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THE POPULAR SCIENCE MONTHLY, 



added to the net premium to defray work- 

 ing expenses, etc., nor "with the excess of 

 interest that may be realized on investments 

 over the assumed rate. It would be a very 

 extraordinary emergency indeed in any 

 well-established company that would call 

 these into requisition for the payment of 

 death-claims, and, when not required for 

 expenses, they are returned annually as 

 surplus in mutual companies. It is stren- 

 uously argued that, because they may^ if 

 necessary, be used for the payment of 

 claims, they should, along with insurance- 

 value as above defined, be taken into ac- 

 count in fixing the maximum "surrender 

 charge." But, as their discounted values, 

 reduced by the improbability of their re- 

 quisition for company use, would not mate- 

 rially differ in proportion from the insur- 

 ance values, the argument for taking them 

 into account is a good deal more nice than 

 wise. 



As the surrender value which can be 

 fairly and wisely stipulated to be paid, if 

 not paid when not stipulated, is a matter 

 of great practical importance, let me ex- 

 plain particularly the case put by my re- 

 viewer of a single premium endowment in- 

 surance for twenty years, to be surrendered 

 at the end of five years. If entered at forty, 

 by the actuary's table, at four per cent., its 

 net single premium would be $511.15 for 

 $1,000. At the age of forty, the natural 

 net premium to insure $1,000 for one year 

 is $9.96. This, at four per cent., will 

 amount at the end of the year to $10.36, 

 so that the company, exclusive of the party 

 himself, by insuring $1,000, runs the risk 

 of losing $989.6-1: if he dies, and of gaining 

 $10.36, if he does not. There is in this 

 case no reserve at the end of the year, and 

 no occasion to use the term "self-msur- 

 ance." But if $511.15, which at the end 

 of the year will amount to $531.60, it runs 

 the risk of losing only $468.40. And, if in 

 the former case the company may properly 

 be said to have insured $1,000, in this it in- 

 sures only -TT^— $1,000=$473.31. For 



this insurance the party paid in advance (by 



part of his interest discounted) at the same 



rate as for the $1,000 in the other case, 



473 31 

 -that is — ^ $9.96 =$4.72 nearly. But if 



he had died during the year, his heirs would 

 have received $1,000, the same as in the 

 other case. Therefore, since the company 

 insured only $473.31, the party himself 

 must have insured the remaining $526.69 ; 

 and this is precisely the reserve which, in 

 Massachusetts, the law requires the com- 

 pany to show on hand at the end of the 

 year, if the party is then alive, as the sum 

 necessary under the assumptions to enable 

 it to carry through the remaining nineteen 

 years of the contract. Hence, the whole 

 of the insurance operation of the first year, 

 under this contract, is, that the company, 

 exclusive of the party himself, will lose 

 $473.31 if he dies, and gain $4.90 if he 

 does not. The amount of the $511.15, 

 after deducting the $4.90, which belongs 

 to the company in case of survival, to pay 

 other death-claims with, is a mere deposit 

 held in trust, subject to the terms of the 

 contract and the provisions of law. 



If, having paid $4.72, the normal cost 

 of the first year's insurance, we find those 

 of all the succeeding years and discount 

 them back to the start by both the assumed 

 interest and mortality, their sum will be 

 what I call the " insurance value " of the 

 policy at its inception — "the sum which, 

 paid in advance, under the assumptions, 

 would exactly pay for all the insurance 

 which the company is to do under the 

 policy, as distinguished from what the par- 

 ty is to do himself." 



Now, if we conceive that this sum, 

 which in this case is $50.42, is a part of 

 the $511.15, the balance, $460.73, is less 

 than what will make the self-insurance or 

 j:'eserve required at the end of the year, and 

 it is more than a sum which " works at 

 compound interest till it amounts to the 

 sum assured" at the end of the term. 

 That would be only $456.39. The truth 

 is, that the $50,42 is not a part of the sum 

 in hand, but one of its functions. The com- 

 plementary function, exhausting the power 

 of the sum, is the $460.73 — the "insurance 

 value" of the self-insurance, so to speak, 

 including in the self-insurance the endow- 

 ment. The endowment, as will easily be 

 perceived, becomes self-insurance, by as- 

 suming, what is the same to the company, 

 that the party, if he lives to enter it, will be 

 sure to die in the last year of the term. 



