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The term "extra premium" in this Act shall be taken to mean the charge for any risk not provided for in the minimum contract premium. If policies are issued in or for any country at rates of premium deduced from tables other than the European mortality tables adopted by the Company, separate schedules similar in form to the above must be furnished.


(FORM referred to under heading No. 7 in Fifth Schedule.) VALUATION BALANCE-SHEET of

To net liability under Assurance and
Annuity transactions (as per summary
statement provided in Schedule 5)
To surplus, if any ...



£ s. d.

The Act further provides (sec. 8) :


as at



£ s. d. By life assurance and annuity funds (as per balance-sheet under Schedule 2 or 4). By deficiency,


8. Every company shall, on or before the thirty-first day of December, 1872, and thereafter within nine months after the date of each such investigation as aforesaid into its financial condition, prepare a statement of its life assurance and annuity business in the form contained in the sixth schedule to this Act, each of such statements to be made up as at the date of the last investigation, whether such investigation be made previously or subsequently to the passing of this Act. Provided as follows:(1.) If the next financial investigation after the passing of this Act of any company fall during the year 1873, the said statement of such company shall be prepared within nine months after the date of such investigation, instead of on or before the thirty-first day of December, 1872. (2.) If such investigation be made annually by any company, such company may prepare such statement at any time, so that it be made at least once in every three years. The expression "date of each such investigation' in this section shall mean the date to which the accounts of each company are made up for the purposes of each such investigation.

The "Sixth Schedule " is as follows:



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(The answers should be numbered to accord with the numbers of the corresponding questions. Statements of re-assurances corresponding to the statements in respect of assurances, under headings 2, 3, 4, 5, and 6, are to be given.)"

1. The published table or tables of premiums for assurances for the whole term of life which are in use at the date above mentioned.

2. The total amount assured on lives for the whole term of life, which are in existence at the date above mentioned, distinguishing the portions assured with and without profits, stating separately the total reversionary bonuses, and specifying the sums assured for each year of life from the youngest to the oldest ages.

3. The amount of premiums receivable annually for each year of life, after deducting the abatements


per cent.


Office yearly

Net yearly
if computed.

Net liability.

made by the application of bonuses, in respect of the respective assurances mentioned under heading No. 2, distinguishing ordinary from extra premiums.

4. The total amount assured under classes of assurance business, other than for the whole term of life, distinguishing the sums assured under each class, and stating separately the amount assured with and without profits, and the total amount of reversionary bonuses.

5. The amount of premiums receivable annually in respect of each such special class of assurances mentioned under heading No. 4, distinguishing ordinary from extra premiums.

6. The total amount of premiums which has been received from the commencement upon all policies under each special class mentioned under heading 4 which are in force at the date above mentioned. 7. The total amount of immediate annuities on lives, distinguishing the amounts for each year of life. 8. The amount of all annuities other than those specified under heading No. 7, distinguishing the amount of annuities payable under each class, the amount of premiums annually receivable, and the amount of consideration money received in respect of each such class, and the total amount of miums received from the commencement upon all deferred annuities.


9. The average rate of interest at which the life assurance fund of the company was invested at the close of each year during the period since the last investigation.

10. A table of minimum values (if any) allowed for the surrender of policies for the whole term of life and for endowments and endowment assurances, or a statement of the method pursued in calculating such surrender values, with instances of its application to policies of different standing and taken out at various interval ages from the youngest to the oldest.

Separate statements to be furnished for business at other than European rates, together with a statement of the manner in which policies on unhealthy lives are dealt with.

ACTUARIAL SOCIETY OF EDINBURGH.-This So. was founded in 1856, on the occasion of a secession from the Institute of Actuaries of Gt. Brit. of most of the Scotch members. The So. embodies all the leading actuaries of Scotland, and in 1868 received a Charter of Incorp. under the title of FACULTY OF ACTUARIES IN SCOTLAND, under which head will be found a more detailed notice.

ACTUARIAL TABLES.-These are of several classes, as Tables of Simple and Compound Int., Tables of Annuities, and Tables of Logarithms. But what may be regarded as coming more closely within the scope of this definition, are Tables of money-values deduced from the combined effects of int. and prob., especially as connected with the duration of human life. We propose here to give a chronological list of Tables answering more particularly to the last definition; adding such observations as seem essential. We believe no such list has been heretofore compiled. Observations and criticisms on the Mort. Tables will be given when we treat of those Tables; and the proper rate of int. to be assumed under given circumstances will be discussed under INTEREST, RESERVE, VALUATIONS, etc. A chronological list of Tables of LOGARITHMS will be given hereafter. Tables of Int. were pub. at a very early date, but the earliest we need note here are those pub. by "John Smart, at the Town Clerk's Office, Lond.," in 1707, viz. :

Tables of Simple Int. and Discount at 3, 4, 5, 6, 7, 8, 9, and £10 p.c. p.a.; also Tables of Compound Int., whereby the amount or present value of any sum of money, or any annuity, or other yearly payment, etc., for any number of years not exceeding one hundred is readily found. (See again 1726)

In 1725 Abraham De Moivre, F.R.S., pub. the first ed. of his Treatise of Annuities on Lives, and thereto was appended a Table: The present value of an annuity of one pound for any number of years not exceeding 100. Int. at 5 p.c. This Table was

founded on the Breslau Mort.

In 1726 Smart pub. 2nd ed. of his Tables, and therein was contained "a Table to calculate the value of annuities upon lives." But this Table was constructed on a plan the very reverse of more modern Tables. It was made to show, not how long the annuitant might be expected to live-but how long he must live in order to be reimbursed the value of his purchase-money.

In 1727 Mr. Richard Hayes pub. a new method for valuing annuities upon lives, showing at sight as follows: 1. How many years, months, etc., purchase an annuity upon life, for any age from 30 to 73 years, is worth, when money yields 4, 5, 6, 7, or 8 p.c. int. 2. How much a year £100 is worth upon life for any of the above ages, etc. 3. How many years an annuitant must live to receive the value of the money sunk, etc., etc. In 1742 Mr. Thomas Simpson pub. The Doctrine of Annuities and Reversions, deduced from general and evident principles, with useful Tables showing the values of single and joint lives, etc., at different rates of int., etc. These Tables were deduced from the Lond. Tables of Mort.

In 1747 Mr. James Hodgson pub. The Valuation of Annuities upon Lives deduced from the Lond. Bills of Mort., wherein was contained Tables of values at 3, 4, and 5 p.c. p.a. In 1751 Mr. Weyman Lee pub. (appended to his work on annuities) Tables of the value of Annuities and Leases certain, for years, and for a single life at every age of life, at the rates of 3, 4, 5, and 6 p. c. int.

In 1754 Mr. S. Stonehouse pub. The Valuation of Annuities on Lives deduced from the Lond. Bills of Mort., with several Tables exhibiting at one view the Values of Lives at different rates of Int., and Tables of Compound Int., and of Fines for renewing College Leases, etc.

In 1762 was pub. Dr. Price's famous work: Observations on Reversionary payments, wherein he gave various Tables, mostly Simpson's, based upon the Lond. Bills of Mort. In 1772 Dale's Calculations, deduced from first principles, was pub. The Tables included therein were Simpson's and others.

In 1779 Mr. Wm. Morgan pub. The Doctrine of Annuities and Assu. on Lives and Survivorships, and therein was contained tables of the values of single lives, of two equal joint lives, and of two lives differing in age by 60 years, computed from the Northampton Tables, not then published.

In 1780 Charles Brand pub. an ed. of Smart's Tables of Int., Discount, and Annuities, etc., enlarged, revised, and improved. It was then regarded as a very important work. In 1783 Dr. Price first pub. his Northampton Table of Mort. with extensive Tables of money-values based thereon. These Tables are so well known that we need not stay to enumerate them.

In 1802 Mr. Francis Baily pub. Tables for the Purchasing and Renewing of Leases for terms of years certain and for lives; with rules for determining the value of the reversion of estates after any such leases, etc.

In 1815 Mr. Milne pub. the famous Carlisle Table of Mort., and at the same time gave a valuable series of Tables of Monetary values deduced therefrom. These also are so well known as not to require detailed enumeration.

In 1825 Mr. Griffith Davies pub. Tables of Life Contingencies, containing the rate of mort. among the members of the Equitable So., and the values of Life Annuities, Reversions, etc., computed therefrom, together with a more extensive scale of prems. for Life Assu. deduced from the Northampton Table than any theretofore pub., and the progressive values of life policies.

In 1832 Mr. T. R. Edmonds pub. Life Tables, founded upon the discovery of a numerical law regulating the existence of every human being, etc. These tables may be regarded as having a scientific rather than a practical value.

In 1840-41 Mr. David Jones's well-known Tables in 2 vols. were pub. The series is very extensive, but the work has the merit of being everywhere known, and therefore requires no detailed notice here.

In 1841 Mr. Edward Sang pub. in Edin., Life Assurance and Annuity Tables, with a copious collection of rules and examples, 2 vols. great folio.-The description and uses of the tables fill 98 pages of intro. ; as there is no index of contents, it becomes necessary to enumerate the tables by groups, in order to give some idea of their extent and variety; premising that the ages are carried from 0 to 100, and that the values are accompanied by their logarithms in five decimals. No distinction is made between male and female life; the values are all based on Carlisle tables at 3 per cent.

1. Logarithms of all numbers under 10000; 2. Numbers to all logarithms of four places. FOR ONE LIFE.-3. Annuity and Assurance, constant and increasing; 4. Annuity and Assurance, short and deferred, and Policy current with risk; 5. Short period premiums for assurance at death, by 2, 3, 4, . . . . 21 annual payments; 6. Variable premiums for assurance at death, increasing and decreasing quinquennially by steps of 10, 15 and 20 per cent. 7. Variable premiums for assurance at death, increasing and decreasing septennially by steps of 10, 15, and 20 per cent. ; 8. Annuities, the payment of which is to cease on the attainment of the ages of 70, 65, 60, 55, 50 years; 9. Premiums for assurance at death, the payment of which is to cease on the attainment of the ages 70, 65, 60, 55, 50 years; 10. Present value of assurances payable at death or on the attainment of the ages of 70, 65, 60, 55, 50 years; II. Annual premiums for assurances payable at death or on the attainment of the ages 70, 65, 60, 55, 50 years; 12. Present value of annuities of which the payment is to commence on the attainment of ages 70, 65, 60, 55, 50 years; 13. Annual premiums for annuities, of which the payment is to commence on the attainment of ages 70, 65, 60, 55, 50 years; 14. Present values of endowments at the ages 70, 65, 60, 55, 50 years; 15. Annual premiums for endowments at the ages 70, 65, 60, 55, 50 years; 16. Present values of endowments 10, 15, 20, 25, 30, years hence; 17. Annual premiums for endowments 10, 15, 20, 25, 30, years hence; 18. Annual premiums for short period assurances, 2, 3, 4,· 21 years; 19. Endowments at the ages 14, 15, 16,

17, 18, 19, 20, 21 years.

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FOR TWO LIVES.-20. Logarithms of joint endowments; 21. Joint annuities, first payment now; 22. Joint annuities, first payment one year hence; 23. Annuity during A's survivorship; 24. Annuity during B's survivorship; 25. Survivorship annuity; 26. Longest-life annuity, first payment now; 27. Longest-life annuity, first payment one year hence; 28. Assurance at A's death, if first; 29. Assurance at B's death, if first; 30. Assurance at first death; 31. Assurance at A's death, if second; 32. Assurance at B's death, if second; 33. Assurance at second death.

In 1843 Mr. Jenkin Jones pub. a series of Tables of annu. and assu., calculated from a new rate of Mort. amongst assu. lives. The first and only set of actuarial Tables deduced from the Experience of the 17 offices in this country.

In 1850 Mr. Wm. Orchard pub. single and ann. prems. for every value of annu. on single and joint lives, or survivorships, adapted to any Table of mort. at 2, 3, 34, 4, 44, 5, 6, and 7 p.c., also a Table for the formation of half-yearly and quarterly assu. prems. Mr. Peter Gray says (Assu. Mag. vol. vi., p. 181):

The values which it has been heretofore customary to tabulate for actuarial purposes, in connexion with specified rates of mort. and int., are those of annu. on single and joint lives at all ages; and from these by operations more or less complex, and with the aid of subsidiary Tables, the actuary has had to

form such other values as might be required in the solution of any particular problem in hand. Of the values thus requiring to be formed, those of the single and ann. prems for assu. occur perhaps more frequently than any others; and hence the desirableness of simplifying as much as possible the operations by which these are deduced from the corresponding annuities. To effect this simplification was the object of Mr. Orchard's work, in which, as will be admitted by all competent to form an opinion on the subject, the author has been completely successful. The arithmetical operation heretofore necessary has been entirely superseded, and the required values are found simply by inspection. In 1850 Mr. Wm. Wood pub. conversion tables, showing the single and ann. prems. for assu. payable on the extinction of any single or of any joint lives, or of the longest of any two or more lives, deduced from the values of life annu. at various rates of int. The purpose of these Tables was the same as that of Mr. Orchard's. Mr. Wood says:

The object of the following tables is to save the labour of calculating, from the values of the annu. the single and ann. prems. for an assu. of a sum payable at the end of the year in which any single life, or joint lives, or the longest of any two or more lives, shall become extinct. The single prems. for £100 are given at 3, 3 and 4 p.c. The ann. prems. are given at 4 p.c. for every difference of one penny. From these the ann. prems. deduced from the same annu. derived from other rates of int. are readily obtained. The tables it will thus be seen are thoroughly practical. The results are of course applicable to any tables of life annu., from whatever rate of mort. they may be derived.

In 1851 Mr. Peter Gray, Mr. W. A. Smith, and Mr. W. Orchard, jointly pub. Ins. and Annu. Tables according to the Carlisle Mort. at 3 p.c. These Tables included present value of annu. and single and ann. prems. for survivorship ins. on every combination of two lives.

Table VII. is a conversion table for passing from the value of an assu. to that of an In the intro. to the vol., believed to have been written by Mr. Gray (Mr. Orchard being then dead), there is the following:


It is proper to mention that the idea of this table belongs to Mr. Orchard, one of the compilers of the present work. Mr. Orchard pub. in May last a work entitled, "Single and Ann. Assu. prems, for every value of Annuity on Single or Joint Lives, or Survivors," etc., at eight rates of int.; the object of which is, as its title imports, from the value of an annuity on a specified status to pass to either the single or the ann. prem. for assu. on the same status. From this the transition to the inverse form of the table here given was easy.

Mr. Orchard exhibited some specimens of his tables, in manuscript, at one of the sessional meetings of the Inst. of Actuaries, on the 8th January, 1850; and singularly enough, at the very next meeting on the 28th of same month, there was laid on the table a copy of the work having the same object in view. It is intituled Conversion Tables, by Wm. Wood, F.S.A., etc. On comparison of the two works, it will appear that while the idea on which they are founded is the same, they have little in common in the manner in which that idea has been carried out by the respective authors.

In 1851 Mr. W. T. Thomson pub. a large Sheet Table comprising annuity values at every age, based upon the Carlisle Table 3 per cent. (See again 1853.)

In the same year Mr. Filipowski pub. (in an appendix to his anti-logarithms), a Table of Annuities for 3 joint lives at 3 per cent. Carlisle. This table arranged for all Quinquennial Combinations was first pub. in 1850.

In 1852 Mr. Benjamin Hall Todd pub. Life Assu. Investigation Tables, showing the value of £100 policy for any number of years (not exceeding 50) interpolated for months, according to the Carlisle T. of Mort. and 3 p.c. int. ; also ann. and single assu. prems., Carlisle T. 3 p.c. int., interpolated for months. The author says:

With the aid of the tables at present in use, the method of valuing policies may be sufficiently curt and convenient for ordinary practical purposes; but when the Actuary has to investigate the affairs of a Co. and to ascertain its true position, the labour attending such an inquiry is very arduous; and from the immense mass of figures to be dealt with, all such investigations require to be very carefully checked to insure that correctness which the importance of the subject demands. It was under

these impressions that the idea of forming a table of the value of policies first suggested itself to the author.

In 1853 Mr. W. T. Thomson pub. Actuarial Tables, Carlisle 3 p.c. single lives and single deaths, with auxiliary tables, in one vol.; a most comprehensive and excellent arrangement characterizes these tables; they are too well known to all actuaries to require detailed notice here.

In the same year there was pub. in Assu. Mag. (vol. iii.) the five orig. Tables compiled by Mr Peter Hardy, deduced from the Mort. experience of the Equitable So. [EQUITABLE So. EXPERIENCE.]

In the same year (1853) the Hon. Elizur Wright, then Ins. Commissioner for the State of Massachusetts, pub. in Boston. U.S., Valuation Tables on the Combined experience rate of Mort. for the use of Life Ins. Cos. These Tables give the ann. monthly and daily values of policies, at 3 and 4 p.c. int., for all periods and ages from 10 to 100; and they constitute the standard by which the position of asso. doing life bus. in that State are annually tested. But for the aid of such a set of Tables, it would be impossible for the officers of the Ins. department to make these yearly tests. A 2nd ed. of these Tables, with many add., has been pub. during the present year. (See 1871.)

In 1854, Mr. Peter Hardy pub. in Assu. Mag. (vol. iv.) a Table showing the present value of I p.a. for any number of years not exceeding 100, at the following rates of int. I, I, II, 11, 21, 28, 2, and 21.

In 1855 there was pub. in Assu. Mag. (vol. v. pp. 363-8) Tables of single and ann. prems. for Joint Life Ins. for all ages between 15 and 60, deduced by William Braid, of Edinburgh, from the Carlisle Table. Int. 3 p.C. Same year there was pub. also in Assu.

Mag. (vol. vi. pp. 115-120) a series of tables

for determining the values of annu. and assu. on 3 lives according to the Carlisle Table of Mort., and showing the values of the annu. payable during the joint lives. Int. 3 p.c. By the same author.

Same year, Assu. Mag. (vol. v.) contains a Table constructed by Charles Gabriel Shaw: value of £1 during the joint continuance of 3, 4, 5, and 6 lives of equal ages. Carlisle. 3 p.c.

In 1857, Mr. W. E. Hillman pub. Tables of the Value of a Policy of Ins. for £1, according to the mort. indicated by the Carlisle observations, and also the Combined Experience of Life Ins. Cos. at 3, 3, and 4 p.c. int., with preparatory Tables for ascertaining the value of such ins. for every age from 14 to 60 years, and of duration from 1 to 50 years. Tables of this description were much required in the profession; but unfortunately these have not quite met the requirement. Mr. Laundy, writing to the Assu. Mag. (vol. ix. p. 239), says, "Instead, however, of obtaining the expected aid, I discovered that a considerable number of the values I had based upon Mr. Hillman's figures were untrue, owing to the extreme inaccuracy of the Table referred to (Experience Table), not a page of which is without numerous errors." Mr. Laundy recalculates the entire table. Mr. Manly (Assu. Mag. vol. xiv. p. 264) says: I can fully endorse Mr. Laundy's remark that no reliance whatever can be placed upon the correctness of the values in Hillman's Tables.

In 1858 Mr. David Chisholm pub. Commutation Tables for joint annu. and survivorship assu. based on the Carlisle Mort. at 3, 3, 4, 5, and 6 p.c. int., with tables of annu. and assu. on single lives, and other useful tables, and an intro. on their construction and "The object of the present pub. is to provide the actuary with a complete series of life assu. tables on the system originated by the late Geo. Barrett, and improved by Mr. Griffith Davies."


In 1859 Mr. Jardine Henry pub. The Government Annuity Tables, embracing the values of annu. on single, and two joint lives, at 3, 4, 5, and 6 p.c. p.a. for every combination of age and sex, founded upon the mort. obs. contained in Mr. John Finlaison's report, 1829. It has always appeared to us that the compiler of these tables has fallen into the error of taking for the base of his calculation, observations No. 8 and 15 of the late Mr. Finlaison, instead of Nos. 13 and 20-which latter were really the ones upon which all the Tables of Life Annuities computed for the service of the Government were based. Has this been previously observed ?

In 1861 Mr. W. Downing Biden pub. Rules, Formulæ, and Tables for the valuation of Estates, whether Freehold, Copyhold, or Leasehold, in possession or in reversion, and dependent on terms of certain duration, or on a Life or Lives; with new Rules and Tables for ascertaining the correct market value or fair price to be given for annu., rev. and next presentations, in order to secure to the purchaser a certain rate of int. on equitable terms; and a set of Conversion Tables for ascertaining from the price of an Annu. the cost of a Rev., to allow the purchaser a given rate of int. with security.

Some of these tables are deduced from the Carlisle Mort., some from the English Life Tables.

In 1863 Mr. Andrew H. Turnbull pub. Tables of Compound Int. and annu., yearly, half-yearly, and quarterly payments in decimals and currency; with rules for determining the amount of principal and int. in any payment of annu., and for the construction of Tables showing the same.

In 1864 Dr. Farr pub. English Life Tables (No. 3.), Tables of Lifetimes, annuities and premiums, with an intro. The tables are very extensive, comprising, in single lives, an entire suit of commutation columns at the several rates of interest from 3 to 10 p.c., for male and female lives separately, by whole years as usual; with additional ones by halfyearly and quarterly values of int. and mort. ; and every possible combination of two joint lives, male and female, two males and two females, interest at 3 p.c. The fundamental logarithmic columns were evolved and printed by Scheutz's calculating machine, made in London by Mr. Donkin. The admirable introduction to the work cannot be too much commended to the actuarial student. It epitomizes the entire analysis of the science; and, amongst its other and various merits, points emphatically to a distinction between interest and discount, which has sometimes been misunderstood.-Paterson.

In 1866 Mr. Jardine Henry pub. vol. I of his Government Life Annu. Commutation Tables for single and two joint lives at 0, 1, 2, 24, 3, 3, 4, 5, 6, 7, 8, 9, and 10 p.c. p.a. ; and for three and four joint lives at 3 and 6 p.c. p.a., founded on the experience of the Government annuitants up to 1823, and on the further experience from 1823 to 1853, with Tables showing on inspection the ann. prems. for an ins of £100, by the above or by any other Tables, for single, two, three, and four joint lives, at 3 p.c., and also at all other rates on addition of constants. The work is to be completed in 8 vols. See an observation we have made regarding his previous work, 1859.

In 1868 the pub. of the ACTUARIAL MAG. was commenced.

of orig. Tables. [ACTUARIAL MAG.]

It contains a number

In 1869 was pub. (part 1) Valuation Tables, prepared specially for the use of the Ins. Department, State of New York, and based upon Homan's Table. Int. 4 p.c. [AMERICAN MORT. TABLES.] The following is a statement of the Tables contained therein :

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