1605:
them; none will die between the ages of 11 and 12, so that annuities will be paid for one year on 9921 lives; 40 attain the age of 12 and die before 13, so that two payments will be made with respect to these lives. Reasoning in this way we see that the annuities on 35 of the nominees will be payable for three years; on 40 for four years, and so on. Proceeding thus to the end of the table, 15 nominees attain the age of 95, 5 of whom die before the age of 96, so that 85 payments will be paid in respect of these 5 lives. Of the survivors all die before attaining the age of 97, so that the annuities on these lives will be payable for 86 years. Having previously calculated a table of the values of annuities certain for every number of years up to 86, the value of all the annuities on the 10,000 nominees will be found by taking 40 times the value of an annuity for 2 years, 35 times the value of an annuity for 3 years, and so on—the last term being the value of 10 annuities for 86 years—and adding them together; and the value of an annuity on one of the nominees will then be found by dividing by 10,000. Before leaving the subject of De Witt, we may mention that we find in the correspondence a distinct suggestion of the law of mortality that bears the name of
Demoivre. In De Witt's letter, dated 27 October 1671 (
609:), an annual charge of a larger amount, but lasting for a short term. The latter is so calculated as to pay off, during its existence, the capital which it replaces, with interest at an assumed or agreed rate, and under specified conditions. The practical effect of the substitution of a terminable annuity for an obligation of longer currency is to bind the present generation of citizens to increase its own obligations in the present and near future in order to diminish those of its successors. This end might be attained in other ways; for instance, by setting aside out of revenue a fixed annual sum for the purchase and cancellation of debt (Pitt's method, in intention), or by fixing the annual debt charge at a figure sufficient to provide a margin for reduction of the principal of the debt beyond the amount required for interest (Sir Stafford Northcote's method), or by providing an annual surplus of revenue over expenditure (the "Old Sinking Fund"), available for the same purpose. All these methods have been tried in the course of British financial history, and the second and third of them are still employed; but on the whole the method of terminable annuities has been the one preferred by chancellors of the exchequer and by parliament.
1951:. The institute was founded in 1848, the first sessional meeting being held in January 1849. Its establishment has contributed in various ways to promote the study of the theory of life contingencies. Among these may be specified the following:--Before it was formed, students of the subject worked for the most part alone, and without any concert; and when any person had made an improvement in the theory, it had little chance of becoming publicly known unless he wrote a formal treatise on the whole subject. But the formation of the institute led to much greater interchange of opinion among actuaries, and afforded them a ready means of making known to their professional associates any improvements, real or supposed, that they thought they had made. Again, the discussions which follow the reading of papers before the institute have often served, first, to bring out into bold relief differences of opinion that were previously unsuspected, and afterwards to soften down those differences,--to correct extreme opinions in every direction, and to bring about a greater agreement of opinion on many important subjects. In no way, probably, have the objects of the institute been so effectually advanced as by the publication of its
1625:, which in 40 B.C. was adopted in the Roman Empire, and which declared that a testator should not give more than three-fourths of his property in legacies, so that at least one-fourth must go to his legal representatives. It is easy to see how it would occasionally become necessary, while this law was in force, to value life annuities charged upon a testator's estate. Aemilius Macer (A.D. 230) states that the method which had been in common use at that time was as follows:--From the earliest age until 30 take 30 years' purchase, and for each age after 30 deduct 1 year. It is obvious that no consideration of compound interest can have entered into this estimate; and it is easy to see that it is equivalent to assuming that all persons who attain the age of 30 will certainly live to the age of 60, and then certainly die. Compared with this estimate, that which was propounded by the praetorian prefect Ulpian was a great improvement. His table is as follows:
678:, vol. ii. (1852) p. 222, and vol. in. p. 93. The former of these contains a translation of De Witt's report upon the value of life annuities, which was prepared in consequence of the resolution passed by the states-general, on 25 April 1671, to negotiate funds by life annuities, and which was distributed to the members on 30 July 1671. The latter contains the translation of a number of letters addressed by De Witt to Burgomaster Johan Hudde, bearing dates from September 1670 to October 1671. The existence of De Witt's report was well known among his contemporaries, and Hendriks collected a number of extracts from various authors referring to it; but the report is not contained in any collection of his works extant, and had been entirely lost for 180 years, until Hendriks discovered it among the state archives of Holland in company with the letters to Hudde. It was the very first document on the subject that was ever written.
1601:
from the mortality that had actually prevailed among the nominees on whose lives annuities had been granted in former years. De Witt appears to have come to the conclusion that the probability of death is the same in any half-year from the age of 3 to 53 inclusive; that in the next ten years, from 53 to 63, the probability is greater in the ratio of 3 to 2; that in the next ten years, from 63 to 73, it is greater in the ratio of 2 to 1; and in the next seven years, from 73 to 80, it is greater in the ratio of 3 to 1; and he places the limit of human life at 80. If a mortality table of the usual form is deduced from these suppositions, out of 212 persons alive at the age of 3, 2 will die every year up to 53, 3 in each of the ten years from 53 to 63, 4 in each of the next ten years from 63 to 73, and 6 in each of the next seven years from 73 to 80, when all will be dead.
624:
arrangement under the authority of parliament. Thus annuities of class (1) fulfil most perfectly the object of the system as explained above; while those of class (2) have the advantage that in times of emergency their operation can be suspended without any inconvenience or breach of faith, with the result that the resources of government can on such occasions be materially increased, apart from any additional taxation. For this purpose it is only necessary to retain as a charge on the income of the year a sum equal to the (smaller) perpetual charge which was originally replaced by the (larger) terminable charge, whereupon the difference between the two amounts is temporarily released, while ultimately the increased charge is extended for a period equal to that for which it is suspended.
1597:
and so on. De Witt states that "annuities have been sold, even in the present century, first at six years' purchase, then at seven and eight; and that the majority of all life annuities now current at the country's expense were obtained at nine years' purchase"; but that the price had been increased in the course of a few years from eleven years' purchase to twelve, and from twelve to fourteen. He also states that the rate of interest had been successively reduced from 6-¼% to 5%, and then to 4%. The principal object of his report is to prove that, taking interest at 4%, a life annuity was worth at least sixteen years' purchase; and, in fact, that an annuitant purchasing an annuity for the life of a young and healthy nominee at sixteen years' purchase, made an excellent bargain.
636:
the national finances. Savings bank depositors are not concerned with the manner in which government invests their money, their rights being confined to the receipt of interest and the repayment of deposits upon specified conditions. The case is, however, different as regards forty millions of consols (included in the above figures), belonging to suitors in chancery, which were cancelled and replaced by a terminable annuity in 1883. As the liability to the suitors in that case was for a specified amount of stock, special arrangements were made to ensure the ultimate replacement of the precise amount of stock cancelled.
663:, put forth a very simple law of mortality: out of 86 children born alive, 1 will die every year until the last dies between the ages of 85 and 86. This law agreed sufficiently well at the Middle Ages of life with the mortality deduced from the best observations of his time; but, as observations became more exact, the approximation was found to be not sufficiently close. This was particularly the case when it was desired to obtain the value of joint life, contingent or other complicated benefits. Therefore, Demoivre's law is devoid of practical utility. No simple formula has sufficient accuracy.
502:) they do not mention the ideal capital sum, but speak of the annuity or annual payment that is received by the public creditor. Other instances of perpetuities are the incomes derived from the debenture stocks of railway companies, also the feu-duties commonly payable on house property in Scotland. The number of years' purchase which the perpetual annuities granted by a government or a railway company realize in the open market, forms a very simple test of the credit of the various governments or railways.
1963:, Mr Jellicoe continuing to be the editor,--a post he held until the year 1867, when he was succeeded by Mr T. B. Sprague (who contributed to the 9th edition of this Encyclopaedia an elaborate article on "Annuities," on which the above account is based). The name was again changed in 1866, the words "Assurance Magazine" being dropped; but in the following year it was considered desirable to resume these, for the purpose of showing the continuity of the publication, and it is now called the
1855:, pp. 1–20 (Sept. 1850), an account of it, with a translation of the passages describing the construction and use of the commutation table, and a sketch of the author's life and writings, to which we refer the reader who desires fuller information. It may be mentioned here that Tetens also gave only a specimen table, apparently not imagining that persons using his work would find it extremely useful to have a series of commutation tables, calculated and printed ready for use.
1859:
Barrett as the originator in
England of the method of calculating the values of annuities by means of a commutation table, and this method is accordingly sometimes called Barrett's method. (It is also called the commutation method and the columnar method.) Barrett's method of calculating annuities was explained by him to Francis Baily in 1811, and was first made known to the world in a paper written by the latter and read before the Royal Society in 1812.
1967:. This work contains not only the papers read before the institute (to which have been appended of late years short abstracts of the discussions on them), and many original papers which were unsuitable for reading, together with correspondence, but also reprints of many papers published elsewhere, which from various causes had become difficult of access to the ordinary reader, among which may be specified various papers which originally appeared in the
2199:
33:
578:, or enter into an alternatively secured pension (ASP). Under an ASP arrangement the rate of income must fall between 55% and 90% of the GAD rate for a 75-year-old. The GAD rates are subject to periodic review and are based on the return of a level, single life annuity paid monthly in arrears without any guarantee or value protection for an individual in good health. These rates are in turn largely dependent on long-term
567:. This is an unsecured pension as opposed to an annuity which is a secured backed pension. Unsecured pensions operate under age-related income limits calculated by the Government Actuarial Department to prevent the fund being eroded too fast. Before A-day, individuals could vary withdrawals between 35% and 100% of a maximum limit, recalculated every three years at what was known as the
432:
ambiguity, it is more commonly said he has "an annuity of £100, payable by half-yearly instalments". An annuity is considered as accruing during each instant of the status for which it is enjoyed, although it is only payable at fixed intervals. If the enjoyment of an annuity is postponed until after the lapse of a certain number of years, the annuity is said to be
1843:, 1779, also contains a commutation table. Morgan gives the table as furnishing a convenient means of checking the correctness of the values of annuities found by the ordinary process. It may be assumed that he was aware that the table might be used for the direct calculation of annuities; but he appears to have been ignorant of its other uses.
571:. Following changes introduced by HMRC as part of the A-day legislation, individuals can now draw an income between zero and 120% of the "GAD rate". On reaching 75, the individual must then secure their pension fund by the purchase of an annuity, except that up to 25% of the fund can be taken as tax-free cash, also known as the
260:
the spouse survives. The annuity paid to the spouse is called a reversionary annuity or survivorship annuity. However, if the annuitant is in good health, it may be more beneficial to select the higher payout option on their life only and purchase a life insurance policy that would pay income to the survivor.
235:
on whose life the annuity is based. The assumed period of the loan is based on the life expectancy of the annuitant but life annuities are payable until the death of the last surviving annuitant. In order to guarantee that the income continues for life, the investment relies on cross-subsidy. Because
1858:
The use of the commutation table was independently developed in
England-apparently between the years 1788 and 1811—by George Barrett, of Petworth, Sussex, who was the son of a yeoman farmer, and was himself a village schoolmaster, and afterwards farm steward or bailiff. It has been usual to consider
1785:
Here also we have no reason to suppose that the element of interest was taken into consideration; and the assumption, that between the ages of 40 and 50 each addition of a year to the nominee's age diminishes the value of the annuity by one year's purchase, is equivalent to assuming that there is no
1596:
It appears that it had long been the practice in
Holland for life annuities to be granted to nominees of any age, in the constant proportion of double the rate of interest allowed on stock; that is to say, if the towns were borrowing money at 6%, they would be willing to grant a life annuity at 12%,
627:
Annuities of class (1) were first instituted in 1808, but were later regulated by an act of 1829. They may be granted either for a specified life, or two lives, or for an arbitrary term of years; and the consideration for them may take the form either of cash or of government stock, the latter being
347:
Other than annuities provided by pension schemes, annuity contracts are usually issued by an insurance company. They are distributed by, and available for purchase from, duly licensed bank, stock brokerage, and insurance company representatives. Some annuities may also be purchased directly from the
1612:
De Witt's report being thus of the nature of an unpublished state paper, although it contributed to its author's reputation, did not contribute to advance the exact knowledge of the subject; and the author to whom the credit must be given of first showing how to calculate the value of an annuity on
635:
Annuities of this class do not affect the public at all, except of course in their effect on the market for government securities. They are merely financial operations between the government, in its capacity as the banker of savings banks and other funds, and itself, in the capacity of custodian of
545:
in 2006. From 2003 the tax deduction in the
Netherlands is only allowed if, without additional savings, the old age income would be less than 70% of the current income. The French government currently honors a very unusual debt contract: an annuity that was issued in 1738 and currently yields €1.20
259:
Although this will reduce the available payments, an annuity can be arranged to continue until the death of the last survivor of two or more people. For example, many annuities continue to pay out (perhaps at a reduced rate) to the spouse of the main annuitant after his or her death, for as long as
1600:
He argues that it is more to the advantage, both of the country and of the private investor, that the public loans should be raised by way of grant of life annuities rather than perpetual annuities. It appears from De Witt's correspondence with Hudde, that the rate of mortality assumed was deduced
497:
Instances of perpetuities are the dividends upon the public stocks in
England, France and some other countries. Thus, although it is usual to speak of £100 consols, the reality is the yearly dividend which the government pays by quarterly instalments. The practice of the French in this is arguably
382:
Because immediate annuities generally provide a series of guaranteed payments, the annuity company normally matches its liabilities with government bonds and other high grade bonds, and the market yield available on these bonds largely determines the retail pricing of the annuities. (The companies
1987:
of the institute has served, we may specify in particular two:--that any supposed improvement in the theory was effectually submitted to the criticisms of the whole actuarial profession, and its real value speedily discovered; and that any real improvement, whether great or small, being placed on
1604:
De Witt calculates the value of an annuity in the following way. Assume that annuities on 10,000 lives each ten years of age, which satisfy the Hm mortality table, have been purchased. Of these nominees 79 will die before attaining the age of 11, and no annuity payment will be made in respect of
328:
Contracts may also be linked to other investments such as property (real estate) or government bonds, or any combination of the above selected by the investor or his advisors. All varieties of deferred annuities owned by individuals have one thing in common in many jurisdictions: any increase in
297:
contract would be purchased at or before retirement but would not commence payments until 20 years after retirement. If the nominee dies before payments commence there is no payable benefit. This drastically reduces the cost of the annuity while still providing protection against outliving one's
1862:
By what has been universally considered an unfortunate error of judgment, this paper was not recommended by the council of the Royal
Society to be printed, but it was given by Baily as an appendix to the second issue (in 1813) of his work on life annuities and assurances. Barrett had calculated
623:
The important difference between these two classes is that an annuity under (1), once created, cannot be modified except with the holder's consent, i.e. is practically unalterable without a breach of public faith; whereas an annuity under (2) can, if necessary, be altered by interdepartmental
406:
Deferred pensions are often used as a savings vehicle by higher rate taxpayers, as in some jurisdictions they get higher rate tax relief on their pension contributions and their fund accumulates without investment returns being subject to tax. The proceeds will be taxed when they are taken as
431:
of the annuity is the sum to be paid (and received) in the course of each year. Thus, if £100 is to be received each year by a person, he is said to have "an annuity of £100". If the payments are made half-yearly, it is sometimes said that he has "a half-yearly annuity of £100"; but to avoid
1609:. vol. iii. p. 107), he speaks of a "provisional hypothesis" suggested by Hudde, that out of 80 young lives (who, from the context, may be taken as of the age 6) about 1 dies annually. In strictness, therefore, the law in question might be more correctly termed Hudde's than Demoivre's.
1959:, appeared in September 1850, and it has been continued quarterly down to the present time. It was originated by the public spirit of two well-known actuaries (Mr Charles Jellicoe and Mr Samuel Brown), and was adopted as the organ of the Institute of Actuaries in 1852, and called the
285:
or those with a particular illness are also available from some insurance companies. Since the life expectancy is reduced, the annuity rate is better (i.e. a higher annuity for the same initial payment). This can have the unfortunate appearance of one "betting against" the nominee.
407:
benefits, but maybe at a lower rate. Those in lower tax brackets may be told to avoid deferred pensions because they may not be able to recoup the charges made by the annuity company. (In some jurisdictions, some or all of the proceeds must by law be applied to purchase a pension.)
1786:
probability of the nominee dying between the ages of 40 and 50. Considered, however, simply as a table of the average duration of life, the values are fairly accurate. At all events, no more correct estimate appears to have been arrived at until the close of the 17th century.
521:, bought by any other means, has an element which is considered return of capital, and only the excess over this is considered a gain that is subject to income tax. The element considered capital return is based on life expectancy and will therefore increase with age.
1620:
Previously to Halley's time, and apparently for many years subsequently, all dealings with life annuities were based upon mere conjectural estimates. The earliest known reference to any estimate of the value of life annuities rose out of the requirements of the
1617:. He gave the first approximately correct mortality table (deduced from the records of the numbers of deaths and baptisms in the city of Breslau), and showed how it might be employed to calculate the value of an annuity on the life of a nominee of any age.
277:
Some providers also offer fixed-term annuities that run for a term of the customer’s choosing, and/or escalating annuities in which income payments begin at a lower level and then rise in line with inflation or at a fixed rate with each year that passes.
1863:
extensive tables, and with Baily's aid attempted to get them published by subscription, but without success; and the only printed tables calculated according to his manner, besides the specimen tables given by Baily, are the tables contained in
Babbage's
558:
contributions into pension savings are generally net of income tax (i.e. tax relief is available), up to certain limits. On retirement if an annuity is not purchased, retirement income up until the age of 75 can be drawn from the pension fund by using
666:
The rate of mortality at each age is, therefore, in practice usually determined by a series of figures deduced from observation; and the value of an annuity at any age is found from these numbers by means of a series of arithmetical calculations.
536:
Immediate annuities are a compulsory feature of certain pension saving schemes in some countries, where the government grants tax deductions, provided that savings are paid into a fund which can only (or mainly) be withdrawn as an annuity. The
480:; but more commonly the simple term "annuity" is understood to mean a life annuity, unless the contrary is stated. The payments can also be paid over the lifetime of the nominee(s) or for a fixed period, whichever is longer. This is known as
397:
For many elderly people, the financial risk of living longer than expected and running out of money is a bigger risk than investment risks such as exposure to a falling stock market. Immediate annuities protect against this risk.
1831:, xii. 328), show the proportion in which a benefit due at one age ought to be changed, so as to retain the same value and be due at another age. The earliest known specimen of a commutation table is contained in William Dale's
631:
Annuities (2) held by government departments date from 1863. They were created in exchange for permanent debt surrendered for cancellation, the principal operations having been effected in 1863, 1867, 1870, 1874, 1883 and 1899.
160:
An immediate annuity is an annuity for which the time between the contract date and the date of the first payment is not longer than the time interval between payments. A common use for an immediate annuity is to provide a
1846:
The first author who fully developed the powers of the table was John
Nicholas Tetens, a native of Schleswig, who in 1785, while professor of philosophy and mathematics at Kiel, published in the German language an
451:
Upon immediate annuitization, a wide variety of options are available in the way the stream of payments is paid. If the annuity is paid over a fixed period independent of any contingency, it is known as an
644:
The mathematical theory of life annuities is based upon a knowledge of the rate of mortality among mankind in general, or among the particular class of persons on whose lives the annuities depend, see
427:, this being a general word chosen in preference to such words as "time", "term" or "period", because it may include more readily either a term of years certain, or a life or combination of lives. The
593:
of the invested pension fund and mortality drag that occurs from the loss of cross-subsidy and advancing average age expectancy that occurs in the time over which annuity purchase is delayed.
204:
An annuity certain pays the annuitant for a number of years designated. This option is not suitable for retirement income, as the person may outlive the number of years the annuity will pay.
314:
and is a vehicle for accumulating savings, and eventually distributing them either as an immediate annuity or as a lump-sum payment. Note that this is different from an immediate annuity.
270:
Annuities with guaranteed periods are available from most providers. In such a product, if death takes place within the guaranteed period, payments continue to be made to a nominated
369:
A wide variety of features have been developed by annuity companies in order to make their products more attractive. These include death benefit options and living benefit options.
494:
If not otherwise stated, it is always understood that an annuity is payable yearly, and that the annual payment (or rent, as it is sometimes called) is a single currency unit.
355:) to an insurance company, and in return pay the annuitant a series of periodic payments for the rest of their life. The exact terms of an annuity product are set out in the
340:. A deferred annuity that permits allocations to stock or bond funds and for which the account value is not guaranteed to stay above the initial amount invested is called a
251:
Cross-subsidy remains one of the most effective ways of spreading a given amount of capital and investment return over a lifetime without the risk of funds running out.
17:
674:, grand pensionary of Holland and West Friesland. Our knowledge of his writings on the subject is derived from two papers contributed by Frederick Hendriks to the
491:. The difference with the period certain annuity is that the period certain annuity will keep paying after the death of the nominee until the period is completed.
1897:, No. 1, p. 1, and No. 2, p. 12; and in particular De Morgan's "Account of a Correspondence between Mr George Barrett and Mr Francis Baily," in the
336:
To complete the definitions here, a deferred annuity where the benefits are fixed at the outset, either in terms of a lump sum or an annuity, can be called a
231:
This annuity can be compared to a loan which is made by the purchaser to the issuing company, who then pay back the original capital with interest to the
1988:
record, successive writers have been able, one after the other, to take it up and develop it, each commencing where the previous one had left off.
50:
605:. This result is attained by substituting for a perpetual annual charge (or one lasting until the capital which it represents can be paid off
362:
In common with other types of insurance contract, both immediate and deferred annuities will typically pay commission to the sales person (or
97:
324:
stock index funds or other stock funds (such as ETFs), where the growth or shrinkage of the account depends on the performance of the market.
1983:; also translations of various papers from the French, German, and Danish. Among the useful objects which the continuous publication of the
69:
144:
is a financial contract which provides an income stream in return for an initial payment with specific parameters. It is the opposite of a
2219:
487:
A hybrid of these is when the payments stop at death, but also after a predetermined number of payments, if this is earlier: known as a
76:
2214:
533:
in old age, annuities often have a favourable tax treatment, which may affect how attractive they are relative to other investments.
83:
670:
The first writer who is known to have attempted to obtain, on correct mathematical principles, the value of a life annuity, was
1874:, a work which contains, among others, two tables, which are confessedly derived from Baily's explanation of Barrett's tables.
529:
Because of cross-subsidy and the guarantees an annuity can give against running out of income and becoming dependent on state
65:
436:. If an annuity, instead of being payable at the end of each year, half-year, etc., is payable in advance, it is called an
2049:
263:
Other features such as a minimum guaranteed payment period irrespective of death, known as life with period certain, or
351:
In a typical immediate annuity contract, an individual would pay a lump sum or a series of payments (sometimes called
116:
1813:, by means of which the value of an annuity at any age and any rate of interest may be found. See also the article
394:. However fixed annuities do not protect the purchaser against the effects of inflation, which is a material risk.
1827:, aptly so named in 1840 by Augustus De Morgan (see his paper "On the Calculation of Single Life Contingencies,"
54:
1851:. This work appears to have been quite unknown in England until F. Hendriks gave, in the first number of the
90:
386:
These investments are generally regarded as less risky than other investments, such as those linked to the
1904:
The principal commutation tables published in
England are contained in the following works:--David Jones,
648:. In practice simply tables may be used, which vary in different places, but which are easily accessible.
321:
bank deposits in that they offer the buyer interest on their money and a guaranteed return of capital, or
2269:
542:
2246:
1936:, 1873; and Dr William Farr's contributions to the sixth (1844), twelfth (1849), and twentieth (1857)
1835:, published in 1772. A full account of this work is given by F. Hendriks in the second number of the
601:
Terminable annuities are employed in the system of British public finance as a means of reducing the
289:
Life annuities are priced based on the probability of the nominee surviving to receive the payments.
2240:
130:
468:. An annuity depending on the continuance of an assigned life or lives would commonly be called a
645:
530:
43:
293:
is a form of annuity that defers commencement of the payments until very late in life. A common
383:
are usually required by law to invest their funds in this way, to reduce the risk of default.)
464:; and if in the latter case it is not to commence until after a term of years, it is called a
579:
145:
216:
or lifetime immediate annuity is most often used to provide an income in old age (i.e., a
168:
It is a financial contract which makes a series of payments with certain characteristics:
8:
2235:
290:
245:
2264:
137:
317:
Under the heading of deferred annuities, there are contracts which may be similar to
187:
during the lifetime or one or more persons, possibly reduced after death of one person
267:
where the payment rises by inflation or a fixed rate annually can also be purchased.
1908:, issued in parts by the Useful Knowledge Society, completed in 1843; Jenkin Jones,
1877:
Those who desire to pursue the subject further can refer to the appendix to Baily's
656:
612:
Terminable annuities, as employed by the British government, fall under two heads:
333:
taxed until those gains are withdrawn. This is also known as tax-deferred growth.
1947:
The theory of annuities may be further studied in the discussions in the English
391:
282:
2250:, vol. 2 (9th ed.), New York: Charles Scribner's Sons, pp. 72–89
590:
583:
555:
506:
225:
2025:
2258:
2210:
2205:
1622:
1614:
602:
149:
513:
purchased with pension funds or by an employer immediately on retirement (a
240:
can be expected to have a distribution of lifespans around the population's
572:
387:
213:
2239:
2223:. Vol. 2 (11th ed.). Cambridge University Press. pp. 75–78.
619:
those held by government departments or by funds under government control.
415:
Actuarial formulae are used to model annuities and determine their price.
671:
538:
271:
1940:
of the Registrar General in England (English Tables, I. 2), and to the
1881:, De Morgan's paper "On the Calculation of Single Life Contingencies,"
1865:
Comparative View of the various Institutions for the Assurance of Lives
1789:
The mathematics of annuities has been very fully treated in Demoivre's
423:
In technical language an annuity is said to be payable for an assigned
689:
Number Living and Dying at each Age, out of 10,000 entering at Age 10.
1818:
294:
244:(average) age, those dying earlier will support those living longer (
221:
651:
32:
1814:
575:
356:
2204:
This article incorporates text from a publication now in the
193:
during the lifetime but not shorter than a minimum number of years
1955:. The first number of this work, which was originally called the
444:, and the person on whose life the annuity depends is called the
217:
190:
during the lifetime but not longer than a maximum number of years
162:
1849:
Introduction to the Calculation of Life Annuities and Assurances
1965:
Journal of the Institute of Actuaries and Assurance Magazine
1961:
Assurance Magazine and Journal of the Institute of Actuaries
589:
Unsecured or alternatively secured pensions carry both the
241:
418:
348:
issuer, i.e., the insurance company writing the contract.
2177:
2175:
2173:
2171:
2169:
2167:
2152:
2122:
2120:
2118:
2116:
2114:
2099:
2089:
2087:
2085:
2083:
2081:
2079:
2077:
2075:
2073:
2058:
2008:
2006:
2004:
2002:
2000:
517:
annuity) is treated as taxable income. The income from
2164:
1833:
Introduction to the Study of the Doctrine of Annuities
152:
is not considered a European annuity for tax reasons.
2111:
2070:
1997:
57:. Unsourced material may be challenged and removed.
541:has such schemes and United Kingdom used to until
652:History of calculating life annuities or pensions
498:more logical. In speaking of their public funds (
220:). This type of annuity may be purchased from an
2256:
460:; if it is to continue for ever, it is called a
172:either level or fluctuating periodical payments
310:came into its own during the 1970s. This is a
1805:; there are also innumerable compilations of
1906:Value of Annuities and Reversionary Payments
681:
616:Those issued to, or held by private persons;
372:
175:made annually, or at more frequent intervals
687:TABLE OF MORTALITY—HM, HEALTHY LIVES—MALE.
410:
1926:Government Life Annuity Commutation Tables
117:Learn how and when to remove this message
18:Annuity (European financial arrangements)
2209:
2181:
2158:
2138:
2126:
2105:
2093:
2064:
2012:
524:
440:. The holder of an annuity is called an
2234:
639:
596:
419:Payment options for immediate annuities
254:
14:
2257:
1916:, 1825 (issued 1855); David Chisholm,
1870:In 1825 Griffith Davies published his
628:cancelled when the annuity is set up.
377:
2026:"Pension Annuity - How does it work?"
1949:Journal of the Institute of Actuaries
1889:chap. viii.; the preface to Davies's
401:
1795:Doctrine of Annuities and Reversions
155:
55:adding citations to reliable sources
26:
1839:, pp. 15–17. William Morgan's
301:
24:
2228:
1930:Institute of Actuaries Life Tables
199:
25:
2281:
2050:Federal Reserve Bank of Chicago,
1922:Contributions to Vital Statistics
66:"Annuities in the European Union"
2197:
1893:; also Hendriks's papers in the
165:to a retired person or persons.
31:
207:
42:needs additional citations for
2132:
2043:
2018:
306:The second usage for the term
13:
1:
2190:
1879:Life Annuities and Assurances
511:compulsory purchase annuities
390:, and probably offer a lower
2052:The Case of the Undying Debt
1872:Tables of Life Contingencies
281:Impaired life annuities for
7:
454:annuity with period certain
10:
2286:
2244:, in Baynes, T. S. (ed.),
1969:Philosophical Transactions
1803:Doctrine of Life Annuities
128:
1817:, and especially that on
682:De Witt's mortality table
561:pension income withdrawal
373:Investment considerations
1991:
1981:Companion to the Almanac
1901:, vol. iv. p. 185.
519:purchased life annuities
482:life with period certain
411:Actuarial considerations
131:Annuity (disambiguation)
2247:Encyclopædia Britannica
2220:Encyclopædia Britannica
1924:, 1857; Jardine Henry,
1885:, xii. 348-349; Gray's
646:actuarial present value
474:life-contingent annuity
184:fixed (annuity certain)
1973:Philosophical Magazine
1841:Treatise on Assurances
1613:correct principles is
489:temporary life annuity
472:, but also known as a
353:annuity considerations
338:fixed deferred annuity
1932:, 1872; R. P. Hardy,
1914:Treatise on Annuities
1910:New Rate of Mortality
1891:Treatise on Annuities
1791:Treatise on Annuities
549:
525:Government incentives
224:(Ireland and the UK,
178:in advance or arrears
2236:Sprague, Thomas Bond
640:Annuity calculations
597:Terminable annuities
573:pension commencement
255:Life annuity options
129:For other uses, see
51:improve this article
2141:, p. 77 cites
1977:Mechanics' Magazine
1912:, 1843; G. Davies,
1887:Tables and Formulae
1799:Tables and Formulae
691:
563:commonly known as
466:deferred perpetuity
378:Immediate annuities
291:Longevity insurance
246:longevity insurance
1957:Assurance Magazine
1942:English Life Table
1918:Commutation Tables
1899:Assurance Magazine
1895:Assurance Magazine
1883:Assurance Magazine
1853:Assurance Magazine
1837:Assurance Magazine
1829:Assurance Magazine
1825:Commutation tables
1793:(1725); Simpson's
686:
676:Assurance Magazine
661:Annuities on Lives
509:, the income from
402:Deferred annuities
329:account values is
238:annuity population
146:settlement funding
138:European Union law
2270:Actuarial science
2241:"Annuities"
2161:, pp. 77–78.
2108:, pp. 76–77.
2067:, pp. 75–76.
1928:, 1866 and 1873;
1920:, 1858; Nelson's
1797:(1742); P. Gray,
1783:
1782:
1594:
1593:
181:duration may be:
156:Immediate annuity
127:
126:
119:
101:
16:(Redirected from
2277:
2251:
2243:
2224:
2203:
2201:
2200:
2185:
2179:
2162:
2156:
2150:
2136:
2130:
2124:
2109:
2103:
2097:
2091:
2068:
2062:
2056:
2047:
2041:
2040:
2038:
2036:
2022:
2016:
2010:
1934:Valuation Tables
1807:Valuation Tables
1640:Years' purchase
1628:
1627:
692:
685:
657:Abraham Demoivre
569:triennial review
478:lifetime annuity
342:variable annuity
312:deferred annuity
302:Deferred annuity
122:
115:
111:
108:
102:
100:
59:
35:
27:
21:
2285:
2284:
2280:
2279:
2278:
2276:
2275:
2274:
2255:
2254:
2231:
2229:Further reading
2213:, ed. (1911). "
2198:
2196:
2193:
2188:
2180:
2165:
2157:
2153:
2137:
2133:
2125:
2112:
2104:
2100:
2092:
2071:
2063:
2059:
2054:, November 2009
2048:
2044:
2034:
2032:
2030:Retirement Line
2024:
2023:
2019:
2011:
1998:
1994:
1811:Interest Tables
1634:Years' purchase
684:
654:
642:
599:
591:investment risk
565:income drawdown
552:
527:
458:annuity certain
421:
413:
404:
392:expected return
380:
375:
304:
257:
210:
202:
200:Annuity certain
158:
134:
123:
112:
106:
103:
60:
58:
48:
36:
23:
22:
15:
12:
11:
5:
2283:
2273:
2272:
2267:
2253:
2252:
2230:
2227:
2226:
2225:
2211:Chisholm, Hugh
2192:
2189:
2187:
2186:
2163:
2151:
2131:
2110:
2098:
2069:
2057:
2042:
2017:
1995:
1993:
1990:
1781:
1780:
1777:
1774:
1771:
1767:
1766:
1763:
1760:
1757:
1753:
1752:
1750:
1749:60 and upwards
1747:
1744:
1740:
1739:
1736:
1733:
1730:
1726:
1725:
1722:
1719:
1716:
1712:
1711:
1708:
1705:
1702:
1698:
1697:
1694:
1691:
1688:
1684:
1683:
1680:
1677:
1674:
1670:
1669:
1666:
1663:
1660:
1656:
1655:
1652:
1649:
1646:
1642:
1641:
1638:
1635:
1632:
1592:
1591:
1588:
1585:
1582:
1579:
1576:
1572:
1571:
1568:
1565:
1562:
1559:
1556:
1552:
1551:
1548:
1545:
1542:
1539:
1536:
1532:
1531:
1528:
1525:
1522:
1519:
1516:
1512:
1511:
1508:
1505:
1502:
1499:
1496:
1492:
1491:
1488:
1485:
1482:
1479:
1476:
1472:
1471:
1468:
1465:
1462:
1459:
1456:
1452:
1451:
1448:
1445:
1442:
1439:
1436:
1432:
1431:
1428:
1425:
1422:
1419:
1416:
1412:
1411:
1408:
1405:
1402:
1399:
1396:
1392:
1391:
1388:
1385:
1382:
1379:
1376:
1372:
1371:
1368:
1365:
1362:
1359:
1356:
1352:
1351:
1348:
1345:
1342:
1339:
1336:
1332:
1331:
1328:
1325:
1322:
1319:
1316:
1312:
1311:
1308:
1305:
1302:
1299:
1296:
1292:
1291:
1288:
1285:
1282:
1279:
1276:
1272:
1271:
1268:
1265:
1262:
1259:
1256:
1252:
1251:
1248:
1245:
1242:
1239:
1236:
1232:
1231:
1228:
1225:
1222:
1219:
1216:
1212:
1211:
1208:
1205:
1202:
1199:
1196:
1192:
1191:
1188:
1185:
1182:
1179:
1176:
1172:
1171:
1168:
1165:
1162:
1159:
1156:
1152:
1151:
1148:
1145:
1142:
1139:
1136:
1132:
1131:
1128:
1125:
1122:
1119:
1116:
1112:
1111:
1108:
1105:
1102:
1099:
1096:
1092:
1091:
1088:
1085:
1082:
1079:
1076:
1072:
1071:
1068:
1065:
1062:
1059:
1056:
1052:
1051:
1048:
1045:
1042:
1039:
1036:
1032:
1031:
1028:
1025:
1022:
1019:
1016:
1012:
1011:
1008:
1005:
1002:
999:
996:
992:
991:
988:
985:
982:
979:
976:
972:
971:
968:
965:
962:
959:
956:
952:
951:
948:
945:
942:
939:
936:
932:
931:
928:
925:
922:
919:
916:
912:
911:
908:
905:
902:
899:
896:
892:
891:
888:
885:
882:
879:
876:
872:
871:
868:
865:
862:
859:
856:
852:
851:
848:
845:
842:
839:
836:
832:
831:
828:
825:
822:
819:
816:
812:
811:
808:
805:
802:
799:
796:
792:
791:
788:
785:
782:
779:
776:
772:
771:
768:
765:
762:
759:
756:
752:
751:
748:
745:
742:
739:
736:
732:
731:
728:
725:
722:
719:
716:
712:
711:
708:
705:
702:
699:
696:
683:
680:
653:
650:
641:
638:
621:
620:
617:
598:
595:
556:United Kingdom
551:
548:
526:
523:
507:United Kingdom
420:
417:
412:
409:
403:
400:
379:
376:
374:
371:
326:
325:
322:
303:
300:
256:
253:
226:Life Assurance
209:
206:
201:
198:
197:
196:
195:
194:
191:
188:
185:
179:
176:
173:
157:
154:
125:
124:
39:
37:
30:
9:
6:
4:
3:
2:
2282:
2271:
2268:
2266:
2263:
2262:
2260:
2249:
2248:
2242:
2237:
2233:
2232:
2222:
2221:
2216:
2212:
2207:
2206:public domain
2195:
2194:
2184:, p. 78.
2183:
2182:Chisholm 1911
2178:
2176:
2174:
2172:
2170:
2168:
2160:
2159:Chisholm 1911
2155:
2149:. vol. xviii.
2148:
2144:
2140:
2139:Chisholm 1911
2135:
2129:, p. 77.
2128:
2127:Chisholm 1911
2123:
2121:
2119:
2117:
2115:
2107:
2106:Chisholm 1911
2102:
2096:, p. 76.
2095:
2094:Chisholm 1911
2090:
2088:
2086:
2084:
2082:
2080:
2078:
2076:
2074:
2066:
2065:Chisholm 1911
2061:
2055:
2053:
2046:
2031:
2027:
2021:
2015:, p. 75.
2014:
2013:Chisholm 1911
2009:
2007:
2005:
2003:
2001:
1996:
1989:
1986:
1982:
1978:
1974:
1970:
1966:
1962:
1958:
1954:
1950:
1945:
1943:
1939:
1935:
1931:
1927:
1923:
1919:
1915:
1911:
1907:
1902:
1900:
1896:
1892:
1888:
1884:
1880:
1875:
1873:
1868:
1866:
1860:
1856:
1854:
1850:
1844:
1842:
1838:
1834:
1830:
1826:
1822:
1820:
1816:
1812:
1808:
1804:
1800:
1796:
1792:
1787:
1778:
1775:
1772:
1769:
1768:
1764:
1761:
1758:
1755:
1754:
1751:
1748:
1745:
1742:
1741:
1737:
1734:
1731:
1728:
1727:
1723:
1720:
1717:
1714:
1713:
1709:
1706:
1703:
1700:
1699:
1695:
1692:
1689:
1686:
1685:
1681:
1678:
1675:
1672:
1671:
1667:
1664:
1661:
1658:
1657:
1653:
1650:
1647:
1644:
1643:
1639:
1636:
1633:
1630:
1629:
1626:
1624:
1623:Falcidian law
1618:
1616:
1615:Edmund Halley
1610:
1608:
1602:
1598:
1589:
1586:
1583:
1580:
1577:
1574:
1573:
1569:
1566:
1563:
1560:
1557:
1554:
1553:
1549:
1546:
1543:
1540:
1537:
1534:
1533:
1529:
1526:
1523:
1520:
1517:
1514:
1513:
1509:
1506:
1503:
1500:
1497:
1494:
1493:
1489:
1486:
1483:
1480:
1477:
1474:
1473:
1469:
1466:
1463:
1460:
1457:
1454:
1453:
1449:
1446:
1443:
1440:
1437:
1434:
1433:
1429:
1426:
1423:
1420:
1417:
1414:
1413:
1409:
1406:
1403:
1400:
1397:
1394:
1393:
1389:
1386:
1383:
1380:
1377:
1374:
1373:
1369:
1366:
1363:
1360:
1357:
1354:
1353:
1349:
1346:
1343:
1340:
1337:
1334:
1333:
1329:
1326:
1323:
1320:
1317:
1314:
1313:
1309:
1306:
1303:
1300:
1297:
1294:
1293:
1289:
1286:
1283:
1280:
1277:
1274:
1273:
1269:
1266:
1263:
1260:
1257:
1254:
1253:
1249:
1246:
1243:
1240:
1237:
1234:
1233:
1229:
1226:
1223:
1220:
1217:
1214:
1213:
1209:
1206:
1203:
1200:
1197:
1194:
1193:
1189:
1186:
1183:
1180:
1177:
1174:
1173:
1169:
1166:
1163:
1160:
1157:
1154:
1153:
1149:
1146:
1143:
1140:
1137:
1134:
1133:
1129:
1126:
1123:
1120:
1117:
1114:
1113:
1109:
1106:
1103:
1100:
1097:
1094:
1093:
1089:
1086:
1083:
1080:
1077:
1074:
1073:
1069:
1066:
1063:
1060:
1057:
1054:
1053:
1049:
1046:
1043:
1040:
1037:
1034:
1033:
1029:
1026:
1023:
1020:
1017:
1014:
1013:
1009:
1006:
1003:
1000:
997:
994:
993:
989:
986:
983:
980:
977:
974:
973:
969:
966:
963:
960:
957:
954:
953:
949:
946:
943:
940:
937:
934:
933:
929:
926:
923:
920:
917:
914:
913:
909:
906:
903:
900:
897:
894:
893:
889:
886:
883:
880:
877:
874:
873:
869:
866:
863:
860:
857:
854:
853:
849:
846:
843:
840:
837:
834:
833:
829:
826:
823:
820:
817:
814:
813:
809:
806:
803:
800:
797:
794:
793:
789:
786:
783:
780:
777:
774:
773:
769:
766:
763:
760:
757:
754:
753:
749:
746:
743:
740:
737:
734:
733:
729:
726:
723:
720:
717:
714:
713:
709:
706:
703:
700:
697:
694:
693:
690:
679:
677:
673:
668:
664:
662:
658:
649:
647:
637:
633:
629:
625:
618:
615:
614:
613:
610:
608:
604:
603:National Debt
594:
592:
587:
585:
581:
577:
574:
570:
566:
562:
557:
547:
544:
540:
534:
532:
522:
520:
516:
512:
508:
503:
501:
495:
492:
490:
485:
483:
479:
475:
471:
467:
463:
459:
455:
449:
447:
443:
439:
435:
430:
426:
416:
408:
399:
395:
393:
389:
384:
370:
367:
365:
360:
358:
354:
349:
345:
343:
339:
334:
332:
323:
320:
319:
318:
315:
313:
309:
299:
296:
292:
287:
284:
279:
275:
273:
268:
266:
261:
252:
249:
247:
243:
239:
234:
229:
227:
223:
219:
215:
205:
192:
189:
186:
183:
182:
180:
177:
174:
171:
170:
169:
166:
164:
153:
151:
150:Swiss annuity
147:
143:
139:
132:
121:
118:
110:
99:
96:
92:
89:
85:
82:
78:
75:
71:
68: –
67:
63:
62:Find sources:
56:
52:
46:
45:
40:This article
38:
34:
29:
28:
19:
2245:
2218:
2154:
2146:
2142:
2134:
2101:
2060:
2051:
2045:
2033:. Retrieved
2029:
2020:
1984:
1980:
1976:
1972:
1968:
1964:
1960:
1956:
1952:
1948:
1946:
1941:
1937:
1933:
1929:
1925:
1921:
1917:
1913:
1909:
1905:
1903:
1898:
1894:
1890:
1886:
1882:
1878:
1876:
1871:
1869:
1864:
1861:
1857:
1852:
1848:
1845:
1840:
1836:
1832:
1828:
1824:
1823:
1810:
1806:
1802:
1798:
1794:
1790:
1788:
1784:
1619:
1611:
1606:
1603:
1599:
1595:
688:
675:
669:
665:
660:
655:
643:
634:
630:
626:
622:
611:
606:
600:
588:
568:
564:
560:
553:
535:
528:
518:
514:
510:
504:
499:
496:
493:
488:
486:
481:
477:
473:
470:life annuity
469:
465:
461:
457:
453:
450:
445:
441:
437:
433:
428:
424:
422:
414:
405:
396:
388:stock market
385:
381:
368:
363:
361:
352:
350:
346:
341:
337:
335:
330:
327:
316:
311:
307:
305:
288:
280:
276:
269:
264:
262:
258:
250:
237:
232:
230:
214:life annuity
211:
208:Life annuity
203:
167:
159:
141:
135:
113:
104:
94:
87:
80:
73:
61:
49:Please help
44:verification
41:
2143:Phil. Trans
672:Jan De Witt
582:yields and
539:Netherlands
438:annuity-due
298:resources.
272:beneficiary
228:) company.
2259:Categories
2191:References
2035:17 January
1979:, and the
1801:; Baily's
1645:Birth – 20
546:per year.
476:or simply
462:perpetuity
456:, or just
265:escalation
107:April 2022
77:newspapers
2265:Annuities
1819:insurance
659:, in his
584:mortality
442:annuitant
429:magnitude
295:longevity
233:annuitant
222:insurance
2238:(1878),
2147:Ass. Mag
2145:. 1693;
1944:, 1864.
1867:, 1826.
1815:interest
1607:Ass. Mag
576:lump sum
434:deferred
357:contract
2215:Annuity
2208::
1985:Journal
1953:Journal
1938:Reports
1779:
1770:44 – 45
1765:
1756:43 – 44
1743:42 – 43
1735:55 – 60
1729:41 – 42
1721:50 – 55
1715:40 – 41
1707:49 – 50
1701:35 – 40
1693:48 – 49
1687:30 – 35
1679:47 – 48
1673:25 – 30
1665:46 – 47
1659:20 – 25
1651:45 – 46
1590:
607:en bloc
554:In the
531:welfare
515:Hancock
505:In the
446:nominee
364:advisor
308:annuity
283:smokers
218:pension
163:pension
142:annuity
91:scholar
2202:
1975:, the
1971:, the
1776:
1762:
1587:
1584:
718:10,000
710:Dying
707:Living
698:Living
586:data.
500:rentes
425:status
136:Under
93:
86:
79:
72:
64:
1992:Notes
1578:6,910
1558:7,030
1538:7,154
1518:7,274
1498:7,387
1478:7,493
1458:7,600
1438:7,696
1418:7,793
1398:7,886
1378:7,970
1358:8,057
1338:8,142
1318:8,223
1298:8,311
1278:8,398
1258:8,479
1238:8,554
1218:8,625
1198:8,701
1178:8,774
1158:8,848
1138:8,913
1118:8,987
1098:9,054
1078:9,125
1058:9,185
1038:9,249
1018:9,297
998:9,361
978:9,434
958:9,493
938:9,560
918:9,616
898:9,684
878:9,743
858:9,784
838:9,784
818:9,806
798:9,846
778:9,881
758:9,921
738:9,921
701:Dying
543:A day
148:. A
140:, an
98:JSTOR
84:books
2037:2024
1809:and
1350:117
1330:119
1310:172
1290:173
1287:1005
1270:191
1267:1196
1250:196
1247:1392
1230:219
1227:1611
1210:226
1207:1837
1190:224
1187:2061
1170:245
1167:2306
1150:241
1147:2547
1130:300
1127:2847
1110:243
1107:3090
1090:268
1087:3358
1070:222
1067:3580
1050:213
1047:3793
1030:246
1027:4039
1010:237
1007:4276
990:220
987:4496
970:220
967:4716
950:215
947:4931
930:206
927:5137
910:200
907:5337
890:191
887:5528
870:186
867:5714
850:184
847:5898
830:153
827:6051
810:156
807:6207
790:152
787:6359
770:150
767:6509
750:153
747:6662
730:129
727:6791
580:gilt
242:mean
70:news
2217:".
1710:10
1696:11
1682:12
1668:13
1654:14
1637:Age
1631:Age
1581:119
1570:10
1561:120
1541:124
1521:120
1510:29
1501:113
1490:36
1481:106
1470:36
1467:116
1461:107
1450:34
1447:150
1430:36
1427:186
1410:74
1407:260
1390:72
1387:332
1370:92
1367:424
1347:541
1327:660
1307:832
704:Age
695:Age
366:).
344:.
331:not
248:).
236:an
53:by
2261::
2166:^
2113:^
2072:^
2028:.
1999:^
1821:.
1773:15
1759:16
1746:17
1738:7
1732:18
1724:9
1718:19
1704:20
1690:22
1676:25
1662:28
1648:30
1575:53
1567:10
1564:96
1555:52
1550:5
1547:15
1544:95
1535:51
1530:0
1527:15
1524:94
1515:50
1507:44
1504:93
1495:49
1487:80
1484:92
1475:48
1464:91
1455:47
1444:90
1441:96
1435:46
1424:89
1421:97
1415:45
1404:88
1401:93
1395:44
1384:87
1381:84
1375:43
1364:86
1361:87
1355:42
1344:85
1341:85
1335:41
1324:84
1321:81
1315:40
1304:83
1301:88
1295:39
1284:82
1281:87
1275:38
1264:81
1261:81
1255:37
1244:80
1241:75
1235:36
1224:79
1221:71
1215:35
1204:78
1201:76
1195:34
1184:77
1181:73
1175:33
1164:76
1161:74
1155:32
1144:75
1141:65
1135:31
1124:74
1121:74
1115:30
1104:73
1101:67
1095:29
1084:72
1081:71
1075:28
1064:71
1061:60
1055:27
1044:70
1041:64
1035:26
1024:69
1021:48
1015:25
1004:68
1001:64
995:24
984:67
981:73
975:23
964:66
961:59
955:22
944:65
941:67
935:21
924:64
921:56
915:20
904:63
901:68
895:19
884:62
881:59
875:18
864:61
861:41
855:17
844:60
835:16
824:59
821:22
815:15
804:58
801:40
795:14
784:57
781:35
775:13
764:56
761:40
755:12
744:55
735:11
724:54
721:79
715:10
550:UK
484:.
448:.
359:.
274:.
212:A
2039:.
841:0
741:0
133:.
120:)
114:(
109:)
105:(
95:·
88:·
81:·
74:·
47:.
20:)
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