are no more, can be predicted from experience with a remarkable approach to precision. The question on which this article proposes to submit a thought or two is, how the law of the average decrement of life, as developed by observation thus far, is to be applied to the regulation of Life Insurance, or in other words, how the public is to be satisfied that any Life Insurance company is reasonably safe. First, however, it deserves to be settled, what expression of the law we will accept as the highest authority. Observations, more or less extensive, on the mass of the population in various localities, as at Northampton, Chester, and Carlisle, in England, were the foundation of the first rates of Life Insurance. The rates charged in this country are generally conformed to the mortality at the latter place. But population taken as it rises may not be an exactly fair representation of the body of insured lives. As those who feel their tenure of life most doubtful will naturally most seek insurance, the company must, of course, guard itself by selecting the best of those who apply. Whether the result will be a body of insured lives above or below the average longevity is a question. As experience is always better than theory, the leading English companies, some fourteen years ago, turned their attention to a practical investigation of this question. They very justly deemed that the actual experience of the past would be the best guide for the future. Seventeen of the oldest offices united their experience, reaching back, in a number of cases, for several generations. The particulars of more than 80,000 policies, that had been terminated by death, were contributed to a common stock, and after rejecting those that did not answer general conditions, such as bad lives, taken at extra rates, 62,535 were taken as the basis of a table of rates. The result was, as might have been expected, favorable to life on the whole, but more so on the earlier than the later ages. That is, the mortality of selected insured lives is rather less for some years than that of the Carlisle table, but rather greater afterwards. But the decrement, as given by this combined experience of insured lives, is more uniform, and exhibits fewer anomalies than the Carlisle, or any other table, based on the mass of the population. This extensive average of lives actually insured the very class of lives that are to be provided for-undoubtedly furnishes the most authoritative expression, within the present boundaries of science, of the law of mortality, as applicable to Life Insurance. The values of life annuities and premiums of insurance deduced from this table of mortality, may be found in the small work of Mr. Jenkyn Jones. But, as he gives the annuities only to three places of decimals, and the last is not always the nearest figure, the writer has recomputed, with some care, the annuities and premiums, carrying them two places further. The result, together with the logarithms most convenient in practice, may be found at the close of these remarks. Life risks differ obviously from those of fire and marine disaster, by extending over a far longer duration of time, and by terminating in certain loss. The business also differs from fire and marine insurance, in that accumulation by interest playing a more important part in it, a company in its earlier years is sure to have on hand a considerable amount of funds beyond current losses, and with these it can make a good show of prosperity, whether or not it is so husbanding them as to be able to pay its larger ultimate losses. As the conformity of the premium to the requirement of the law of mortality is no more than a right outset, and does not secure a right progress afterwards, it is important to have some gauge or line by which the accumulation may be tested afterwards, and how this is to be had, may be best illustrated by an example. The average age at which insurance is effected is probably somewhere between 37 and 38, at which age the expectation or average of future life is 29 years. For the sake of having a medium example, let us suppose that a company insures for life 5,000 persons at this mean age, each paying $30 per annum for a policy of $1,000. Taken one with another, each will pay twenty-nine premiums of $30, amounting to $870, and will receive by his heirs $1,000. The $130 and its expenses the company is to provide for by the interest. And more than this it may easily do, for the premium charged is about $6 higher than that which would be sufficient to amount to the $1,000, at compound interest at 3 per cent, taking the losses one with another as they occur in the table. This excess is designed to meet necessary expenses and extraordinary mortality, and under the mutual system of insurance it returns, so far and so fast as it is not needed for these purposes, to those who have paid it. How far and how fast it may return is to be decided. Pursuing our example, we see that the company will the first year receive from its 5,000 insurees $150,000, and we will suppose that this sum is increased by interest to $156,000. According to the law of mortality above referred to, it may expect to lose the first year $49,000 by 49 deaths. Suppose it should so lose, it will still have $107,000 left; or, what is quite probable, it may experience no more than 30 losses, amounting to $30,000, and leaving $126,000, (to say nothing of more interest in this case.) But this large amount is not entirely profit or surplus. If not the whole, the greater portion of it must be retained productively invested for the future, to meet engagements certain in amount and, in the aggregate, certain in time. If the company has had to pay only $30,000 for losses, then the other $19,000, which it might have paid according to the table, it has still to pay. It has not gained the principal, but only the opportunity of acquiring more interest. The favorable contingency is doubtless beneficial to the company, and will enable it to return more than it otherwise would. But how much more? is the question. Here a vital practical rule, founded on the law of mortality, comes in, and it is, that a company must always keep its available assets equal to its MATURED liabilities. The matured liability on each policy is its value, according to the law of mortality, and such a rate of interest as may be considered permanent and certain, or it is the difference between the single premium, which the holder of the policy would have to pay to insure the same amount at his present age, and the present worth of what he will pay, at the aforesaid rate of interest in both cases, having entered into the engagement at an earlier age. This difference, or value of the policy, the company is bound to hold in trust, productively invested. If it be returned, or otherwise expended, it must be made good by a robbery of the future, or the company will, some time or other, fail to meet its engagements. The aggregate of these values or differences, calculated to any given time, is the matured liability of the company at that time, or it is just what it would have to pay in equity to be released from its engagements. Let us suppose, which will not be far from the fact, assuming 3 per cent as the permanent rate of interest, that each of the policies in our example has a value at the close of the first year, and before the second premium is paid, of $15. In case, then, 30 policies have expired by death, $74,550 will be the matured liability of the company, and reserving this, it will have $51,450, minus its expenses, to return. If it has had the medium loss of $49,000, then it must reserve $74,265, and will have $32,735, minus expenses, to return. If, again, the losses have amounted to 60, it will have to reserve $74,100, and, supposing the extra losses not to have diminished the income from interest, it will have only $21,900, minus expenses, to return. It is quite plain, so far as this example represents the truth, that a company must be very fortunate indeed to be able, after paying 10 per cent commissions to agents, office rent, salaries, printing bills, postage, &c., to return 33 per cent of its premiums. It is true that companies do add to the surplus to be divided something from the profits of lapsed policies and temporary assurance, but not often a considerable per centage of the receipts by premiums. At all events, our example makes it perfectly clear that a company can never know how much it has a right to return, without first accurately ascertaining the values of all its policies to a certain day. As policies are dated all the working days of the year, and change their value from day to day, and as the ages of the insured are various, calculating all the policies of an extensive company to a given day requires a good deal of arithmetical labor. But it must be done, or a company cannot be sure of its solvency any more than a merchant who neglects to balance his books. A navigator might as safely be ignorant of his latitude and longitude in midIt is a business in which all the accuracy which the nature of the case admits should be secured at whatever cost. ocean. By some companies in this country, policies are carefully estimated, and assets balanced against matured liabilities yearly. By others, there is reason to believe that the liabilities have been rudely and lumpingly guessed at, and by some others still, it is probable no such estimation has been made or attempted in one way or another. As the principal executive officer of one company lately expressed to the writer of this article his doubt as to the possibility of "fixing a value to an uncertainty," meaning by an “uncertainty" a life policy, it is pretty certain that that company gets on without calculating its policies. In this state of things, it is not without good reason that several State Legislatures have interested themselves to guard their constituents against the mismanagement of Life Insurance offices. New York has required of each company doing business in that State, wherever chartered, to deposit $100,000 with the State Controller, for the benefit of the insured in that State. This safe-guard is of very doubtful utility, and surely very awkward. The sum held may be too much or too little, and requiring it tends to discourage the business and confine it to narrow limits, whereas its safety lies in expanding over a broad surface. Massachusetts has for several years required of insurance companies chartered in other States, and doing business within her limits, a statement of their affairs, to be sworn to, and lodged with the Secretary of State, but unfortunately such a statement as was conclusive of nothing in the case of Life Insurance companies! It got merely a sort of puff advertisement, the figures of which indeed might all be true enough, and yet the company be worthless. Her last Legislature has passed a more stringent, enactment, and in it required a return of the real liability of the company as well as its assets. It is curious, however, to observe, and it argues the imperfect acquaintance with this subject, which prevails that this act not only requires a return of the aggregate value of the policies on the first of July of each year, but also the present This latter return, having value of the future premiums at the same date! nothing to balance against it, is of no significance whatever to the public. The father of the act, by attempting to show a little more knowledge than he possessed, imposed a quite needless labor on the companies. This act, however, hits the nail on the head, notwithstanding. It is an "Assembly's shorter catechism," which no company can honestly answer without informing the public whether it has been safely and correctly managed up to the date of the return. Such a balance of its assets against its matured liability, as estimated by a mathematician known to be competent and trustworthy, every Life Insurance company should feel required, by a regard for its own credit, to make annually. And the insured should no more allow the directors to go on from year to year without reporting this balance than the stockholders of a railroad would allow their directors to report their receipts without reporting their running expenses. E. W. VALUES OF LIFE ANNUITIES, AND SINGLE AND ANNUAL PREMIUMS OF ASSURANCE, FOR ONE DOLLAR, ON SINGLE LIVES, BY THE COMBINED EXPERIENCE RATE OF MORTALITY, AT 3 PER CENT INTEREST. Living at Age, each uge. 10. 100,000 Value of Logarithm of L garithm of annuity. annuity. 1+ annuity. 23.35587 1.3683960 1.3866035 .3658673 Annual Logarithm of premium. annual prem. .0119317 -2.0767022 11. 99,324 23.22027 .3841779 .0121616 .0849907 12. 98,650 23.08027 .3632411 .3816694 .0124008 13. 97,978 22.93573 .3605127 .3790467 .0126523 14. 97,307 22.78671 .3576816 .3763344 15. 96,636 22.63330 .3547479 .3735244 16. 95,965 22.47528 .3517052 .3706108 17. 95,293 22.31279 .3485539 .3675943 .0137687 18. 94,620 22.14564 .3452883 .3644692 .0140785 19. 93,945 21.97390 .3419072 .3612347 .0144015 20. 93,268 21.79741 3384048 .3578855 .0147384 21. 92,588 21.61621 .3347796 .3544198 22. 91,905 21.43018 .3310256 .3508327 23. 91,219 21.23907 .3271355 .3471166 .0158398 24. 90,529 21.04298 .3231072 .3432704 .0162397 25. 89,835 20.84170 .3189332 .3392864 .0166578 26. 89,137 20.63506 .3146057 .3351581 .0170951 27. 88,434 20.42307 .3101210 .3308817 .0175525 28. 87,726 20.20553 .3054703 .3264491 .0180313 29. 87,012 19.98247 .3006491 .3218566 30. 86,292 19.75413 .2956579 .3171045 31. 85,565 19.51913 .2904605 .3121589 32. 84,831 19.27869 .2850775 .3070398 .0201867 33. 84,089 19.03222 .2794905 .8017291 34. 83,339 18.77965 .2736875 .2962186 35. 82,581 18.52084 .2676607 .2904985 36. 81,814 18.25505 .2613830 .2845446 .0228082 37. 81,038 17.98275 .2548561 .2783591 .0235532 38. 80,253 17.70340 .2480568 .2719206 39. 79,458 17.41695 .2409722 Single premium. .2906063 2945573 .0934497 .2986200 .1021695 .3028430 .0129141 .0131870 .0134718 .1110642 .3071833 .1201460 .3116524 .1294256 .3162541 .1388929 3209869 .1485564 .3258553 .1584077 .8308575 .1684503 .3359980 40. 78,652 17.12307 2335816 .4960158 .5182584 .5130497 .5280425 .5303392 .5379513 .5479087 .5479904 .5657062 .5581191 .5837880 .5683616 .6021436 .5786986 52. Living at Age. each age. 67,253 .1054071 Annual Logarithm of premium. annual prem. .0417603 .6207634 .0436186 .6396717 .5996115 .1381978 .7383683 .6527397 .7590239 .6634406 .7800039 .6741403 .8012665 6848026 .8228164 .6954136 .8446343 .7059489 53. 66,046 12.74668 .0699253 .0735740 .8667244 .7163958 .0774579 .8890657 .7267304 .9116539 .7369368 5.44124 .7356977 .8089695 .1261234 5.14841 .7116733 .7887628 4.86315 .6869174 .7681298 .1414310 77. 19,548 4.58533 .6613707 .7470489 .1499142 78. 17,369 4.31540 .6350207 .7255357 .1590065 15,277 4.05353 .6078332 .7035947 .1687553 13,290 3.79936 .5797102 .6811831 .1792350 11,424 8.55255 .5505397 .6582544 .1905311 9,694 3.31213 .5201078 .6346921 .2027776 8,112 3.07681 .4881002 .6103200 .2161639 6,685 2.84560 .4541736 .5849639 .2309113 85. 5,417 2.61704 .4178104 .5583533 .2473429 86. 4,306 2.39104 .3785863 .5303751 .2657399 87. 8,348 2.16747 .3359529 .5007123 88. 2,537 1.94615 .2891761 .4692547 .3103000 89. 1,864 1.72827 .2376124 .4358862 .3374124 90. 1,319 1.51565 .1806001 .4006508 3683848 .6063903 .9327548 .6483358 .9885655 Ir is said that the name Tobacco was given by the Spaniards to the plant, because it was first observed by them at Tabasco or Tabaco, a province of Yucatan in Mexico. In 1560, Nicot, the French ambassador to Portugal, having received some tobacco from a Flemish merchant, showed it, on his arrival in Lisbon, to the grand prior, and on his return into France, to Catherine of Medicis, whence it has been called Nicotiana by the botanists. Ad |