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who are short-lived will be the losers ;" and the reviewer sanctions this opinion, which I think I can show to be erroneous. The average age at which persons insure lives, is about forty-six: I will suppose that one hundred persons of that age insure their lives for 100l. The expecta tion of life to each is twenty years; they ought, therefore, to pay such an annual premium as would, after paying the expenses of the society, at the end of twenty years leave a balance of 10,000l., to pay 100%. to each assurer. I will, for example's sake, suppose that four per cent. is exactly adapted to that purpose. If fifty of them die before the end of twenty years, the other fifty must live as many years respectively, after the twenty years, as the former died before them. I will take an extreme case: A. dies at the end of one year; B. must therefore live thirty-nine years to compensate for A.'s early death. A. will receive 100%. after having paid 41. 48. including the year's interest on the premium ;. B. will afterwards receive the same sum, after having paid 4567. 78. 6d., calculating the amount of the annuity paid by him at compound interest of five per cent. C. dies at the end of twenty years, when he will get back exactly what he has paid. Here can be no bonus on the supposition that four per cent. premium would exactly pay every assurer; if there was, who ought to have it? for that is the simple question. I should say, neither A., nor C., but B. only. The equitable rule, then, would be, that the bonus should be given to those only who have survived the expectation of life. Now if five per cent. premium instead of four be paid, the additional 17. will in time furnish a bonus; C. will now have paid his 100l. rather before the end of twenty years, and whenever that is, that is the exact period when he ought to begin to receive it, and in an increasing ratio, and at a faster rate, as he gets older. If this be a correct view of the subject, the opinion of the longest livers being the gainers, and the short-lived the losers, must be erroneous; and the principle adopted by the Equitable is, in some degree, correct. As they cannot calculate for every particular case, some general plan must be adopted. That of dividing the members into nearly two equal parts, and giving the bonus to the earlier half of the members, is on the principle I have stated; but I must allow that a much more equitable mode might be adopted. For if D. insures at twenty, and immediately after E. at seventy, according to my principle D. ought not to receive any of the bonus till he has been a member nearly thirty-three years, but E. after rather less than eight years; whereas it appears to me that by the plan adopted by the Equitable, they will come among "the elect" about the same time. I know nothing of the detail of a life-assurance office, and therefore, perhaps, my plan may be impracticable on account of the trouble it would occasion; but at present it appears to me that the following might be adopted :-There are about 10,000 members in the Equitable, and if the average of the lives, when they begin insuring, is forty-six, they would, I believe, die in about twenty-five years, though not according to the Northampton tables; consequently, to keep up the number, there must annually be four hundred new members. They might be put into classes differing in their ages five years; i. e.
2 R 2
from twenty to twenty-five, from twenty-five to thirty, and so on: against each class might be put the expectation of life appertaining to it, taking into the calculation how much earlier it ought to be in consequence of the premium received being greater than is necessary, and at the end of that period, the class would come in among "the elect." This plan I should think might be rendered practicable, and I am sure it is equitable; but that of giving new members a bonus before they have paid up the sum insured, when the old ones have paid so largely, would be "inequitable."
I am aware of the note at p. 25, and am so puzzled by it, that I suspect there must be some error in the premises. It cannot for a moment be disputed, that the society must lose by every member who dies before he has paid in premiums, with the accumulated interest on them, the amount of his policy: the note says it loses by the old members; it necessarily follows that the intermediate members must suffer; for if one set gain, another must lose, to make things even. Be that, however, as it may, the principles I have laid down do not appear to me to be affected by it. There have been, I suspect, two sources of profit to the Equitable, which have not been sufficiently considered by the public. The society had to feel its own way, and therefore, very properly, they were parsimonious at first in the division of their savings, which having gone on accumulating at compound interest, when the public funds were low, and their calculations were only at the rate of three per cent. interest, have now amounted to a vast sum. A part of this ought, in equity, to be given to the heirs of those members who died after they had paid in premiums the amount of their policies: this, I suppose, is impossible, and therefore the old members now may be deriving a more than equitable advantage from the above forbearance in not making an earlier distribution of the savings. I hope this accumulation will never make this society, under any future actuary, too prodigal of its bounty: during its existence, no mortal epidemic has prevailed; but the society ought not to act as if no such disorder ever could happen.
I suspect that another source of profit to the society, and which of course did not enter into their calculations when first established, arises from the policies which they purchase, which, I understand, are numerous, and for which they give a very inadequate value. A friend of mine applied, about ten years since, to the society to purchase his policy, for which they offered him 4871. I had great difficulty in prevailing on him not to sell it, as the offer was a very inadequate one. It was a mere whim that he wished to get rid of it, as he did not want the money, and the premium was at the time no object to him; had he wanted the money, so little did he understand the business, that I am sure he would have taken the 4871. Had I offered him 600l., I have no doubt but he would have accepted the offer, and this I was only prevented doing by his being a particular friend: I should have thought I had done wrong had his early death made it a profitable concern to me. I prevailed on him to keep it, and about nine years after, as one of his executors, I received from the office above five times the amount
of what he had been offered by the society. If, therefore, the society had purchased this policy, they would have derived great profit from it This person was, I think, a member about twenty-three years; that is, he had paid twenty-three premiums,-his bonus amounted either to sixty-six or seventy-three per cent., (not having the accounts at hand, I cannot exactly say which, but I think the former.) He had survived the expectation of life some years; and he did not get a great deal beyond what compound interest would have given him. I conceive that the waste of life is much less than it was thirty or forty years since, judging from the population returns; and if this be true, it is an unanswerable argument against the opinions of those who are factiously crying out that the poor are much worse off than formerly; for though temperance is the parent of longevity, distress and want cannot be.'
We shall, ere long, enter at greater length into the subject to which this communication refers, but in the meantime thought it fair to the author and to the Assurance Offices to give publicity to his suggestions in this manner.
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