The life we have been tacitly consider ing, when we talked of an annuity being worth fourteen years' purchase, at five per cent., is one of about thirty-six years of age. The first impression must be, that the proposed premium is ridiculously small. Make it up to 21., and it will be fifty years before the premiums reach 100/. Some such consideration must have moved the law officers of the crown in 1760, when they refused a charter to the Equitable Society, then charging a per mum of about 41. at the age of thirty six, on account of the lowness of their terms. But it is to be remembered, that those who receive the premiums are to invest them immediately at five per cent., and are to invest the interest, thus making compound interest ; persons aged thirty six live, one with another, about thirty years, which is sufficient time for the premiums, with their interest, to realize 1001. for each person, one with another.
We now show the manlier in which a simple result of calculation answers its end. To simplify the case, suppose an office starts with 5642 individual sub scribers, each aged thirty years, the mor tality among them being that of the Carlisle Table. The bargain is for a short assurance, as it is called, of twenty years, and of 1000/.; that is to say, the executors of each one who dies within twenty years are to receive 1000/. at the end of the year of death. Money makes three per cent. once a year. According to the table then, there are 57, 57, 56, &c., deaths in the successive years, and the following is the result, the proper pre mium being calculated at III. 12s. 84d. each person, or more exactly 11,6141.16s. for 1000 persons. It is supposed that there are no expenses of management. At the outset the office receives 65,530/. from the 5642 persons assured: this is immediately invested at three per cent, and yields 1966/. by the end of the year, making 67,4961. But at the end of the year, the claims of the executors of fifty seven persons who have died during the year are to be satisfied, which requires a disbursement of 57,0001., reducing the society's accumulation to 10,4961. The contributors who are left, 5585 in number, now pay their second premiums, 64,8691., so that, these being immediately invested, the company has 75,365/. at interest during the second year. This yields 22611., so that by the end of the year 77,626/. is accumulated. Then comes the demand of 57,000/. on behalf of fifty-seven contributors deceased during the year, which reduces the accumulation to 20,6261. This is more than it was at the same time last year. In this way the company goes on, accumulating to an amount which would lead a person unac quainted with the subject to conclude that the premium must be too large ; in fact, ten years give an accumulation of 91,8091. But now the state of affairs begins to change ; the contributors have been di minishing, while the claims have been increasing, until the yearly incomings no longer equal the outgoings. The accu mulations then come in to make good the difference in such manner that by the time the remaining contributors come to be fifty years of age, and the claims of sixty-one who died in their fiftieth year have been satisfied, there only remains 81. of the 91,809/. ; and this 8/. is merely the error arising from omitting shillings, &c., in the calculation. Something of
the same kind must take place in every office which dies a natural and solvent death ; the only difference being that, when new business ceases, instead of a number of contributors all of the same age, and under similar contracts, both ages and contracts vary considerably.
There are certain tables which are variously named (sometimes after Mr. Barrett, the inventor, sometimes after Mr. Griffith Davies, the improver ; some times after D and N, letters of reference used in them), but which we call commu tation tables. They are described in the "Treatise on Annuities," in the Library of Useful Knowledge, and a copious col lection is given also in an article in the Companion to the Almanac' for 1840. They very much exceed in utility those which preceded them.
An assurance company is a savings' bank, with a mutual understanding, pre sently to be noticed, between the coutri butors. To make out this proposition, let us suppose that A borrows money, and insures his life for the amount as a se curity to his creditor. For this he has to pay a premium. If life were certain, the office of the company would be to receive and invest these premiums, which would be calculated in such a manner as with their interest to amount to a sum suffi cient to discharge the loan in a settled time. At the end of this time the cre ditor (who has been all this while re ceiving interest for his money from A) calls upon A to make his claim upon the office, and repay the loan with the money received. If such an office existed, life being certain, the rationale of the pro ceeding would be that the creditor, though tolerably confident of A's power and will ingness to make any yearly payment, whether of interest or instalment, will not trust him steadily to lay by and improve yearly instalments, but requires that he should make his instalments payable to third parties, who are engaged not to re turn them on demand until they amount to a sum sufficient for the discharge of the debt. Such an office certainly could not exist, on account of the uncertainty of individual life. At soon, however, as it is known that the duration of masses of individuals can be calculated with to lerable accuracy, there is a remedy for the individual uncertainties. Let a large number of debtors, similarly situated with A, agree to be guarantees for one another ; that is, let each of them pay during his life not only his own instal ments, but such additional sums as will provide the means of meeting the deficits of those who die, and the savings' bank thus constructed will become an assurance office. Of course, it matters nothing whether these debtors pay their instal ments to a person agreed on among themselves, or go to a company which un dertakes the management of such con cerns. And again, it makes no difference whether the instalments are for liquid ation of debt, or to accumulate a provision for widows and children. We have taken the case of debtors, because in such a case an office looks more like a mere in demnity-office than when its contributors enter for the benefit of their families still however, in the former case, it is evic dent that the premiums are partly instal ments of debts, partly sums intended to make good the deficiency of the life-in stalments of those who die.