Page:The American Cyclopædia (1879) Volume X.djvu/438

 432 LIFE INSURANCE long to remedy. His remedy is, so to invest the self-insurance or "how much in deposit" part of the funds, that no policy holder's share of it can be used by the company to pay ex- penses or any death claim but his own. The same is the object of American laws prescribing a fixed standard of reserve and net valuation. But it is in its bearing on short endowment in- surance, or that which never extends beyond 75, that the distinction between insurance and self -insurance becomes vitally important ; and the present decay and unpopularity of that branch of the business, which flourished so marvellously from 1858 to 1869, must be at- tributed to its being wholly ignored up to the latter date. This great practical mistake seems to have arisen from an unfortunate, though not incorrect, definition or analysis of the en- dowment insurance policy, the effect of which is described as follows in the u Insurance Times" for November, 1873 : " Endowment insurance is commonly defined as the union of insurance with endowment in the same policy. If the en- dowment is of the same amount as the insurance, as is almost invariably the fact, and for the same term, then the whole policy may be and commonly is regarded as the jmion of a simple term insurance with a pure endowment for the same term. If the life contingency, or risk of death-, is considered as a positive quantity in the former, it is a negative quantity in the latter. This means that if the company loses by the death during the term in the former case, it gains by it in the latter. According to this commonly accepted definition, this very useful policy, which provides for one^s dependents in case of his own death, and for his own old age in case of his survival, is analyzed into two, both of which are affected by the law of mortality in contrary senses. The more you analyze in this way, the more people not well versed in algebra are mystified ; for no other language than algebra has power to deal satisfactorily with positive and negative quantities in the same calculation. By a different analysis the negative quan- tities will all disappear. If, instead of regarding the policy as composed of the insurance of a given invariable amount for a term of years, united with an endowment of the same amount at the end of the term in case of survival, we regard it as the insurance of a decreasing series of sums, united to an increas- ing accumulation, the amount of which latter at any period of the term, added to the sum then insured, shall equal the face of the policy, we shall have precisely the same thing as be- fore, with the contingency, so far as the company is concern- ed, all on one side. The 'endowment' in a technical sense is annihilated. We have in its stead a mere series of savings-bank deposits, subject to certain peculiar conditions, or, in other words, a series of self-insurances, supplementary to the series of yearly insurances done bv the company. Without affecting the practical results at all, we have got a new point of view from which the whole matter is as plain as insurance for a single year." Had the companies regarded the increase of the net premiums of the endowment insurance policies over those of the ordinary life poli- cies, not as insurance premium at all, but mere self-insurance or savings-bank deposit, they would have abstained from doing two or three very unfortunate things. They would not have added more margin to the net en- dowment premiums than to the smaller net life premiums, but rather less. They would not, whatever the premium might be, have paid more to procure a given amount of short-term endowment insurance than of long, but rather less. They would not have assessed more for expenses on a given amount of short endow- ment insurance than of long, if as much. The consequence of paying the agent no more, if not less, for bringing in $100 of endowment insurance premium, than for bringing in $25 of life premium, would doubtless have been a slower growth of this branch of the busi- ness. But, if there had been less of it, and less overloading and over-assessment, it would not now be showing signs of wasting away. The force of these remarks cannot be fully appre- ciated without recurring to the elementary principles, and perceiving how the commuted premium operates from the start. After once finding it, no matter whether it be single, lim- ited annual, or annual during the term, the effect on the company's risk, and the reserve that must be on hand at the end of each suc- ceeding year, can be very readily ascertained by means of the tables already given. Take for example the net annual premium for 32, death or 40, to insure $1,000, which we find to be $108 69. The claim being payable at the end of the year, if only the natural premium ib paid at 32 for $1,000, and a claim occurs on the policy the first year, the co-insurers will have to pay $991 25 ; if $108 69 is paid, they will have to pay only $886 96. Hence, in this latter case the company insures only - -~ of the face of the policy ; the rest the person in- sures himself, and it should therefore cost him normally, in advance, only J^|? x $8 41, to pay for carrying the risk, or $7 52. (See table No. 1.) Deducting this from the net pre- mium, we have $101 17 for deposit, which at the end of the year will amount to $105 21. This is the first year's self -insurance. It will go to make up the $1,000 if the policy turns up a claim ; otherwise it must be on hand, for a reason that will be plain enough at the end of eight years. All that this policy contributes the first year to death claims, if the person does not die himself, is $7 52 (or $7 52, to be exact), instead of the natural premium of $8 41. The other 88 cents is accounted for as the normal cost of the self-insurance, at the rate of $8 41 per $1,000. In the same way, for the next year, adding the net premium to the reserve and accumulating at 4 per cent., we find the co-insurers will pay in case of death $777 54, instead of the $991 08 they would have paid if the natural premium only had been paid. Hence the year's risk costs -j^g x $8 58=$673; and the deposit is $101 96, which added to $105 21, and increased by the inter- est, makes the self-insurance of the second year $215 45. In this way columns B, E, and F, in table No. 1, are completed, columns B and E being simply the analysis of the net premi- um. The same is true of the same columns in No. 2, where the first eight years of a long en- dowment insurance, entered at the same age, are given. It is plain that if a dollar were borrowed out of the deposits, or reserve, in columns E and F (No. 1), it must be returned with interest, or the company would not be able to pay the $1,000 to the person himself on