Such terms were in the highest degree extravagant; particularly as no attention was paid to difference of ages. Assuming no frauds had been committed on the Government, these terms yielded the lender 10 p.c. in the case of the two lives, and 9 p.c. in the case of three. But there is reason to believe that serious frauds were committed. The amount of the annuities at first was about £22,800. In 1762 (68 years afterwards) they had only been reduced by deaths to £9215; while 20 years later (1782) they remained at £8027. See 1718.
It was in the preceding Act that mention is first made of annu. granted upon more than one life.
In 1694, also, by 5 & 6 Wm. & Mary, c. 5—An Act to enable such persons as have estates in life annu. payable by several former Acts therein mentioned, to purchase or obtain further or more certain interests in such annuities; and in default thereof for admitting other persons to purchase or obtain the same, for raising moneys for carrying on the War against France-it was provided that the person who had purchased annu. under the Acts of 1692-3, might exchange their life annu. for others of 96 years certain, upon paying into the Exchequer £63 in add. to the £100 originally paid.
It is thus seen that the difference between 14 p. c. for life, and 14 p.c. for 96 years, was sold for £63, or 4 years' purchase. In other words an annu. of £50 could be secured for 99 years by payment of £675. Such an annu. is now worth £1500, or considerably more than double. But Adam Smith, reviewing the transaction and the period, says that "such was the supposed instability of the Government that even these terms procured few purchasers."
By the 7 & 8 Wm. 3, c. 2 (1695), the opportunity of embracing the advantages of the last-named Act were extended to a longer period; and for 5 years' purchase, or £70, persons not such original purchasers might obtain an annuity of 14 for 96 years.
The purchasers appear to have well understood their own interests: the instability of Government would affect life annu. as much as long annu. ; but the life annu. at 7 years' purchase was by far the best bargain, for the int. of money being 6 p.c., the life annu. was worth, at Halley's estimate, 13 years' purchase (13'4 at the age of 10), and an annu. for 96 years was worth only 16% years' purchase. The value of a life annu. of £100 was 1300, which was obtained for £714; and the new offer to such a purchaser was, that, if he would advance £450 more, he should obtain an annu. worth £1660; by accepting the offer he would have gained £496 on £1164; by rejecting it, his profit was £586 on £714.
These schemes of the Government drew much attention to the subject of life annu., and induced several projects to be set on foot on very fallacious foundations. We must notice several of these.
On the 24th Oct. 1695, a scheme was set on foot for making a fund for granting Annuities for Lives, etc. The same was proposed to be worked in connexion with a then existing inst. called the "Million Bank." In the proposals it was provided that any person might subscribe money or land for granting annuities for terms of years, or for 1, 2, or 3 lives, at 10, 12, and 14 years' purchase, renewable at any time for a reasonable fine. The money subscribers were to have 6 p.c. p.a. for their money; and the subscribers for land were to be accommodated with money at 3 p. c. p.a., and the remainder of the profit to be divided between the land and the money. Any person might subscribe to purchase annuities at the aforesaid rates, and the subscribers of money might, if they thought fit, transfer the same to the account of annuities for a term of years, or for 1, 2, or 3 lives, as they liked best. But that the money or what is purchased therewith should in the first
place be liable to pay the said annuities, and in case they fell short, the land to be charged, with liberty given to the subscribers to revoke up to 4th Nov. then following.
Of £120,000 to be paid up before 9th Nov., 100,000 was to be laid out in purchasing £20,000 p.a. in reversions "on the lives in the Exchequer ;" and the remaining £20,000 to buy about £3000 p.a. in lottery tickets for 15 years which £20,000 p.a. in Reversion and the 3000 p.a. in possession for 15 years, is to be backt with £20,000 p.a. land, whereupon to grant annuities for one, two, or three lives, to the value of £20,000 p.a. ; which at II years' purchase (the medium of the rates proposed) will come to £220,000, with £120,000 of which they proposed to purchase £17,000 p.a. more of lottery tickets, to make the first £3000 p.a. £20,000 p.a. in possession; and the remaining 100,000 was to be lent to the land subscribers at 3 p.c. p.a., and the remainder of the profits was to be divided, viz., two-thirds to the subscribers of the £120,000 in money and one-third to the subscribers of £400,000 value in land, being £20,000 p.a. at 20 years' purchase; which (they say) by a modest computation may make 16 p.c. p.a. to the money, and near 30 p.a. on every £100 p.a. in land. And that the said fund might not fail, one-fifth part of the profits should during the 15 years be annually laid out to purchase something to answer those lives that may happen to be then left, of those that the reversions were purchased from the Exchequer.
It was, in a word, one of those complicated schemes of this period devised to evade the usury laws, and which broke down by reason of those very complications.
In 1698 an annuity project was set up by the Mercers Company, mainly at the instigation of Dr. Assheton. The scheme was for granting life annuities to the widows of the members at the rate of £30 for every £100 paid down by the member or subscriber. A scale was formed by which married men under 30 were allowed to subscribe £100; under 40, not more than £500; and under 60, they were limited to 300. A full history of this project will be given under MERCERS COMPANY.
In 1699 or 1700 another similar institution was formed, under the name of The Society of Assurances for Widows and Orphans, which has long since passed away. There were
probably several others.
The following lines are from the Postboy of 3rd Jan., 1698, and clearly relate to the annuity and other bubbles of the period.
We have methods wholly new,
Strange, late invented, ways to thrive,
To make men pay for what they give,
Of their hereditary lands,
And out of what does thence arise,
To make 'em buy annuities.
We've mathematic combination
In 1698 John Ward, of Chester, pub. a compendium of Algebra, and thereto was an Appendix concerning compound int. and annuities. But as the same writer goes into the subject more at large in another work, pub. 1710, we shall defer our analysis of his views until we arrive at that date.
In 1703 a money Act was passed-2 & 3 Anne, c. 3-in which life annu. were granted upon a similar plan to that in the previous Acts, but upon less favourable terms to the purchasers. In place of seven, eight and a half, and ten years' purchase, the prices were for one life at the rate of nine years' purchase, or for two lives at the rate of eleven years' purchase, or for three lives at the rate of twelve years' purchase (sec. 10). Annu. for 99 years were to be bought at 15 years' purchase. All the annu. granted under this Act were ultimately taken up by the South Sea Co.
In 1704 by 3 & 4 Anne, c. 2-An Act for raising monies by sale of several annu. for carrying on the present war-"natives or foreigners were entitled to exchange any life annu. purchased under the preceding Act into an annuity for 99 years certain, on payment of 6 years' add. purchase; or in case of an annu. orig. granted for two lives, and where one life had dropped, for 4 years' purchase; or in case of three lives for 3 years' purchase (sec. 3).
This persistence in imaginary estimates, notwithstanding that Dr. Halley had ten years previously illustrated the importance of distinction as to age, etc., portrays that the new doctrine of life-valuation was as yet but little appreciated, being prob. overlooked, or deemed still more fanciful than even the ordinary methods then in use.-Farren.
In 1706 the Amicable So. for Perpetual Assu. obtained its charter, under which there was power to grant life annu.
About the year 1707 a curious project was set on foot under the title of The Proprietors of the Traders Exchange House. The projector was Charles Povey, the founder of the Sun Fire Office. It was part of the scheme that at the end of the first five years, 50 of the poorest members were to receive an annu. of £10 for life; and after another five years, fifty others. [PROPRIETORS OF TRADERS EXCHANGE HOUSE.]
In this year was first pub. Smart's Interest Tables, of which we shall have to speak hereafter (see 1726).
At the close of 1709 a scheme was announced, which partook in some respects of the nature of a Tontine. Its preliminary announcement was headed: "The lucky 70, or the longest lives take all." But the more matured project took the form following:
A proposal for annu. for life, with the benefit of survivorship, such as the purses of the generality of
the people may be able to compass issuing out of the annu. granted by Parl. for a term of 99 years, and lottery annuities for 32 years, and the reversions of annu. Hence great profits will arise to such as shall live long, and an immediate income to all the subs. tax free, and payable half-yearly during the lives of their respective nominees. The least sum to be subs. is £10, but any contributor or such person as shall be employed by such contributor, may subscribe for as many sums of 10 as he or she shall think fit. Subs. are taken from 2 till 5 in the afternoon, at Haberdashers Hall, in Maiden Lane, near Wood Street, Lond., where may be seen the art. of agreements, the method in disposing of the subs. monies, and the allowances to the subs. of the first £20,000, and other particulars relating to the said proposal. Note-There are four subscription books marked A. B. C.D., that is to say, A. for nominees of any age; B. for nominees not under 20; C. for nominees not under 30; and D. for nominees not under 40 years of age.
This was, we believe, the first instance of any classification of ages being introduced. What was the fate of the project we do not learn. It is not surprising that outside speculators saw that money was to be made out of the Government annu. projects. But as every one could buy from the Government direct, there was not much need for the founding a special asso.
In 1710 there was a lottery drawn in Lond. consisting of 150,000 tickets valued at £10 each every ticket being entitled to an annuity for 32 years, the blanks to 145. p.a.; and the prizes to various annu. ranging from £5 to £1000.
The annuity-mongers of this period afforded some points for the satirists. selects a character whom he speaks of as Africanus :
One who has long been conversant in bartering; who knowing when stocks are lowest it is the time to buy, therefore with much prudence and tranquility thinks it the time to purchase an annu. for life. Again: Sir Thomas added he would have bought twelve shillings a year of him, but that he feared there was some trick in it, and believed him dead already!
In 1710 was pub. by John Ward, a little book called Clavis Usure or a Key to Interest, etc., which confirms in a very marked manner some of the preceding details: The way generally used in buying of annu, or letting of leases for lives, is only by an imaginary valuation grounded upon custom, and not upon any consideration that is had to the age of the persons whose lives are to be inserted in the lease, etc. 'Tis true indeed that there can be no certain rules prescribed for their true valuation, because the lives of all mankind are uncertain; and 'tis possible and daily seen that a young man may die before one of greater age. But yet there is a greater prob. of a young man's living longer than an old one; and not only so, but there's a proportional likelihood of the length of men's lives according to their different degrees of age. The which being duly considered, must needs be found of good use in estimating the values of annu. or leases for lives, much better than by a mere guessing only as usual; and that such a proportional likelihood is worth the consideration will appear from what follows.
He then recites Sir Wm. Petty's Use of Duplicate Proportion, afterwards adding by way of comment :
Thus you have a learned gentleman's opinion concerning the likelihood of the length of men's lives according to rules of duplicate proportion, which was a very ingenious thought of his. But I must beg pardon that I cannot agree with him in that part of it which asserts that 21 years is the age for whole life or lease is most valuable. For, although 'tis true that according to our law a man is said to be at his perfect or full age as to the enjoyment of an estate, or managing his affairs without a guardian, etc., yet I shall rather adhere to the close of his discourse wherein he says that he found that if the sum of all ages of the 330 souls (in a certain parish) being divided by their number, made the quotient between 15 and 16. Whence I take 16 to be the age for whose life a lease is most valuable.
Upon that supposition he calculated the following table, "according to the aforesaid rules of Duplicate Proportion":
This table (he says) shows by inspection the value of every five years of any single life from the birth to 71 years old. Supposing that any annuity or lease, etc., is really worth nine years' purchase for one life, which is according to the rate that the annuities settled by a late Act of Parl. for lives were valued at, and from thence the rest are computed. He then notices Dr. Halley's estimate, and after inserting the relative table of annuities, adds:
This table being of the same nature with that in page 107 (ie. the table above), there needs no other explanation or example to show its use, than what has been already said about that table: only here I must again beg leave to give my opinion about the difference of the proportions in the two tables, which is, that as the table in page 107 may not be thought a sufficient guide to be depended upon in estimating the length of men's lives, etc., because it's only deduced from the bare rules of art, viz., that of duplicate proportion; so on the other hand, I doubt the estimates of the value of any annu. taken from this table (ie. Dr. Halley's), will be found too great in this country (viz. in England), which I much fear hath not so good or salubrious an air as that at the city of Breslaw, from whence these calculations are drawn. But if in imitation hereof, the curious in other cities and large towns would attempt something of the same nature; then without all doubt this method of estimating the prob. of the length of men's lives would prove the best, and become more universally useful than can be expected from this one single instance, more especially if such observations were continued for any considerable time, as 20 or 30 years successively.-p. 111.
The above quotations from a little interest-book pub. in 1710 sufficiently illustrate that however much the subject of distinctive life valuations might be generally overlooked, yet that it was gradually attracting the attention of occasional writers.-Farren.
In 1711 Mr. Edward Hatton pub. his Index of Interest, and therein was contained: Tables showing by inspection the present worth of annuities, and the purchase thereof. Tables of the amount and present worth of any sum of money and of annuities to 61 years, and rules to apply them for 122 years. "Likewise easie rules for valuation of
1, 2, and 3 lives, etc., etc." This was the first attempt at popularizing the arithmetic of Life annuities-the first of many hundreds.
In the same year Mr. Thomas Langham pub. Tables of Simple and Compound Int. and therein was contained : Tables "whereby the amount or present value of any sum of money or any annuity, or lease, either in possession or reversion, from I year to 61, at the several rates of 3, 4, 5, 6, 7, 8, 9, and 10 p.c., is exactly calculated to the hundreth part of a penny;" but not a word concerning life annuities.
In the Post-Boy of 7th Feb., 1712, there was the following, by way of adv.: "If any person is willing to grant an annuity for Life upon good security, he may find one that has 2000 to lay out in that way. Enquire of Mr. Collins, Bookseller, at the Black Boy, over against St. Dunstons Church," etc.
In 1713 the legal rate of int. was reduced from 6 to 5 p.c., at which it remained from that period down to the abolition of the Usury Laws in 1854.
We now approach a period of more intense speculation in the matter of Life Annu. projects than any which we have yet passed. It was the period of the South Sea scheme, some six years preceding its grand but fatal climax. During this period any and every thing that could be associated with ins. or annu. seemed to find some measure of public support. The igenuity of honest projectors became in the end eclipsed by the daring audacity of bubble-mongers; but we must advance by gentle stages. Hardly anything in the way of ins. or annu. has been attempted during the century and a half which has since passed that was not in some form introduced or suggested at that period : hence the special attention which we call to it. When Mr. Fred. Hendriks, some years since, approached this period, he made the following judicious and almost necessary preliminary observation (Assu. Mag., vol. iv., p. 129):
The reader is presumed to be acquainted with the peculiar features of the hist. of the times when these subs. lists, and those of countless other projects, were formed and engrossed the attention and cupidity, not only of the trading classes, but of kings, nobles, clergy, and even of the fair sex, who had their 'Change hours in London, Paris, and Amsterdam. In the latter city there seems to have been almost as many insurance projects as in London.
Although we chiefly confine our attention in these pages to annuities on lives, we cannot pass over the fact of annuities being used as a means of raising cap. for the purposes of mercantile enterprise without some notice. The first announcement was the following, under date 5th January, 1714:
Given gratis at the Oil Annuity Office, against the Upper end of Montague House in Gt. Russel-st., Bloomsbury, a book entitled: An impartial account of the nature, benefit, and design of a new discovery and undertaking to make oil from the fruit of the beech tree. By authority of Her Majesty's Letters-Patents under the Great Seal of Gt. Britain. With answers to all that can possibly be said against it; and proposals for raising a stock of £20,000 upon annuities for 14 years at 50 p.c. p.a. upon a good and solid security.
On the 5th Jan. it was announced that the book of subscribers was open; and on the 21st of the same month that the subs. was complete. On the 1st March there appeared very lengthy "proposals" signed "A. Hill," for the formation of a Beech Oil Co., by sale of 5000 shares at £5 5s. a share, which throws some light upon the "good and solid security" held out to the annuitants :
This company is in a pretty considerable state of forwardness, and some hundred shares are bought. Shares will be sold daily till 1st May next in the mean time, first payment to annuitants will become due Lady-day, amounting to £3750, and shall be discharged out of my own pocket. As to the 30s. p.a. p. share, which must be paid to certain annuitants, I own it would have been more to my satisfaction that there had been no occasion to pay the money but the sharers will soon find that they have too good a bargain to complain for such a trifle.
Then on the 6th of May, same year, there were issued: Proposals for raising a stock of £100,000 for laying up great quantities of beech-mast for two years, at an int. of 45 p.c. p.a. to the subs.; and upon a security whereby they will always have in their own hands above ten times the value of the sum they contribute. To which is added a particular account of the nature, benefit, and design of the undertaking.
On the 26th Jan., same year, there appeared the following; and here the life element is introduced :
This day subs. will be taken for granting annuities (to raise a stock for improving the Fishery) in a method as advertised, and on a fund as good and well secured as ever was proposed, for £20 a year for Life, or 21 years, which shall first end, may be bought for £41, and a greater or lesser annuity in proportion. And that there may be no reason for suspicion or colour of fraud, the purchase-money will not be desired untill the subs. be complete, and directors chosen to receive it, and such as will pay double interest will be allowed 6 or 12 months longer; but no subs, will be received after 1st day of March next. The office is at the Crown in Fleet-street, near Water-lane, up one pair of stairs.
On the 2nd March, same year, there was another announcement introducing some modifications:
The subs. for raising a stock to improve the fishery by granting annuities of £20 a year for life, or 21 years, which shall first end, being near full, and those of £20 a year for life certain, and of £10 a year for life or 21 years, which shall first end, not above half full; and several persons declaring the time so short too inform their friends: until the last day of the month (if not full sooner) but no longer, annuities for £20 a year for life certain may be bought for £81, and those that remain of £20 a year for life, or 21 years, which shall first end, for £41; and £10 a year for £21, etc.
On the 2nd Oct., 1714, there was pub. in Lond. a proposal for settling jointures and granting annu. after the rate of 40 p.c. p. a. The scheme appears to have been built upon the plan of the Mercers Co.; indeed, the prospectus itself announces the fact:
The proposal now offer'd to the world has been maturely consider'd both by the proposers and