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whole period of ten years. If the mortality of the assured should be exactly equal to that of the persons selected for the formation of the tables, it would, probably, be less in the first five, and greater in the second five years. The company would appear to make profits, then, in the first pe. riod, and to lose in the second. If therefore, they should divide all the apparent profits in the first five years, they would be unable to meet all their losses in the second. The experience of two of the companies recently established, the Nautilus and the New York, Mutual Life, has furnished confirmation of this position. In both, no losses were had in the first year. If then, the whole apparent profits had been divided at the end of this time, there would not have been reserved a sufficient fund to meet the losses that would probably happen in subsequent years. To divide all, would be unjust to the new members who are admitted af. ter the first division. If they, for example, should happen to be of the same age as the first set of assured now are, both would be contributing equally to the funds of the company in the second period. The first, by their annual premiums, and by the reserved fund thrown into the common stock, would be paying as much as the larger annual premiums of the second set; yet, as the losses are less likely to happen among the recent members, they suffer by the connection. If the company had any means of examining the assured, at the time of the division, they might learn how many had their constitutions too much impaired to justify the second company in insuring them at the usual 'rates for healthy persons. But this would be troublesome, and lead to no satisfactory result. Even if they should learn that the health of some had suffered, no rules could be laid down for determining their expectation of life, and for thus fixing on a suitable sum to be laid aside out of the accumulated fund, to meet the extra losses anticipated from this source. The proper way to meet the difficulty, would be to make a deduction from the expectation of life of all the assured, by reckoning them all a little older than they really are, when the profits are determined. What this deduction should be, it would be extremely difficult to say. After a long experience, the companies might construct a table from the deaths of the assured, in the first five and second five years after each one's insurance. No such table has yet been made up, and, in the mean time, it is necessary to determine it as near as possible from other sources. If we should examine a list of persons between the ages of twenty and thirty, taken at random in society, there would not be found many whom a company would be unwilling to insure—not, probably, over 3 or 4 per cent of the whole number. Of these, some would be afflicted with hereditary diseases; some would have had their constitutions impaired in early life, so that they could never have obtained insurance in any com: pany. It is not, therefore, probable that over 2 per cent of those insured by the first company would be objectionable to the second. . The expectation of life to some of these, might yet be considerable ; to all of them it would be something. If, out of one thousand, ten had had their constitutions so injured that their expectation of life was reduced one-half, and the other ten of the 2 per cent could only expect to live a single year, the average duration of the life of the whole thousand would be reduced from 37.86
years to 37.30, which is nearly the expectation at twenty-six, instead of
twenty-five years of age. This reasoning is not very satisfactory; but the following will lead to a similar result. Of all who are alive between the
ages of twenty and thirty, less than 2 per cent die annually. Of these, the great majority die without anticipating their end but a short time. Certainly not over one-fourth have looked forward to death for more than a month. Of these, some may have been invalids for two or three years, some for five, and some for a longer period. Out of ten thousand persons at this age, one hundred and sixty may be expected to die in a single year. Of these, one hundred and twenty die at a short warning, so that, at a particular time, of not over ten of these could it be said, these will probably die this year. Of the remaining forty, the greater part may be expected to die within the year. Of the deaths of the following year, a smaller portion may be anticipated, say three-fourths of those who do not die sud
denly ; and the same proportion for subsequent years. This will give the following table:—
--------------------------- 372,968 “ which gives an expectation of 37.29 years, differing but little from 37.14, the expectation at the age of twenty-six, instead of twenty-five years. If the persons selected for examination had been older, the reduction would have been greater. But if all the assured should be esteemed, in the calculation of the profits, a year older than they are, the result would not, probably, vary much from what would be right and proper. It cannot, indeed, be pretended that this result is accurate. But it is so important to keep the company perfectly safe, that it is better to estimate the profits too little than too much. Some allowance of this kind ought most certainly to be made, and there can be no doubt that it is more just and fair to all the members, both the new and old, to make this reduction, In the example given above, the amount laid by for re-insurance would be $16,883X4.61, or $77.83, instead of $16.074 × 4.50, or $72.33.
When the profits are cautiously and correctly determined, they belong to the assured, and may be paid out to them with propriety and safety. They may be retained for the purpose of securing to the company more of the public confidence, or of giving greater benefit to the family of each member, by making the company a kind of savings bank to accumulate his earnings. How, now, ought these profits to be divided among the assured 1 The gains from expired policies should evidently be divided in proportion to the interest each one has in the company. So, also, if the different members be supposed to have paid too large a premium, or if the interest received by the company from its investments has been larger than was expected, the earnings of this kind should be divided in proportion to the payments of each. There will be a little difference, on account of interest, between those who insure at the beginning, and those at the
end of the five years. Every dollar paid too much by the first, will
Profits from Profits from Amount divided, if Amount divided, if
payments of payments of in ratio of the the interest is old inembers. new niembers. payments. first credited.
In 5 years, 5.63 3.51 5.71 3.43 5.71 3.43 10 * 6.85 3.51 6.48 3.88 6.93 3.43 15 “ 8.34 3.51 7.41 4.44 8.42, 3.43 20 “ 10.18 3.51 8.56 5.13 10.26 3.43 25 “ 12.35 3.51 9.91 5.95 12.43 3.43 30 “ 15.02 3.51 11.58 6.95 15.10 3.43
From this table it appears that the new member admitted in the 26th year, receives more than twice as much profits on a division, as the one admitted in the first year, if no allowance is made for interest on the balances due to the old member; which is manifestly unjust and improper. The increase is derived from the profits of the older member. He who has longest trusted to the company, who has run most risk from their failure or mismanagement, who will receive at last little or no benefit from his insurance, on account of the large amount he has had to pay in premiums, this man is made to divide the interest from his accumulated profits to one whose only connection with the company is one of great advantage. In fact, the old member ought to receive all his profits, and the compound interest on those profits at the full rate received from the company's investments. If the company make more than 4 per cent on his money, he should receive more.
It will be well, perhaps, to refer to a charter of one of these companies, and show how these principles are to be applied. The charter of the Mutual Life Insurance Company of New York requires an account to be opened with the assured ; and in this, each is to be charged with a proportionate part of the losses and expenses, and to be credited with his premium, and with an equal share of the profits of the company derived from investments and earnings in proportion to his premium. This account is to be made up every five years, and the balance paid to each member at his decease, but not till then.
The losses and ordinary expenses are known from the books of the company. Under the head of expenses must be included the cost of reinsuring each of the surviving members, and that cost must be determined by imagining each one of the assured to take out policies in a new company, reckoning their ages to be one year greater than they really are. After the first division of profits there must be estimated, also, as part of the expenses, the amount due to those who have a balance to their credit, at the preceding distribution, for interest on this balance; the interest to be compound, and at the rate the company shall actually receive on their investments. These are real expenses, not paid out, indeed, but none the less real ; the first for a fund to meet the future losses, the other for interest on sums belonging to the assured, but retained by the company for the sake of increasing the strength of the company, and for other purposes. The credit side of the account, as far as made up from premiums, will be easily determined from the books of the company. The profits from investments and earnings will be found by taking losses and expenses from the premiums received, understanding by expenses what has just been explained. The account would stand as follows:—
second Five YEARS.
To losses....................... By premiums.............................
It would not do to keep the profits in two separate items of interest and earnings; for, after a while, the interest might exceed the profits. Should it never exceed the profits, as the charge for losses cannot, according to the charter, exceed the premiums, the assured would ultimately receive his assurance, and all the interest ever earned by the company; which, of course, might not happen.
In conclusion, it cannot be impressed too strongly on the companies to use caution and wisdom in determining their profits. Life insurance companies, with a paid-up capital, are exposed to failures; and the weaker basis of the mutual system renders this prudence the more necessary. Let no anxiety to declare large profits lead to an over-estimate of the gains they have made. Ignorance, miscalculations, extravagant estimates of the value of stocks belonging to the company, besides the ordinary sources of failure, mismanagement, unfortunate investments, and corruption of officers, may ruin the company, and change what promised to be a blessing to the assured, into a curse. The mutual system is not only honest and fair, but eminently suited for this kind of insurance. The objections that lie against it in fire and sea risks, do not apply in life insurance; for the laws which govern the duration of life are far more regular than those which govern the preservation of houses and ships. The effect of an epidemic is never so irregular as a great fire or a sea-storm. But, while the system is good, it must be managed, not only with integrity and prudence, but with all that skill and exactness which mathematical science can bring to its aid. The former are necessary for success, but not more so than the latter. Both are indispensable.
Art. II-ADMINISTRATION OF THE RAILROADS OF MANSACHINETTS:
WITH REFERENCE TO THE RATES OF FREIGHT AND FARE.
To construct a railroad in Massachusetts, has ceased to be a Herculean enterprise. Experience and science now light the path of the engineer, and indicate the route, materials, and mode of construction. Capital, too, has ceased to be coy and repulsive when the line is feasible and the traffic sufficient. The undertaking, however, is not complete when the rails are down. The first movement of the locomotive opens another field of action; a field which demands close investigation and rigid analysis, which puts in requisition commercial as well as professional skill, and philosophical research. The administration of a great line of iron-way, affecting both public and private interests, with powers still undefined, and latent resources still undeveloped, is a subject alike worthy of the study of the merchant, the man of science, and the philanthropist. '
In discussing the rates of charge appropriate to a modern railroad, its relation to the State must not be forgotten.
One of the first objects of association, and one of the first trusts which devolves on government, is the construction of roads; without them, property is nearly worthless, and society but little advanced from barbarism.