recognized as influencing the relative annuity values, all life estimates were too imaginary and inconsistent to be even worthy of the name of calculated results.-Farren.

In 1692 the first attempt was made by the English Government to raise money by means of life annuities; and hence there arises the first mention of life annuities in the English Statute book. This was by 4 Wm. & Mary, c. 3, known as the "Million Act." Its object was to raise one million sterling, "to carry on the war against France," by means of tontine annuities, for the int. upon which £100,000 p.a. was to be set apart until A.D. 1700, and then £70,000, but in the event of the entire million not being so subscribed by a given date, those who did sub. were to have, in lieu of the tontine advantages, an annuity of £14 in respect of every £100 subs., during the remainder of their own or their nominee's lives. There were no provisions or restrictions as to age. Even on these terms however, only £881,493 12s. 2d. could be raised.

Great efforts were made to float this loan, and there was pub., apparently by authority, the following Tabie predicting the course of death of the entire 10,000 nominees. A copy of the table still exists in the British Museum; and we think it sufficiently remarkable to be given here entire, with the following explanation, which, in the original, is given at the foot of the Table:

This Table designed for the encouragement of contributors to advance monies upon the funds and terms expressed in the Act of Parl. newly passed, for granting to their Majesties certain rates and duties of excise upon Beer, Ale, etc., and being applicable to the first proposal therein mentioned, upon terms of yearly payments during life, with advantage of survivorship, was calculated upon this supposition, that the whole sum of Ten Hundred Thousand Pounds may be advanced, and consequently as many nominees as there are shares or 100 advanced, viz. 10,000. The following example will show the use of the table. Look in the left-hand column for the number of years desired. Suppose 22; you will find in the columns answerable to it that at the end of 22 years, there are 5034 nominees dead, and 4966 living, and that each contributor (whose nominee is then alive) will receive that year for interest £14 15. for each share or £100 by him advanced.

A table shewing how many out of 10,000 Lives or Nominees will be likely to die in any number of years proposed during the term of 99 years, and the yearly interest due, etc.

The first consideration which strikes us in reference to this Tablé 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.

TABLE-6 p.c.
Age.

Age.

Years'
Purchase.

Years' Purchase.

I

10:28 40 10'57

5

13'40

9'91

13'44

50

9'21

15

13'33

8.51

20 12.78 60

7.60

25

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

35

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 163/5 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 11 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,
To get the Rents into our hands

Of their hereditary lands,

And out of what does thence arise,

To make 'em buy annuities.

We've mathematic combination
To cheat folks by plain demonstration,
Which shall be fairly manag'd too-
The undertaker knows not how.

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