ASSUMPTION

, a feast celebrated in the Romish church, in honour of the miraculous ascent of the Holy Virgin, as they describe it, body and soul, into heaven. It is kept on the 15th of August.

ASSURANCE on Lives, a compact by which security is granted for the payment of a certain sum of money on the expiration of the life on which the policy is granted, in consideration of such a previous payment made to the assurer as is accounted a sufficient compensation for the loss and hazard to which he exposes himself.

The sum at which this compensation should be valued, depends principally on these two circumstances, viz, 1 st, On the rate of interest given for the use of money; and 2d, On the probability of the duration of the life assured, and the values of annuities. For, 1st, If the interest of money be high, the value of the assurance will be proportionally low, & è contra; because the higher the rate of interest, the less will be the present value which amounts to a certain proposed sum in any given time. Also, if the probability of the duration of life be high, the value of the assurance will again be proportionably low, & è contra; because the longer the time is, the less will be the principal which will amount to any assigned sum. Thus, if it be required to know the premium or present value, to be given for 100 pounds to be received at the end of any time, as suppose 10 years; then, if the interest of money be at the rate of 5 per cent. the answer, or present premium, would be 61l. 7s. rod; but at four per cent. it would be 67l. 11s. 1d; and at 3 per cent. it would amount to 74l. 8s. 2d. Again, suppose it were | required to assure 100l. on a life, for any time, for instance 1 year; that is, let 100l. be supposed to be payable a year hence, provided a life of a given age fails in that time: here it is evident that, whatever be the rate of interest, the less the probability of the life failing within the year, the less the risk is, and the less the premium ought to be. In effect, the rate of interest being 5 per cent, if it were sure that the life would fail in that year, the value of the assurance would be the same as the present value of 100l. payable at the end of the year, which is 95l. 4s. 9d. But, if it be an equal chance whether the life does or does not fail in the year, in which case the probability of failing is 1/2; then the value of the assurance will be but half the former value, or 47l. 12s. (4 1/2)d. Or if the odds against its failing be as 2 to 1, that is, if one person out of every 3 die at the age of the proposed life, the probability of dying being only 1/3, the value of the assurance will be 1/3 of the first value, or 31l. 14s. 11d. And if the odds be 19 to 1, or one person die out of 20, of that age, the probability of dying will be 1/20, and the value of the assurance will also be 1/20 of the sirst value, or 4l. 15s. 3d. nearly. Lastly, if only one person die out of 50 at the given age, the probability of dying will be 1/50, and the value of the assurance will be accordingly only 1/50 of the sirst sum, or 1l. 18s. 1d: the interest of money being all along considered as after the rate of 5 per cent.—Now, according to Dr. Halley's table of observations, one person dies out of 3, at the age of 87; one in 20 at the age of 64; and one in 50 at the age of 39: It follows, therefore, that the value of the assurance of 100l. for one year, on a life aged 87, is 31l. 14s. 11d; on a life aged 64, it is 4l. 15s. 3d; and on a life aged 39, it is 1l. 18s. 1d: reckoning interest at 5 per cent. But if interest were rated at 3 per cent. these values would be 32l. 7s. 3d, and 4l. 17s. 1d, and 1l. 18s. 10d.

The assurances most commonly practised, are such as these, on single lives, and for single years. But many private assurers, and even some large assuring offices, either from ignorance or imposition, pay no regard to any difference of age, but demand 5l. from all ages indiseriminately, for the assurance of 100l. for one year: a practice very absurd and inequitable; for it appears that this is more than the value of the assurance of a life of 64 years of age, and even more than double the value of the assurance of a life of 39 years of age; allowing the assured to make 5 per cent. of the money he advances.

When a life is assured for any number of years; the premium or value may be paid, either in one single present payment; in consequence of which the sum assured will become payable without any farther compensation, whenever, within the given term, the life shall happen to drop: or the value may be paid in annual payments, to be continued till the failure of the life, should that happen within the term; or, if not, till the determination of the term. And the determination of the value of assurance, in all cases, is to be made out from the rules for computing annuities on lives; the principal writers on which are Halley, De Moivre, Simpson, Smart, Kersseboom, De Parcieux, Price, Morgan, and Maseres. See also Life ANNUITIES, Reversion, &c.

Assurances may be made either on single lives; as above explained; or they may be made on any number of joint lives, or on the longest of any lives; that is, an assurer may bind himself to pay any sums at the extinction of any joint lives, or the longest of any lives, or at the extinction of any one or two of any number of lives. There are further assurances on survivorships; by which is meant an obligation, for the value received, to pay a given sum or annuity, provided a given life shall survive any other given life or lives. For which see SURVIVORSHIP.

The principal offices for making these insurances, in England, are the “London and the Royal Exchange Assurance Offices;” “the Amicable Society, incorporated for a perpetual Assurance Office;” “the Society for equitable Assurances on Lives and Survivorships;” and “the Westminster Society for granting Annuities and insuring Money on Lives.”

The first two of these offices, having chiefly in view assurances on ships and houses, deal but little in the way of assurances on lives; and all the business they transact in th<*> way, is at 5l. for every 100l. assured on a single life for a single year, without paying any regard to the ages of the lives assured.

The next, or Amicable Society at Serjeant's Inn, requires an annual payment of 5l. from every member during life, payable quarterly. The whole annual income, hence arising, is equally divided among the nominees, or heirs, of such members as die every year. But this society engages that the dividends shall not be less than 150l. to each claimant, though they may be more. No members are admitted whose ages are greater than 45, or less than 12; nor is any difference of contribution allowed on account of difference of age. The society has subsisted ever since the year 1706, and its credit and usefulness are well established.

The Equitable Society for Assurances on Lives and Survivorships, which meets at Black-Friars' Bridge, was established in the year 1762, in consequence of proposals which had been made, and lectures, recommending such a design, which had been read by Mr. Dodson, author of the Mathematical Repository. It assures any sums or reversionary annuities, on any life or lives for any number of years, as well as for the whole continuance of the lives; and in any manner that may be best adapted to the views of the persons assured: that is, either by making the assured sums payable certainly at the failure of any given lives; or on condition of survivorship; and also, either by taking the price of the assurance in one present payment, or in annual payments, during any single or joint lives, or any terms, less than the whole possible duration of the lives. In short, there are no kinds of assurances on lives and survivorships, which this society does not make.

In doing this, the Society follows the rules which have been given by the best mathematical writers on the doctrine of Life Annuities and Reversions, particularly Mr. Thomas Simpson, professor of Mathematics in the Royal Military Academy. It is to be observed however that the Society takes the advantage of making its calculations on the supposition that the interest of money is at so low a rate as 3 per cent, instead of the usual interest of 4 per cent; which consequently raises the insurance proportionally higher; and it also founds its calculations | on the tables of the probabilities and values of lives in London; another circumstance which secures a very advantageous profit to the Society, as experience has proved that the deaths are really in a much lower proportion than according to those tables, and even lower than those of Dr. Halley, which are founded on the bills of mortality of Breslaw. By these means the Society finding itself, by experience, well secured against future hazards, and being unwilling to take from the public an extravagant profit, have determined to reduce all the future payments for assurances, one tenth, and also generously to return, to the persons now assured, one tenth of all the payments they have made: and it seems there is reason to expect that this will be only a preparation to farther reduction.

From the foregoing account of this society, it is manifest that its business is such, that none but skilful mathematicians are qualified to conduct it. The interest of the society therefore requires, that it should make the places of those who manage its business sufficiently advantageous, to induce the ablest mathematicians to accept them: and this will render it the more necessary for the society to take care, in filling up any future vacancies, to pay no regard to any other considerations than the ability and integrity of the candidates. The consequence of granting good pay, will be a multitude of solicitations on every vacancy, from persons who, however unqualisied, will hope for success from their connexions, and the interest they are able to make. And should the society, in any future time, be led by such causes to trust its business in the hands of persons not possessed of sufficient ability, as mathematicians and calculators, such mistakes may be committed, as may prove, in the highest degree, detrimental and dangerous. There is reason to believe, that at present the society is in no danger of this kind; and one of the great public advantages attending it, is, that it has established an office, where not only the business above described, is transacted with faithfulness and skill; but where also all persons, who want solutions of any questions relating to life annuities and reversions, may apply, and be sure of receiving just answers. The following is a

Table of the rates of assurance on single lives in the Society for Equitable Assurances. The Sum assured 100l.
Age.For one year.For seven years at an annual payment ofFor the whole life at an annual payment of
l.s.d.l.s.d.l.s.d.
1019611072210
1511101127266
2011311116021210
251177202306
302262603811
3528721423179
4021923514711
4531103186500
50448411251211
555095117693
605191616107177
65701181301039

These rates are 10 per cent. lower than the true values, according to the decrements of life in London, reckoning interest at 3 per cent; but at the same time, it is to be observed that, for all ages under 50, they are near one third higher than all the true values, according to Dr. Halley's table of the decrements of life at Breslaw, and Dr. l'rice's tables of the decrements of life at Northampton and Norwich. But as the society has lately found that the decrements of life among its members have hitherto been lower than even those given in these last tables, it may reasonably be expected, that they will in time reduce their rates of assurance to the true values, as determined by these tables.

As to the Westminster Society for granting Annuities, and insuring Money on Lives, lately established, viz, in the year 1789, from the number and respectability of its members, the equitable terms upon which it proposes to deal, and the known ability and accuracy of the mathematicians and calculators employed in conducting it, there is every reason to expect an honourable and equitable treatment of the public, and a permanent continuance of its usefulness.

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Entry taken from A Mathematical and Philosophical Dictionary, by Charles Hutton, 1796.

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ASCENSIONAL Difference
ASCENT
ASELLI
ASPECT
ASPERITY
* ASSUMPTION
ASTERISM
ASTRAGAL
ASTRAL
ASTRODICTICUM
ASTROGNOSIA