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THE 
 
 ABC 
 
 OF 
 
 Life Insurance. 
 
 By CHARLES E. WILLARD. 
 
 ^ OF THE 
 
 \ 
 
 
 NIVERSITY 
 
 OF . 
 
 ypOURTH 
 
 EDITION. 
 
 i 
 
 PUBLISHED BY 
 
 i THE : 
 
 SPECTATOR COMPANY 
 
 1 
 
 New 
 
 York. 
 
 1897 
 

 :t^ERAL 
 
 Entered in the office of the Librarian of Congress, at Washington, D. C, in 
 the year 1897, by The Spectator Company, New York. 
 
PREFACE TO FIRST EDITION. 
 
 To ejcr^iain and illustrate some of the fundamental and ele- 
 mentary principles of Life Insurance so simply that they can 
 rpor^vJily fc understood by men who have not been specially 
 
 trained i>fnathematicians, or have not had their attention par- 
 
 iCIarly directed to the theory and mathematics of Life Insur- 
 ance, 4 tne aim of this Uttle book. For those who already 
 possess this elementary knowledge, there are many excellent 
 hand-books which carry the discussion much further, and 
 cover the entire subject in the ablest and most satisfactory 
 manner. But as an introduction to these, a beginning, an 
 **easy lesson," it is hoped that the following pages will have 
 their use. They owe their existence to the impossibility of 
 findmg among the text-books already published anything 
 which seemed exactly adapted to this purpose. C. E. W. 
 
 New York, November i, 1888. 
 
 ^ 
 
 PREFACE, TO FOURTH EDITION, 
 
 A demand for the ABC requiring a fourth edition to meet it 
 is evidence that every year a very considerable number of men 
 wish to know what Life Insurance is. It is a pleasure to pre- 
 sent to them a revised and enlarged edition of the book, con- 
 taining a more extended discussion of net premiums, a presen- 
 tation of the theory of surrender values and surrender charges,, 
 and a new table of *' Combined Experience, 4 per cent" net 
 premiums, and, in its references to the actual conduct of the 
 business, informing to the latest practice. C. E. W. 
 
 New ^'ork, November i, 1897. 
 
THE 
 
 ABC 
 
 OF 
 
 LIFE INSURANCE 
 
 CHAPTER I. 
 
 A PRELIMINARY STUDY. 
 
 Insurance, in its simplest form, is indemnity for loss. 
 Or it may be described as a method of distributing an 
 individual's loss among a large number of other persons 
 who are willing to assume each his small share of it, ia 
 return for the certainty that if a similar loss falls upon any- 
 one of them, the loser, or those dependent upon him, will 
 in like manner be indemnified. If a building or stock of 
 goods is burned, so much capital is destroyed. If a pro- 
 ductive human life ends, so much capital in another form is 
 destroyed. For convenience in apportioning the loss, or 
 dividing it among those interested, the machinery and organ- 
 ization of a company are invoked. The company contracts 
 to pay the loss, the company collects the premium, the 
 company pays the loss if it occurs. Consequently, the com- 
 
 Note. — It is sometimes flippantly said that insurance is simply a form 
 of gambling, the company betting a large sum that a certain loss will not 
 occur, the insured bettinsf a small sum that it will; if the loss occurs, the 
 company pays the bet. In so foolish a statement as this, only the element 
 of chance is taken into account. No consideration is had of the fact that 
 the insured receives the worth of his money, in any event, in the protec- 
 tion afforded — the certainty that he will be indemnified if the loss falls on 
 him. A bet involves the payment of money without any equivalent in 
 return. 
 
6 The A B C of Life Insurance, 
 
 pany is said to insure each individual, but it must be 
 remembered that the actual function of the company is 
 that of a medium through which the business is transacted, 
 and that the result is simply the apportionment of such 
 individual losses as occur, among a large number of insured 
 who assume the payment of these losses from year to year 
 in order that they may themselves claim a like indemnity 
 should the occasion arise. If this fact were thoroughly 
 understood in life insurance, as it is in fire, more correct 
 ideas of the values of life policies would prevail even among 
 those who have no technical knowledge of the subject. 
 
 Two or three elementary principles constitute the foun- 
 dation of all life insurance. They are so simple that they 
 need only to be presented to be comprehended by any 
 person of ordinary intelligence. Their practical application 
 to various contingencies may, and often does, involve 
 mathematical calculations which are not only very lengthy 
 but also very intricate. This fact has thrown a veil of 
 mystery over the whole subject, which does not properly 
 belong to it. One need not be an actuary or expert 
 mathematician to have a very fair knowledge of the funda- 
 mental principles. The following example will enable us 
 to study these principles : 
 
 // should be understood in advance that the supposed con- 
 ditions of this example^ so far as the rate of 7nortality {or 
 number of deaths in a year) is concerned, are not those 
 which we meet in actual experience. The ter7n of life is 
 shortened from ninety -six years to fifty, that the calculation 
 may be proportionately shortened. The number of deathc^ 
 each year, and the amount of insurance on each individual^ 
 are purposely such as to make the calculation very simple^ 
 and susceptible of instant verification. Consequently, our 
 
 
I 
 
 The A B C of Life Insurance. 
 
 results will not be the results of actual experience. The 
 premium will be very much too high, the annual cost of the 
 insurance very much too great, the accumulation of reserve 
 very much too rapid. 
 
 But the two or three elementary principles which we wish 
 to study are perfectly and exactly illustrated. As will be 
 shown later on, the same process applied to the conditions 
 which actually exist, will secure correct results. 
 
 Bearing the above in Mind : 
 
 Let us suppose that a company is formed of i ooo men ; 
 that the age of each man is 40 ; that each is insured for 
 $ijop^»that 100 men will die during the first and each 
 succeeding year ;* that every man remains in the company 
 until his death occurs ; that the company receives nothing 
 for interest on money in its hands, and pays nothing for the 
 expense of conducting the business. Suppose, also, that 
 for the sake of convenience these men agree to pay a uni- 
 form amount each year so long as they live, as a premium 
 for the insurance. 
 
 It is evident that the total amount of insurance to be 
 paid would be 1000 x $1100, or $1,100,000. 
 
 It is also evident that there would be 1000 men to pay 
 premiums the first year, 900 the second year, 800 the third 
 year, and so on. The total number of premium payments 
 made would be 5500. Each payment therefore must be 
 $1,100,000 -f- 5500, or $200, which, upon our assumption, 
 
 * As a matter of fact, we should expect that the number of deaths among 
 1000 men, age 40, would be but 9 or 10 the first year, and that i or 2 of 
 the 1000 men would survive the age of 90. To make our supposition 
 conform to these facts would extend our calculation over 50 years. The 
 assumption which is made above, reduces the term to 10 years, and so 
 avoids the tediousness of the calculation based upon the longer, actual 
 term. 
 
8 
 
 The A B C of Life Insurance, 
 
 would be the anriTial, whole-life premium for an insurance ot 
 $1 loo upon the life of a man aged 40. 
 
 The results would be as follows : 
 
 i.cxx) X $200 = 
 
 100 X $1,100 =: 
 
 $200,000, Premiums received beginning of 
 110,000, Losses paid durmg 
 
 $90,000, Amount in hand at end of 
 900 X $200 = $180,000, Premiums received beginning of 
 
 $270,000, Total am't in hand beginning of 
 100 X $1,100 = 110,000, Losses paid during 
 
 $160,000, Amount in hand at end of 
 800 X $200 = 160,000, Premiums received beginning of 
 
 $320,000, Total am't in hand beginning of 
 100 X $1,100= iio.ooo, Losses paid during 
 
 $210,000, Amount in hand at end of 
 700 X $200 = 140.000, Premiums received beginning of 
 
 $350,000, Total am't in hand beginning of 
 100 X $1,100= 110,000, Losses paid during 
 
 $240,000, Amount in hand at end of 
 600 X $200 = 120,000, Premiums received beginning of 
 
 $360,000, Total am't in hand beginning of 
 100 X $1,100= 110,000, Losses paid during 
 
 $250,000, Amount in hand at end of 
 500 X $200 = 100,000, Premiums received beginning of 
 
 $350,000, Total am't in hand beginning of 
 loo X $1,100= iio.ooo. Losses paid during 
 
 $240,000, Amount in hand at end of 
 400 X $200 = 80,000, Premiums received beginning of 
 
 $320,000, Total am't in hand beginning of 
 ICO X $1,100= 110,000, Losses paid during 
 
 $210,000, Amount in hand at end of 
 
 First 
 
 Year, 
 
 Age 40. 
 
 Second 
 
 Year, 
 
 Age 41. 
 
 Third 
 
 Year, 
 
 Age 42. 
 
 Fourth 
 
 Year, 
 
 Age 43. 
 
 1 Fifth 
 \ Year, 
 I ^ge 44- 
 
 ) 
 
 Sixth 
 S- ifear, 
 Age 45. 
 
 Seventh 
 
 Year, 
 Age 46. 
 
300 X $200 = 60,000, Premiums received beginning of 
 
 $270,000, Total am't in hand beginning of 
 
 100 X $1,100= 110,000, Losses paid during 
 
 $160,000, Amount in hand at end of 
 
 200 X $200= 40,000, Premiums received beginning of 
 
 $200,000, Total am't in hand beginning of 
 
 100 X $1,100= 110,030, Losses p-^id during 
 
 Eighth 
 
 Year, 
 
 Age 47. 
 
 Ninth 
 
 Year, 
 
 Age 48. 
 
 $90,000, Amount in hand at end of j 
 
 100 X $200 = 20,000, Premiums received beginning of ^ T th 
 
 $110, oco. Total am't in hand beginning of Y Year, 
 100 X $1,100= 110,000, Losses paid during J 8' 49' 
 
 00 
 
 Now it is evident that the principles involved in fixing 
 the premium and collecting the necessary amounts to pay 
 losses in full, until the last contract is met, must be the 
 same whether the death rate be 9 or 100 per annum, and 
 the term 10 or 50 years. Let us see, then, what can be 
 discovered by a study of the above. 
 
 In the first place it is evident that the cost of the insur- 
 ance — i. e., the amount of the losses in any one year 
 divided by the number of men living at the beginning of 
 that year — ^varies from year to year, although the annual 
 premium remains the same. The losses for the first year 
 are $110,000. The number of men to pay premiums 
 is 1000. The cost of the insurance, therefore, is 
 $110,000-5-1000, or $110 per man. The second year 
 the losses are $110,000. There are but 900 men, how- 
 ever, to pay premiums, 100 men having died. Conse- 
 quently, the cost of the insurance is $110,000 -^ 900, or 
 $122.33 P^r man. In the same way the cost the third 
 year is $110,000.00-7-800, or $137.50 per man; the 
 fourth year, $110,000-^700, or $157.14 per man — and 
 so on. When we reach a point where more than one-half 
 
lo The A B C of Life Insurance. 
 
 of the original number of men is dead, or will have died 
 before the end of the year, the cost will exceed the premium. 
 Thus, in the sixth year, the cost is $110,000 -^ 500, or 
 $220.00 per man. And, from this point, the cost con- 
 tinues to exceed the premium by an annually increasing 
 amount to the end. 
 
 It is evident, therefore, that a uniform or, as it is usually 
 called, a " level " premium, involves the annual payment of 
 a sum in excess of the current cost of the insurance during 
 a part of the term, and the annual payment of a sum less 
 than the current cost of the insurance during the remainder 
 of the term. Consequently; whatever is overpaid during 
 the former portion of the term must be held in hand, 
 reserved^ to provide against the deficit which would other- 
 wise occur during the latter part of the term. 
 
 The same fact appears from an inspection of the figures 
 above, without stopping to calculate the cost of the insur- 
 ance. Thus we see that the premiums received exceeded 
 the losses paid by $90,000 the first year, $70,000 the 
 second year, and so on up to the sixth year. Then the 
 losses began to exceed the premiums, the excess being 
 $70,000 in the ninth year, and $90,000 in the tenth year. 
 If, now, the company finding itself with $90,000 in hand at 
 the end of the first year, $160,000 at the end of the second 
 year, $210,000 at the end of the third year, had overlooked 
 the call to be made upon these funds in the future, and had 
 spent or, through carelessness or misfortune, lost some of 
 these funds, had failed to keep the full amount intact, there 
 would have been finally a deficit of exactly the amount so 
 lost or spent. Ten thousand dollars a year might be spent 
 for several successive years without affecting the company's 
 ability to pay its current losses, but the time would surely 
 come when the absence of the money would show itself in 
 
The A B C of Life Insurance, ii 
 
 the inability of the company to carry its contracts of insur- 
 ance to the end. It is plain, therefore, that at the end of 
 each year the company would have in its possession a sum 
 of money which it must carefully reserve for the future 
 fulfillment of its existing contracts. 
 
 Another point. At the beginning of each year (for the 
 above example supposes that the company receives all its 
 premiums at the beginning of the year), there would be on 
 hand the money brought over from the preceding year plus 
 the premiums for the current year. A portion of this 
 total amount would have to be held for the payment of the 
 current losses of this year. To distinguish this from the 
 amount to be carried forward at the end of the year, we will 
 call it the insurance reserve. Since this would be paid out 
 at intervals during the year, as losses occurred, the sum left 
 in the company's hands would slowly diminish until, at the 
 end of the year, the insurance reserve would be entirely (and 
 properly) expended in the payment of losses, and only that 
 amount of money which must be held for the future would 
 remain. This latter amount, since it must be held for a 
 series of years, and might be invested in interest-bearing 
 securities, we will call the investment reserve. 
 
 This suggests another point, viz.: that while the reserve of 
 a policy may be said to increase each year that the insur- 
 ance is in force, this increase, so long as premiums are paid, 
 is not an absolutely uniform one. The reserve is greater at 
 the beginning of the year, because it includes both the 
 insurance and the investment portions ; diminishes during 
 the year, because the insurance portion is expended grad- 
 ually in the payment of losses ; but at the end of each year 
 is greater than at the end of the preceding year, because the 
 investment portion of that year is added to the investment 
 portion of the preceding year or series of years. 
 
12 The A B C of Life Insurance. 
 
 If we divide the amount of money in the hands of our 
 supposed company at the end of the first year by the num- 
 ber of survivors at the end of that year, we have $90,000 -^ 
 900, or $100. This is the amount of reserve for each policy 
 (or insurance) at the end of the first year. After the pre- 
 miums have been paid at the beginning of the second year, 
 and before any deaths have occurred for that year, the reserve 
 on each policy would be $270,000 -5- 900, or $300. At the 
 end of that year the reserve would be $160,000 -5- 800, or 
 $200 on each insurance. By putting the figures of reserves 
 at the beginning and end of several years in parallel col- 
 umns, this point will be more clearly seen : 
 
 Beginning End 
 
 of Year. of Year. 
 
 Reserve second year $3cx) $20c 
 
 Reserve third year 400 30c 
 
 Reserve fourth yeai 500 400 
 
 Reserve fifth year 600 500 
 
 This may be represented by a diagram as follows : 
 
 Fifth Year. 
 
 2 
 
 \A 
 
 'S 
 
 w 
 
 *s 
 
 
 
 
 
 a 
 
 •a 
 
 
 '& 
 
 
 •F5, 
 
 & 
 
 
 ^ 
 
 
 & 
 
 Perhaps the function of the investment reserve may be 
 shown in another way. Suppose that the company of 1000 
 
I^n 
 
 The A B C of Life Insurance. 13 
 
 b had agreed to pay each year the exact cost of the 
 insurance for that year. Taking our figures of cost on page 
 8, the results would be as follows : 
 
 1,000 X $110 =$110,000, Premiums rec'd beginning of ^ p' st ' 
 100 X $1,100 = 110,000, Losses paid during i Year, 
 
 00, Amount in hand at end of J & 4 • 
 
 I. 
 
 $122.23 = $110,000, Premiums rec'd beginning of ^ 5, , 
 
 100 X $1,100 = 110,000, Losses paid during i Year, 
 
 — I Age 41 
 
 00, Amount in hand at end of j ^ "* ' 
 
 800 X $137.50 = $110,000, Premiums rec'd beginning cf "^ Th' d 
 
 1 
 
 00, Amount in hand at end ot J 
 
 etc., etc., etc. 
 
 Here, as the increasing premiums take care of the current 
 losses for each year, there is no need of carrying any amount 
 forward from one year to another, and the investment re- 
 serve disappears altogether. The insurance reserve at the 
 beginning of each year is the full amount of the expected 
 losses for that year. As these losses occur and are paid the 
 reserve diminishes, and at any time during the year is 
 measured by the amount of expected losses for the re- 
 mainder of the year. At the end of the year, all losses 
 having been paid, it is nothing. 
 
 It appears then, that, leaving out the question of ex- 
 penses, the level premium is made up of two parts — the 
 insurance portion, which pays the current losses of the 
 year, and the investment portion, whose sole purpose and 
 use are to keep the premium level. The investment reserve 
 (and this is what is usually meant by the term *' Reserve ") 
 may be defined as that part of a level or uniform premium, 
 not needed for current losses, which is set aside for pur- 
 
1^ The A B C of Life Insurance, 
 
 poses of accumulation, to be used, with its accretions, im 
 payment of future losses. 
 
 Incidentally, it should be noted that the reserve of each \ 
 policy in our example at the tenth or final year, plus the 
 premium for that year, is $iioo, and that the actual cost 
 of the insurance for that year is also $iioo, 
 
 From this preliminary study, then, it is evident that a 
 company must either collect an annually increasing pre- 
 mium, correctly adjusted to the annually increasing cost, or 
 must accumulate from a level or uniform premium an invested 
 reserve fund; that this reserve, if accumulated, must be 
 kept intact until needed for its legitimate purpose, viz.: the 
 payment of such a portion of each policy as that policy has 
 contributed to it; that the waste or loss of this reserve 
 means ultimate bankruptcy, on account of the increasing 
 cost of the insurance for which the level premium, without 
 the accumulated reserve, does not provide ; and that the 
 reserve upon any policy increases with the age of that 
 policy or the number of years it has been in force. We can 
 also see that the man who wishes insurance must continue 
 
 Note. — Another definition of a reserve is " The difference between 
 the present value of the insurance, and the present value of the future 
 premiums on that insurance." As an illustration of this definition, our 
 example is very crude, since it ignores the question of compound interest, 
 which is the important factor in determining present values. Neverthe- 
 less, it suggests the method of calculating the reserves for insurances at 
 different ages and under policies upon which premiums have been paid 
 for different terms of years, as actually practiced. Thus, in our supposed 
 company, at the end of the third year there were 700 survivors, upon each 
 one of whom there was an insurance of $1100, or a total of $770,000. The 
 total amount of premiums to be paid during the remainder of the term of 
 years covered by the example was $560,000. Of course, if interest is to 
 be ignored, there is no difference between present and future values. 
 Consequently, the present values of the insurances and of the future 
 premiums would be their full amounts. The difference, $210,000, is the 
 amount of the reserve at the end of the third year given in our example. 
 
The A B C of Life Insurance, 15 
 
 to pay his premiums thereon ; that the men who die during 
 the earlier part of the term do not pay the company, in pre- 
 miums, an amount equal to the amount of their insurance ; 
 and that the men who live to the latter part or end of the 
 whole-life term pay, in premiums, more than the amount 
 of their insurance. 
 
 Simple and elementary as is the preceding discussion, it 
 will repay careful study by anyone unfamiliar with the 
 theory of insurance. And when its points have been mas- 
 tered thoroughly, the preparation will be ample for a 
 ready understanding of what follows in this little volume. 
 
 Our illustration was based upon the supposition that the 
 1000 men were all of the same age ; that no other men came 
 into the arrangement; that none of the original number 
 dropped out by the way ; that in each year the number of 
 deaths was exactly what it was expected to be when the 
 company was formed ; that nothing was realized for interest 
 by the investment of funds on hand ; and that there was no 
 expense connected with the transaction of the business. In 
 actual experience, men of all ages are insured in the same 
 company; new members are continually coming in; old 
 ones are dropping out ; new sets of reserves are taking the 
 places of those which have been applied in the payment of 
 losses or have been withdrawn ; the rate of mortality varies 
 more or less from the tabular rate ; interest is received on 
 investments; and expenses are incurred in various ways. 
 An attempt will be made in the following pages to discuss 
 some of these matters briefly and simply, but to carry the 
 discussion only so far as may be necessary to an intelligent 
 comprehension of the subject in a somewhat general way. 
 
1 6 The A B C of Life Insurance. 
 
 CHAPTER II. 
 MORTALITY TABLES. 
 
 If insurance is simply a method of distributing or appor- 
 tioning individual losses among a large number of persons 
 who enter into the arrangement for mutual protection, the 
 fact will at once suggest itself that each person should pay 
 not only in proportion to the amount of his possible loss, 
 but also in proportion to the likelihood that that loss will 
 occur. Risks are classified for fire insurance according to 
 the hazard of fire. In like manner, the life most likely to 
 end should pay the highest premium. Asid : from the 
 special risk to which any individual hfe may, at any given 
 time, be subjected by reason of sickness or accident, 
 it is evident that the older a man grows the nearer he 
 is to death. Consequently, in determining the amount of 
 premiums which any individual should pay, it is evident 
 that his age must be the prime factor. The first thing, 
 then, to be determined is the effect of age upon the rate of 
 mortality — in other words, how many deaths within a year 
 may be expected among a given number of men of any given 
 age. 
 
 No business in the world has a more reliable basis upon 
 which to make its calculations than that of life insurance. 
 The rate of mortality among lives of different ages has 
 been made a matter of study and record for more than 150 
 years. The tabulated results are known as " Mortality 
 Tables" or "Tables of Mortality." 
 
The A B C of Life Insurance, 17 
 
 The first used as a basis for life insurance was the North- 
 ampton Table. This was formed by Dr. Price from obser- 
 vations on the mortality in the town of Northampton, Eng- 
 land, from 1735 to 1780. This table is no longer used for 
 valuations, and has never been used in this country. 
 
 The Carlisle Table was formed by Mr. Milne from obser- 
 vations in the town of Carlisle, England, from 1778 to 1787. 
 It is still in use to a limited extent. 
 
 The Actuaries* or Combined Experience Table, published 
 in 1843, was compiled from the experience of seventeen 
 English companies. It is used in this country as the legal 
 standard for computing reserves with four per cent interest, 
 but in England has been largely superseded by the later 
 Actuaries' or H. M. (Healthy Males) Table. 
 
 The Farr Table, No. 3, was constructed by Dr. Farr from 
 observations upon the mortality of the entire population of 
 England, and was published in 1864. It is not now in use. 
 
 The American Experience Table was formed from the 
 experience of the Mutual Life of New York by Mr. Sheppard 
 Homans, actuary of that company. It is in general use in 
 this country for the computation of premiums, and as the 
 legal standard for computing reserves with four and one- 
 half per cent interest. 
 
 The experience of thirty American companies was tabu- 
 lated by Mr. L. W. Meech, and the results pubHshed in 
 1 88 1. This table is generally known as the Meech Table. 
 It is very valuable as a record of actual experience, but is 
 not used in valuations. 
 
 For present purposes it is necessary to give the Actuaries* 
 and American ExperienceTables only. These will be found 
 on pages 68, 71 and 72. 
 
 From the latter table anyone who is interested to do so, 
 and has the time to spare, can substitute the proper figures 
 
i8 The A B C of Life Insurance. 
 
 for those given in the preHminary example, and can calcu- 
 late the necessary annual, whole-life premium for any age 
 without allowance for interest or expenses. 
 
 By dividing the number of deaths during any year by the 
 number of persons living at the beginning of that year, we 
 obtain the percentage of mortality as given in connection 
 with these tables. 
 
 From the mortality tables, also, by averaging the after-life 
 time of the number of persons living at any given age, we 
 obtain the table of the Expectation of Life given on page 50. 
 This table is interesting, but not particularly useful. It is 
 never employed in making calculations. The supposition 
 that the annual premium to be paid by a person of any 
 given age is the sum which, invested at four or four and a 
 half per cent during the "expectation" of that person, 
 would equal the amount insured ; or that the present value 
 of an insurance, payable at death, can be ascertained by 
 discounting the amount of the insurance at four or four and 
 a half per cent for the number of years represented by the 
 " expectation " of the insured, is wholly erroneous. 
 
 So, too, the average age of a number of Hves is not a 
 reliable measure of the risk upon them all. Thus, the 
 average age of 10 men aged 98, and 10 men aged 30, 
 would be 64 years. Among these 20 men we should 
 expect at least 10 deaths during the year, while among 20 
 men aged 64 we should not expect more than one death. 
 
The A B C of Life Insurance, 19 
 
 CHAPTER III. 
 NET PREMIUMS, 
 
 A net premium is one in the calculation of which due 
 allowance has been made for the interest which a company 
 may receive upon its investments, but with no allowance for 
 the expenses of the business. 
 
 Thus far we have, for the sake of simplicity, neglected the 
 question of interest. But, since a company may realize con- 
 siderable amounts in the way of interest upon judiciously 
 invested funds, not needed for present use, it is plain that, 
 in determining the premium which it is necessary to charge, 
 due consideration of this source of income should be had. 
 Obviously, the rate of premium will be reduced by the fact 
 that interest receipts are to be added to the company's in- 
 come. If too great a reduction is made, however, the pre- 
 mium will not be sufficient. And, as life insurance contracts 
 may cover a very long period, premiums must be based 
 upon assumptions which are likely to be realized in actual ex- 
 perience through an indefinite term of years. With this fact 
 in view, 4 per cent has been taken as the probable rate of 
 interest, in ihe calculation of premiums. 
 
 The following explanation of the method of calculating a 
 net annual premium for an insurance for the term of five 
 years, presents only the very simplest form of such calcula- 
 tions, the design being rather to illustrate principles and the 
 method of their application, than to present or attempt to 
 demonstrate intricate mathematical problems. 
 
20 The A B C of Life Insurance. 
 
 What should be the net annual premium (level) for an in- 
 surance of $1000, for the term of 5 years only, upon the life 
 •of a man aged 40, according to the American Experience 
 Table with 4 per cent interest ? 
 
 An annuity is the recurring annual payment of a uniform 
 amount. Consequently the annual premium is an annuity 
 paid by the insured to the company. Manifestly, there- 
 fore, the proper method of ascertaining the required pre- 
 mium is to ascertain the present value of the insurance, and 
 then to determine the amount of an annuity whose present 
 value is equal to the present value of the insurance. We 
 will calculate the present value of an insurance for $1 and 
 then find the corresponding annuity. The latter will be the 
 annual premium for an insurance of $1, which must be 
 multiplied by the number of dollars of any desired insurance 
 to obtain the necessary premium therefor. 
 
 In thiSy and in all similar calculations ^ the premium is 
 considered payable at the beginning of the year, and the loss 
 at the end of the year. 
 
 Present value of (or, in other words, single premium for) 
 an insurance of $1, for a term of 5 years, upon the life of 
 a man aged 40. 
 
 By the American Experience Table (page 68) it appears 
 that, out of 78,106 person living at age 40, there will die 
 
 In the I St year, 765 persons 
 
 In the 2d 
 
 " 774 
 
 In the 3d 
 
 '' 785 
 
 In the 4th 
 
 " 797 
 
 In the 5th 
 
 " 812 
 
 An insurance of $1, therefore, upon each person, would 
 require the payment of $765.00 at the end of the first year, 
 $774.00 at the end of the second year, and so on. From the 
 
I 
 
 The A B C of Life Insurance. 21 
 
 table of present values of $1 (page 76) we find that the 
 Present value at 4 per cent of $1 payable in i year 
 
 is $0.961538. 
 Present value at 4 per cent of $1 payable in 2 years, 
 
 is $0.924556, etc. 
 Therefore the present value of the above losses is as 
 follows : 
 
 Of the $765.00. $765 X .961538 ^7355? 
 
 Ofthe 774.00, 774 X .924556 715.60 
 
 Ofthe 785.00, 785 X .888996 697.86 
 
 Of the 797.00, 797 X .854804 681.28 
 
 Of the 812.00, 812 X .821927 667 40 
 
 Total present value of losses $3,497-72 
 
 If the 78,106 persons living at the beginning of the term 
 were to divide this present value into 78,106 single pay- 
 ments, to be made at once, the result would be $3,497.72 
 -i- 78,106, or $0.04478, and this would be the present value 
 of an insurance of $1, and consequently the single pre- 
 mium which each man should pay in advance for such an 
 insurance. 
 
 But we wish to find an annual premium (or annuity) 
 whose present value shall equal the above present value of 
 the insurance. This will, of course, be an annuity for 5 
 years contingent upon the lives of 78,106 persons, aged 40. 
 We will first find the present value of such an annuity 
 for $1. 
 
 By the same table of mortality, we find that if each per- 
 son living at the beginning of each year should pay $1, 
 the company would receive 
 
 At the beginning ofthe ist year, $78,106.00. 
 
 At the beginning ofthe 2d year, 77,341.00. 
 Lt the beginning of the 3d year, 76,567.00. 
 Lt the beginning of the 4th year, 75,782.00. 
 
 At the beginning of the 5th year, 74.985.00. 
 
22 The A B C of Life Insurance. 
 
 Of course, the present value of the first payment would 
 be the entire amount of that payment, since it is made at 
 once. The present value of the second payment would be 
 the present value of -that amount payable in i year ; of the 
 third, the present value of that amount payable in 2 years ; 
 and so on. Resorting again to the table of present values 
 of $1, we have 
 
 Present value of the $78,106.00 $78,106.00 1 
 
 Present value of the 77,341.00 = $77,341 x .961538 74,36631 
 
 Present value oi the 76.567.00 = 76,^67 x ,924556 70,790.48 
 
 Present value of the 75,782.00 = 75,782 x .888996 67,369.89 
 
 Present value of the 74,985.00 = 74,985 x .854804 64,097.48 
 
 Total present value of all the payments $354-73° i^ 
 
 This total depends upon the lives of 78,106 persons — the 
 number living at the beginning of the first year. Conse- 
 quently, the amount depending upon the life of any one per- 
 son must be $354,73o-i6 ^ or $4.54164. This, then, is the 
 78,106 
 
 present value of an annuity of $1 for 5 years, contingent 
 upon the life of a person aged 40. This value is much 
 larger than the value of the insurance, which is only 
 $0.04478. Consequently the required annuity or annual 
 
 premium will be only . of $1, or $0.00986. This is 
 
 the net annual premium for an insurance of $1 for the 
 term of 5 years on a life aged 40. The premium for an 
 insurance of $1000 would be 1000 x $0.00986, or $9.86. 
 
 It will'be seen at once that, if the term of the insurance 
 instead of being limited to 5 years, had covered the entire 
 term of life according to the American Experience Table, 
 the result would have been the net annual, whole-life pre- 
 mium. 
 
The A B C of Life Insuraui.^, 
 
 23 
 
 The following example carries the premium, interest, re- 
 serve and loss accounts through the five-year term, with the 
 above premium and with the rate of mortality shown by 
 the American Experience Table : 
 
 78,106 X $9.86 = $770,125 16, Premiums rec'd beginning of ' 
 30,805.01, 4 per cent interest 
 
 765 
 
 77,341 
 
 774 
 
 76,567 X 
 
 785 
 
 ^800.930,17, Total 
 765,000.00, Death claims during 
 
 $9.86 : 
 
 $35,930.17, Reserve end of 
 
 762.582.26, Premiums rec'd beginning of ^ 
 
 512 43, Total beginning of 
 31,940.50, 4 per cent interest 
 
 $830,452.93, Total 
 000 = 774,000.00, Death claims during 
 
 $56,452.93, Reserve end of 
 ).86 = 754,950,62, Premiums rec'd beginning of ^ 
 
 $811,403.55, Total beginning of 
 32,456 14, 4 per cent interest 
 
 $843,859.69, Total 
 Jiooo = 785,000,00, Death claims during 
 
 75,782 X $9 86 : 
 
 797 
 
 74.985 X $9.86 : 
 
 812 X $1000 : 
 
 $58,859.69, Reserve end of 
 
 747,210.52, Premiums rec'd beginning of ' 
 
 $806,070.21, Total beginning of 
 32,242.81, 4 per cent interest 
 
 $838,313.02, Total 
 797,000.00, Death claims during 
 
 $41,313.02, Reserve end of 
 
 739,352.10, Premiums rec'd beginning of ^ 
 
 $780,665.12, Total beginning of 
 31,226.60, 4 per cent interest 
 
 $811,891.72, Total 
 : 812,000.00, Death claims during 
 
 First 
 
 Year, 
 
 Age 40. 
 
 Second 
 
 Year, 
 
 Age 41. 
 
 Third 
 
 Year, 
 
 Age 42. 
 
 Fourth 
 
 Year, 
 
 Age 43. 
 
 Fifth 
 Year, 
 
 Age 44, 
 
 Excess of death claims, $108.28 
 
 The excess of the death claims, $108.28, represents about 
 one-seventh of a cent for each person living at the end of 
 
24 The A B C of Life Insurance, 
 
 the fifth year. It is impossible to express the premium 
 more exactly, in dollars and cents, than $9.86. A premium 
 of $9.87 would show an excess of receipts over death claims 
 of about $4,207.52, or 5.6 cents for each person living at 
 the end of the term. 
 
 Endowment policies, so-called, are, strictly speaking, en- 
 dowment insurance policies. To the agreement to pay say 
 $1000 in the event of death within the endowment term, they 
 add the agreement to pay $1000 also provided the insured 
 shall live to the end of that term. Thus if A has what is 
 usually called a " twenty-five-year endowment " policy, his 
 beneficiaries will receive $1000 if he shall die within the 
 twenty-five years, and he will himself receive $1000 if he 
 shall live out the twenty-five years. Manifestly here is 
 a double provision, the one contingent upon death and the 
 other upon life. The former is pure insurance, the latter is 
 pure endowment. 
 
 What should be the net annual premium for a five-year 
 endowment insurance of $1000 upon the life of a man aged 
 40, according to the American Experience Table, with four 
 per cent interest ? 
 
 The net premium for the insurance part of this contract 
 we have just found to be $9.86. If, then, we ascertain the 
 net premium for the endowment part and add it to the 
 $9.86, the result will be the net premium for the double 
 contract. 
 
 Pure endowment provides nothing for the beneficiaries of 
 those who die, but is solely concerned for those who live. 
 Consequently for our immediate purpose we wish to know 
 the probable number of persons who will be living at the 
 beginning of each year to pay premiums, and the probable 
 number who will survive the fifth year and, on the first day 
 of the sixth, will be living to claim the endowment. The 
 
I 
 
 The A B C of Life Insurance, 25 
 
 probable number of premium payments will, of course, be 
 the same as in the preceding example. A glance at the 
 American Experience Table shows that the probable num- 
 ber of persons who will live out the five-year term and reach 
 age 45 will be 74,173. A pure endowment of %\ for each 
 of these will, of course, amount to $74,173. The method 
 of computing the net annual premium necessary to provide 
 this amount is practically the same with the method of com- 
 puting the insurance premium already explained, viz.: as- 
 certain the single premium for the pure endowment, and 
 then the equivalent five-year annuity. 
 
 Since no part of the pure endowment is payable until the 
 expiration of five years, while at that time the whole must 
 be paid, it is evident that the present value would be the 
 present value at four per cent of $r, payable in five years, 
 multiplied by the total amount of the pure endowment. 
 $745173 X .821927 =$60,964.79, the present value. If the 
 78,106 living at the beginning of the term were to divide 
 this into 78,106 single payments, to be made at once, the 
 result would be $60,964.79 -f 78,106 = $0.78050, which 
 would be the net single premium which a man aged 40 
 should pay in advance to secure a pure endowment of $1 at 
 the end of five years. 
 
 Now, as we found on page 22, the present value of an 
 annuity of $1 for five years, contingent upon the life of a 
 person aged 40, is $4.54164. This is larger than the value 
 of the pure endowment, and consequently the required an- 
 nuity will be ^ '^^^ of $1, or $0.17186, which is the net 
 454,164 
 
 annual premium for a five-year pure endowment of $1 on 
 the life of a man aged 40. The premium for such an en- 
 dowment of $1000 would be, of course, 1000 x $0.17186, 
 or $171.86. Add the pure insurance premium, $9.86, to 
 
26 The A B C of Life Insurance, 
 
 the pure endowment premium, $171.86, and we have 
 $181.72 as the net annual premium for an endowment in- 
 surance (ordinarily termed endowment) of five years on the 
 life of a man aged 40. 
 
 On page 23 an example carried the insurance part of this 
 contract through the five years. The subjoined carries the 
 endowment part through the same period. 
 
 78,106 X $171.86 = $13,423,297.16, Prems. rec'd beginning of ^ p. . 
 
 536,931.89, 4 per cent interest j. Year, 
 
 * Age 40. 
 $13,960,229.05, Reserve end of J 
 
 77,341 X $171.86 = 13,291,824.26, Prems. rec'd beginning of ; 
 
 $27,252,053.31, Total 
 
 1,090,082.13, 4 per cent interest 
 
 $28,342,135.44, Reserve end of 
 76,567 X $171.86 = 13,158,804.62, Prems. rec'd beginning of ^ 
 
 Second 
 Year, 
 Age 41. 
 
 Third 
 Year, 
 Age 42. 
 
 Fourth 
 
 Year, 
 
 Age 43. 
 
 $4 [,500, 940. 06, Total 
 
 1,660,037.60, 4 per cent interest 
 
 $43,160,977.66, Reserve end of 
 75,782 X $171.86= 13,023,894.52, Prems. rec'd beginning of 
 
 $56,184,872.18, Total 
 
 2,247,394.89, 4 per cent interest 
 
 $58,432,267.07, Reserve end of 
 74,985 X $171.86= 12,886,922.10, Prems. rec'd beginring of ") 
 
 $71,319,189.17. Total [ ™^^ 
 
 2,852.767.57, 4 per cent interest 1 Age 44. 
 
 $74,171,956.74, Fund in hand end of ) 
 
 r Amount required to pay \ 
 74,173 X $1000 = 74,173,000 00, ■? endowments at the be- | Sixth 
 
 (^ ginning of \ Yea'-, 
 
 Age 45. 
 
 Excess of endowments, $1,043.26, j 
 
 This excess of the endowments over the fund in hand is 
 less than a cent and a half for each person living at age 45 
 and consequently entitled to draw $1000 from the fund. 
 The addition of one cent to the annual premium would 
 
I 
 
 ^H The A B C of Life Insurance. 27 
 
 have made the fund in hand exceed the amount required 
 for the endowment by about $3275. 
 
 For the sake of the demonstration and of the lessons'* 
 which may be learned from the illustration, we will now 
 take the net premium, $181.72, for the pure insurance 
 and the pure endowment combined, and by an example 
 which will be, of course, a combination of that on page 23 
 and that on page 26, will carry the premium, interest, death 
 loss, reserve and endowment accounts through the five-year 
 term. 
 
 78,106 X $181 72 : 
 
 765 X $1000 : 
 
 77,341 X $181.72 : 
 
 774 X $1000 : 
 
 76,567 X $181.72 : 
 
 785 X $1000 : 
 
 75,782 X $181.72 : 
 
 797 X $1000 = 
 
 : $14,193,422.32, 
 567,736.90, 
 
 $14,761,159.22, 
 : 765,000.00, 
 
 $13,996,159.22, 
 : 14,054,406 52, 
 
 $28,050,565.74, 
 1,122,022.63, 
 
 $29,172,588.37. 
 774,000.00, 
 
 $28,398,588.37, 
 ■• 13.913.75524, 
 
 $42,312,343.61, 
 1,692,493.74, 
 
 $44,004,837.35, 
 785,000.00, 
 
 $43,219,837 35, 
 : 13,771,105.04, 
 
 $56,990,942.39, 
 2,279,637.70, 
 
 $59,270,580.09, 
 797,000.00, 
 
 $58,473,580.09, 
 
 Prems. rec'd beginning of 
 4 per cent interest 
 
 Total \ 
 
 Death claims during 
 
 Reserve end of 
 
 Prems. rec'd beginning of ") 
 
 Total beginning of 
 4 per cent interest 
 
 Total 
 
 Death claims during 
 
 Reserve end of 
 
 Prems. rec'd beginning of ' 
 
 Total beginning of 
 4 per cent interest 
 
 Total 
 
 Death claims during 
 
 ResTve end of 
 
 Prems. rec'd beginning of ' 
 
 Total beginning of 
 4 per cent interest 
 
 Total 
 
 Death claims during 
 
 Reserve end of 
 
 First 
 . Year, 
 Age 40. 
 
 Second 
 Year, 
 Age 41. 
 
 Third 
 Year, 
 Age 42. 
 
 Fourth 
 Year, 
 Age 43. 
 
28 The A B C of Life Insurance, 
 
 74.985 ^ $181.72 = 13,626.274.20, Prems. rec'd beginning of ^ 
 
 $72,099,854.29, Total beginning of 
 2,883,994.17, 4 per cent interest 
 
 •ay "^ Sixth 
 in- > Year, 
 ) Age 45. 
 
 Fifth 
 Year, 
 
 $74,983,848.46, Total I Age 44. 
 
 812 X $1000 = 812,000.00, Death claims during 
 
 $74,171,848.46, Fund In hand end of 
 
 C Amount required to pay 
 74,173 X $1000= 74,173,000.00, ^endowments at begin- 
 
 Cning of 
 
 Deticit... $1,15154 
 
 This deficit is made up of the " excess of death claims, 
 $108.28," found on page 23, and the "excess of endowments, 
 $1,043.26," found on page 26. An addition of five-six- 
 teenths of a cent to the premium would be more than suffi- 
 cient to cover it. 
 
 A comparative study of these three examples on pages 23, 
 26 and 27 can be made interesting and instructive. Note that 
 in the first (five-year term insurance) the reserve increases 
 for a while, then decreases, and finally is exhausted in the 
 payment of the fifth year's death claims ; that in the second 
 (pure endowment) the reserve increases steadily to the end 
 of the term, and is then exhausted in the payment of the 
 endowments ; that in the third (endowment insurance) the 
 reserve steadily increases from year to year, is always at the 
 end of any given year the sum of the reserves for the cor- 
 responding year in the first and second examples, and is 
 finally exhausted in the payment of the fifth year's death 
 claims and of the endowments. Note also that the reserve 
 at the end of any year contains a certain amount, greater or 
 smaller as the case may be, which has been derived from 
 premium payments (with interest thereon) made by persons 
 who have died. Note also the part which compound inter- 
 est plays, and the vital importance of the interest earnings 
 to any company. 
 
The A B C of Life Insurance. 29 
 
 Still further, in term insurance, as illustrated in the first 
 example, the fund in hand at the end of the fifth year is not 
 equal to the total amount of the outstanding insurance, but ' 
 is equal to the amount of insurance which is to be paid as 
 death claims during that year. Under the endowment in- 
 surance the fund in hand at the end of the fifth year is equal 
 to the total amount of the outstanding insurance, because 
 every person insured will have a claim upon the fund either 
 because of his death during the fifth year or because of his 
 survival to the beginning of the sixth. Whole-life insurance 
 must provide a fund at the end of the last year which shall 
 equal the total amount of the outstanding insurance, 
 because, by the end of that year, the few survivors who 
 began the year will have died. It is often said that a 
 whole-life policy (American Experience Table) is " prac- 
 tically an endowment at age 96.'' This is correct to the 
 extent that the reserve under such a policy at age 96 will 
 equal the face of the policy — the full amount of the insur- 
 ance. It has happened at least once in the history of life 
 insurance in this country that a man holding a whole-life, 
 annual-premium policy carried the policy and paid the pre- 
 miums until he was 96 years old. According to the Mor- 
 tality Table he should have been dead. He had made all 
 the payments theoretically required under his contract, and 
 the accumulated reserve under his policy was equal to the 
 full amount of his insurance. Very properly, the company 
 in which he was insured paid him his money without waiting 
 for his actual demise. 
 
 For the sake of brevity a five-year endowment was chosen 
 for our example. In actual practice so short endowments are 
 rarely issued, and consequently the very great disproportion 
 between the insurance and the endowment elements which 
 
 Vears in the preceding examples exists in frequen tly in 
 
30 The A B C of Life Insurance. 
 
 practice. The premiums under longer endowments — ten, 
 fifteen, twenty-five or more years- — must, of course, make 
 provision for a greater amount of death claims during the 
 term, and for a smaller amount of endowments at its end. 
 
 The foregoing illustrations show that a considerable 
 amount of work is involved in determining the premium for 
 ordinary forms of insurance for one age only, and for so 
 short a term as five years. It will be seen at once that the 
 computation of premiums for every age and for long terms 
 would be an exceedingly laborious process. And when dif- 
 ferent forms of insurance and contingencies involving more 
 than one life are to be considered, the mathematical prob- 
 lem may be one of great intricacy and difficulty. Log- 
 arithms, the processes of algebra, and various devices, such 
 as ** Commutation Columns," for lightening the labor of 
 computation, are employed by the actuaries or expert mathe- 
 maticians who make the calculations. One who desires to 
 acquaint himself with the mathematics of Hfe insurance can 
 find a large number of text books from which to choose. 
 For our purpose it is unnecessary to follow the subject 
 further. Tables of net annual and single whole-life pre- 
 miums will be found on pages 69 and 73. 
 
The A B C of Life Insurance . 31 
 
 CHAPTER IV. 
 
 GROSS OR OFFICE PREMIUMS. 
 
 To the net premium must be added a certain amount 
 with which to pay the expenses of conducting the business 
 and to provide for contingencies. This amount is called 
 the margin or loading. It is usually a percentage of the 
 net premium. The loading and net premium together con- 
 stitute the gross or office premium — that which the com- 
 pany charges for the insurance. Thus, from our example 
 illustrating the computation of a net premium we have 
 
 Net premium for a five-year term insurance of $1000, age 40 $9.86 
 
 Margin or loading, say 33^^ per cent 3.29 
 
 Gross or office premium $13-15 
 
 The loading is usually a percentage of the net premium. 
 Its amount varies with the form of the insurance and the 
 objects which the company has in view. If it is intended 
 to return a portion of the premium in the shape of divi- 
 dends to the policyholder, the loading will be higher than 
 when no such return is contemplated. Premiums so loaded 
 are called "mutual" or "participating" premiums. Those 
 from which no dividend is paid are called "stock " or " non- 
 participating " premiums. 
 
 All annual premiums are supposed to be paid at the 
 beginning of the policy year. If, by consent of the com- 
 pany, the premiums are paid semi-annually or quarterly, the 
 unpaid installments of the annual premium are called 
 "deferred" premiums. Interest is charged on them, and 
 
32 The ABC of Life Insurance, 
 
 their amount is always deducted from the amount of the 
 insurance in case of a claim. As has already been stated, 
 premiums are computed upon the theory that the full 
 annual premium is paid at the beginning of the year, and 
 the premiums are smaller than they would otherwise be. 
 Consequently the company is fairly entitled to retain the 
 unpaid installments. This is equity also between different 
 poh'cyholders. One man pays a full annual premium and dies 
 within three months. Another who has taken his insurance 
 at the same premium rate, theoretically, pays but one- 
 quarter of his annual premium and also dies within three 
 months. Manifestly equity between these two men, insur- 
 ants in the same company, would be observed by deducting 
 from the amount of insurance on the latter the amount of 
 the three unpaid quarters of his annual premium. 
 
 An analysis of the first year's whole-life premium at differ- 
 ent ages, showing what portion of the net premium is in- 
 tended for death claims and what for reserve, the amount of 
 a uniform loading of forty per cent at all ages, and the 
 gross premium made up of these three items, is given on 
 page 70. Special attention is called to the note regarding 
 this table on page 77. 
 
The A B C of Life Insurance. 33 
 
 CHAPTER V. 
 RESERVES J LOANS ; REINSURANCE, 
 
 But little need be added to what has already been said 
 concerning reserves. Their nature and function have been 
 fully explained. Nor is it necessary to attempt an explana- 
 tion of the method of calculating them. Remembering the 
 definition of a reserve, " the difference between the present 
 value of the insurance and the present value of the pre- 
 miums thereon," it will be seen that compound interest is 
 again an important factor. The interest received upon the 
 fund representing the reserve, or upon the securities in 
 which that fund is invested, may be added to the fund from 
 time to time, thus lessening the amount of the principal 
 which must be set aside for investment. 
 
 To put it in another way, it is evident that if a company 
 is to receive interest on its investments, it need not reserve 
 so much money at the present time to meet a certain 
 amount of future liabilities as it would have to reserve if no 
 interest were to be received. Also, the higher the rate of 
 interest the smaller the reserve required. If you must have 
 $1000 at the end of a year, and can get but 4 per cent 
 interest, you must put aside or reserve at the beginning of 
 the year $961.54. But if you can get 10 per cent you 
 need reserve only $909.09. Reserves are usually calculated 
 upon the basis of the Actuaries' Table with 4 per cent 
 interest, or the American Experience Table with ^\ per 
 cent interest. Of course those calculated on the latter 
 basis are the smaller. The following table shows the 
 
34 The A B C of Life Insurance, 
 
 reserves on a policy of $1000, issued at age 35, computed 
 according to the different standards: 
 
 American Experience Actuaries' 
 with \%, per cent Interest, with 4 per cent Interest. 
 
 End of 1st year $9.82 $11.48 
 
 End of 5th year S3.20 6134 
 
 End of loth year 1 17-45 133 41 
 
 End of 15th year 193-43 21430 
 
 End of 20th year 279.59 301.35 
 
 The percentage of difference decreases with the age of 
 the policy, that is, the number of years it has been in force. 
 
 Tables of Reserves according to the higher standard, the 
 Actuaries' Table of Mortality with 4 per cent interest, are 
 given on pages 74 and 75. These are the reserves on pre- 
 mium-paying, ordinary life policies. The reserves on paid-up 
 policies are, of course, the net single premiums given in the 
 table on page 73. 
 
 There are many forms of insurance, as will be seen from 
 chapter VI I. Each corresponding form of policy has its own 
 special premium, which must, of course, provide for its own 
 sufficient reserve. The net premiums and reserves given in 
 the tables herewith, are those on the most ordinary form of 
 life policy only. These are sufficient, in the wav of 
 elementary illustration, for the present purpose. 
 
 From the nature of a reserve, it is always reckoned a 
 liability of the company. It must be kept intact for its 
 proper use, as already explained. If it is not, and the im- 
 pairment is too great to be made good, the laws of the dif- 
 ferent States require, under differing conditions, the winding 
 up of the company, upon the theory that, although the 
 company may be amply able to pay its current claims, the 
 time will surely come when it will be unable to do so. 
 Consequently the matter of suitable investments which shall 
 be safe, and at the same time shall return a fair rate of in- 
 
The A B C of Life Insurance, 35 
 
 terest, is one of prime importance to a company. The 
 laws of most States prescribe the forms of investments which 
 a company may make. 
 
 It should be noted in passing that the larger the reserve 
 on a poHcy, the less the amount which the company has at 
 risk in the insurance. Thus, if the reserve on a policy of 
 $1000 is $500, it is evident that the company need add but 
 $500 from its current income to make up the full amount 
 of the insurance. From this point of view, and regarding 
 the reserve in the light of a deposit made by the policy- 
 holder with the company, Mr. Elizur Wright gave to the re- 
 serve the definition of " self-insurance." The actual loss to a 
 company through death claims is not the total amount of 
 those claims, but the difference between that amount and 
 the total amount of the reserves credited to the policies 
 under which the claims are paid. 
 
 The following table shows the accumulation of the re- 
 serve under a policy of $1000, ordinary Hfe plan, issued at 
 age 40. Column i gives the portion of the premium which 
 is set aside each year for reserve. This diminishes each 
 year, as the actual cost of insurance increases each year. 
 Column 2 gives the total amount of the reserve held by 
 the company at the end of each year. Of course, at the end 
 of the first year, this is the reserve portion of the first year's 
 premium, with one year's interest at four per cent added. At 
 the beginning of the second year, the reserve portion of the 
 second year's premium is added to the total amount of reserve 
 held at the end of the first year. To this sum, one year's 
 interest at four per cent is added, and the total is the reserve 
 at the end of the second year. And so on for each year. 
 
 The net amount at risk is obtained by subtracting the re- 
 serve held by the company at the end of each year, from 
 $1000, the full amount of the insurance. 
 
36 
 
 The A B C of Life Insurance. 
 
 Accumulation of Reserve; Decrease of Amount 
 AT Risk. 
 
 Amount insured, $1000. Ordinary life plan. Age at 
 issue, 40. Reserve computed according to American Ex- 
 perience Table, with four per cent interest. 
 
 Year. 
 
 Reserve Portion 
 of Premium. 
 
 Accumulated Re- 
 serve at End of Year 
 
 Net Amount 
 at Risk. 
 
 1st 
 
 $13.06 
 12.99 
 12.91 
 12.82 
 12.70 
 
 12.57 
 12.40 
 
 12.22 
 
 12.00 
 
 11.73 
 
 11.43 
 
 11.08 
 
 10.71 
 
 10.29 
 
 9.83 
 
 9.34 
 
 8.80 
 
 8.23 
 
 7.65 
 
 6.96 
 
 etc. 
 
 $13.59 
 27.65 
 42.18 
 5720 
 72.70 
 88.68 
 
 105-13 
 122.05 
 
 139.41 
 157.19 
 175.37 
 193-91 
 212.80 
 232.02 
 251-52 
 271.30 
 291.31 
 311-52 
 33191 
 352.42 
 etc. 
 
 $986.41 
 
 972.35 
 957-82 
 942 80 
 927.30 
 911.32 
 894.87 
 
 877-95 
 860.59 
 842.81 
 824.63 
 806.09 
 787.20 
 
 2d 
 
 Qd , 
 
 o*-* • 
 
 4th 
 
 5th 
 
 6th 
 
 7th 
 
 8th 
 
 Qth 
 
 lotn 
 
 nth 
 
 i2th 
 
 iqth 
 
 14th 
 
 767.98 
 748.48 
 728.70 
 
 15th 
 
 i6th 
 
 17th 
 
 708.69 
 688.48 
 668.09 
 
 i8th 
 
 19th 
 
 20th 
 
 647-58 
 etc. 
 
 etc. 
 
 Premiums are sometimes paid, by consent of the com- 
 pany, partly in cash and partly in notes. These notes are 
 available as a part of the reserve. The cash part of the 
 premium is used to pay expenses and current losses, and 
 the note is laid away as part of the reserve. Such notes 
 are called " premium notes " and in reality constitute a loan 
 to the policyholder. The premium note system has not 
 always proved very satisfactory. The notes accumulate and 
 finally constitute a considerable lien upon the insurance, 
 which is deducted from the amount of the insurance in case 
 
The A B C of Life Insurance. 37 
 
 of claim. In companies whose dividends are large, the 
 accumulation of these notes is diminished by applying the 
 dividends towards their payment. There are very few com- 
 panies at present which use the note system. 
 
 Policies having a large reserve value are sometimes used 
 as collateral for loans. Their main value for such purpose 
 lies in the reserve. The insurance itself is payable only 
 upon the happening of a certain contingency, /. ^., the death 
 of the insured, and, of course, constitutes a very indefinite 
 form of security. Endowments (policies payable when the 
 insured reaches a certain age, or at prior death) are more 
 available as collateral security, but even here the definite 
 value of the collateral is largely dependent upon the amount 
 of the reserve. 
 
 The amount of money allowed by a company for the 
 surrender of a policy is governed by the reserve, unless 
 the insured is in poor health. In that case the prospect of 
 his early death, which would make the policy a claim for 
 the full amount of the insurance, would give an added 
 present value to the policy. It is evident, however, that, 
 if the insured be in good health, the reserve on his policy 
 represents his entire equity in the insurance, since the 
 remaining portion of his premiums has been used for the 
 payment of current losses and expenses. As a matter of 
 fact, the reserve represents more than the entire equity of 
 the policyholder and, for that and other reasons, should be 
 subject to a " surrender charge." This will be considered 
 in a subsequent chapter. 
 
 In cases of reinsurance, the reserve is again the important 
 element of the transaction. If a company wishes or is 
 forced to withdraw from business, it sometimes reinsures its 
 risks, i. <?., transfers them to another company. This latter 
 company assumes the contracts of the former, and charges 
 
38 The A B C of Life Insurance, 
 
 the same premium tor the insurance which each policyholder 
 was paying the original company. To enable it to do this, 
 the reserve fund accumulated by the original company 
 must be transferred to the reinsuring company, else the lat- 
 ter company would be the loser by the transaction, by at 
 least the deficiency of the reserve. Consequently, a com- 
 pany which has impaired its reserve to any considerable 
 extent cannot reinsure its risks. 
 
 The reserve is sometimes called the "reinsurance" re- 
 serve. 
 
The A B C cf Life Insurance, 39 
 
 CHAPTER VI. 
 
 SURPLUS J DIVIDENDS, 
 
 The surplus of a company is the excess of its assets over 
 its liabilities. The former include such real estate as the 
 company may own, cash on hand and in course of trans- 
 mission, stocks, bonds, mortgage loans, loans on collaterals, 
 premium notes, accrued rents and interest, and deferred 
 premiums less the loading. The liabilities include the re- 
 serve, unpaid death claims and all unpaid bills or current 
 obligations. The reserve will be the largest item of liability , 
 unless the company has been doing business but a very 
 short time. If it is calculated upon a At\ per cent basis 
 it will be smaller than if upon a 4 per cent basis. 
 Consequently, the surplus at 4^ per cent will be larger than 
 at 4 per cent, by exactly the difference between a 4 per 
 cent and a 4^ per cent reserve. In some of the older and 
 larger companies this difference amounts to several million 
 dollars. 
 
 The principal sources of surplus are ordinarily: 
 A lower rate of mortality than was assumed in the compu- 
 tation of the premiums ; 
 
 A higher rate of interest, actually received, than was 
 assumed in that computation ; and 
 
 The use of a less amount of money for expenses than was 
 provided for by the loading of the premiums. 
 
 If exactly the tabular rate of mortality were experienced, 
 exactly the assumed rate of interest were realized, and ex- 
 
40 The A B C of Life Insurance. 
 
 actly the amount of the loading were used for expenses, the 
 company would at all times have its reserve on hand, but 
 not a dollar of surplus. (Surplus and reserve should be 
 carefully distinguished. They are entirely separate and dis- 
 tinct. One is an asset, the other a liability. One can be 
 used for such purposes as the company thinks best. The 
 other should be used only in the manner and for the pur- 
 pose which have been so fully explained and illustrated in 
 the preceding pages.) 
 
 The rate of mortality in any well-managed company 
 should be less than the assumed or tabular rate. 
 
 The rate of interest has for many years averaged more 
 than 4 per cent. For at least ten years subsequently to 
 1865 it averaged 8 per cent. Its constant tendency, how- 
 ever, is to become lower. Consequently, one exceedingly 
 important factor in producing surplus in earlier years has 
 grown less and less important in later years. 
 
 The amount used for expenses ought not to equal the 
 loading in any company which has a considerable amount 
 of business, especially if the premiums are heavily loaded. 
 
 After retaining a surplus sufficiently large to provide for 
 contingencies, it is customary among companies which issue 
 policies on the mutual or participating plan to divide the 
 remainder of the surplus among such of its policyholders as 
 are entitled to share in it. This is, in reality, the return of 
 
 Note— Formerly, if a policy " lapsed," the entire reserve was forfeited 
 to the company, and thus no inconsiderable additions were made to the 
 surplus. Now, however, a more equitable practice prevails, and the ad- 
 ditions to the surplus from this source are now less than formerly. In 
 general, the most considerable gain from lapsed policies, at present, 
 arises from forfeitures of contingent dividends and a portion of the reserve 
 under the " Tontine " system as explained on page 57. As the Tontines 
 form a special class, they are not included above in considering sources of 
 surplus. 
 
The A B C of Life Insurance, 41 
 
 an overcharge, but it is customary to call it the payment of 
 a dividend. 
 
 The principal plans upon which dividends are distributed 
 are the percentage plan and the contribution plan. The 
 former allows dividends as a percentage, either on the 
 amount of the insurance or on the sum of all premiums 
 paid. The latter takes account of the sources of surplus 
 and of the amount which each individual policy has contrib- 
 uted. For example: if the mortality has been but 80 per cent 
 of the tabular rate, 20 per cent of the cost of the insurance 
 under A's policy is credited to him ; if interest has been 6 per 
 cent, instead of 4 per cent, 2 per cent upon the reserve 
 under his policy is also credited A ; if the expenses have 
 been 90 per cent of the loading, 10 per cent of the loading 
 of A^s premium is also credited him. The sum of these 
 three items is the amount of the dividend received by A. 
 This plan, now almost universally adopted, was devised by 
 Mr. Sheppard Homans, assisted by Mr. D. P. Fackler. 
 
 Dividends are paid sometimes in cash, sometimes in 
 reduction of the next year's premium, sometimes by the 
 addition of a certain amount of insurance to the original 
 amount of the policy. In the latter case they are known as 
 " reversionary " dividends. 
 
 The frequency with which the accumulated surplus is 
 divided, and, consequently, the periods at which dividends 
 are declared, vary with different forms of policies and the 
 practice of different companies. Sometimes dividends are 
 paid annually. In other instances, as under policies written 
 upon the twenty-year distribution plan, they are paid once 
 in twenty years, and only upon such policies as are then in 
 force. 
 
42 The A B C of Life Insurance. 
 
 CHAPTER VII. 
 TERMINATIONS AND SURRENDER VALUES. 
 
 Policies of insurance which from any cause cease to be in 
 force are said to " terminate." The methods of termina- 
 tion may be classified as follows : By " death," when the 
 policy becomes a claim on account of the death of the in- 
 sured; by "maturity/* when an endowment, for instance, 
 becomes payable because the end of the endowment period 
 has been reached; by " expiry," when a term insurance has 
 been carried to the end of the term for which it was issued 
 and consequently is no longer in force ; by " lapse," when 
 the policy is terminated solely by reason of the non-pay- 
 ment of a stipulated premium when due ; by " surrender," 
 • when the legal liability of the company under the policy is 
 voluntarily canceled by the insured and beneficiary for a 
 consideration allowed by the company, which consideration 
 is called the " surrender value." 
 
 Evidently the payment of a death claim or an endowment 
 when due meets the full measure of a company's responsi- 
 bility under such a policy. From what has been said in the 
 preceding pages the reader will understand that a five-year, 
 ten-year or any other purely term insurance which has ex- 
 pired has no subsequent value. But in the case of a lapsed 
 whole-life or endowment policy, for example, to what con- 
 sideration in the way of a surrender value is the insured 
 equitably entitled? 
 
 It is not at all unusual for such a person to say, " The 
 
I 
 
 The A B C of Life Insurance. 43 
 
 company has paid out nothing under my policy. I have 
 not died nor has my pohcy matured ; consequently my in- 
 surance has cost the company nothing. I ought to have 
 my premiums returned to me, to say the least, and even then 
 the company will have had the interest on my money." The 
 obvious answer to this is that the risk carried by any com- 
 pany is the total amount of its insurance in force, not 
 simply that portion of the total amount which becomes a 
 claim by death or maturity ; that each policy is a part of 
 the aggregate, and consequently contributes to the total 
 cost as well as to the total income; and that while the 
 total loss is, so to speak, individualized by the death of cer- 
 tain persons, nevertheless the cost actually, and properly, 
 falls on all the insured, those who do not die receiving the 
 full worth of their money in the protection afforded. The 
 aggregate of all the premiums paid by all the insured is 
 used to pay expenses and death losses so far as it is re- 
 quired for that purpose, and from each individual premium 
 is taken its proper proportion. 
 
 On the other hand, in the early history of life insurance 
 no surrender value was allowed in case of lapse. Under 
 this practice no account was taken of the fact that, after de- 
 ducting the cost of his insurance and his proper contribu- 
 tion to expenses, the insured had still paid to the company 
 an amount in excess of both these items, which was repre- 
 sented by the " reserve," and for which at the date of lapse 
 he had received no consideration. Gradually this fact and 
 the equities involved in it were recognized, and out of this 
 recognition, stimulated to some extent by legislation and to 
 a much larger ex'ent by the competition of the companies 
 for business, has grown the elaborate modern system of sur- 
 render values. 
 
 In discussing this system let us use for the purpose of 
 
44 Tf'i^ A B C of Life Insurance, 
 
 illustration the whole-life policy only, while recognizing the 
 fact that endowments, annuities and other forms are issued' 
 by the same company, and that what is said concerning the 
 whole-life policy may require some modification in apply- 
 ing the general principle to a specific instance of another 
 form of insurance. 
 
 What is the exact status of both parties to an ordinary 
 whole-life contract? The insured has requested in his 
 "application" that the company, in consideration of the 
 annual paymen*^ of a specified premium so long as the in- 
 sured shall live, shall bind itself to pay a specified amount 
 to the designated beneficiary whenever the insured shall die. 
 The company, in compliance with this request, has issued ai 
 contract (policy) by which it is so bound. The presumption 
 is that this is a contract which will be maintained during 
 the lifetime of the insured, and the company relies upon the 
 annual payments of premium as a revenue from which it 
 will derive a certain contribution to the payment of its 
 death losses, another to the payment of its expenses^, 
 another to the making of a reasonable profit from its busi- 
 ness. The company has exactly the same right to expect ; 
 these things which the insured has to expect the prompt 
 payment of his loss when it occurs. If, now, the policy- 
 holder fails to pay all the premiums contemplated by his 
 contract, the company is at once cut off from that source of 
 income and profit, and, at considerable expense, must seek 
 another customer to replace the one which it has lost. The 
 policyholder has had his insurance at its cost plus expenses, 
 and has an equity in the accumulated reserve. That he 
 " owns " the specific amount of the reserve on his individual 
 policy, as has been vehemently asserted in some quarters, 
 cannot be true. In the first place, there has never been a 
 year in which the reserve credited to his policy has been 
 
The A B C of Life Insurance, 45 
 
 made up entirely of his own money with interest accretions, 
 and consequently it is not true that that reserve stands 
 e xactly in the light of a deposit made by fiimself out of his 
 own funds. Part of the reserve was contributed by men 
 who died in prior years. If the reader is interested to work 
 out an illustration of this fact for himself, let him take any 
 one of the three examples on pages 23, 26 and 27. and note 
 the number and amount of premiums in excess of the actual 
 cost of the insurance paid each year by those who die dur- 
 ng that year, and compute their aggregate with compound 
 nterest accretions. Of course, under the pure endowment, 
 page 26, since there is no insurance there can be no cost of 
 insurance, and the reserve at the end of each year includes 
 every cent which has been paid by all those who have died. 
 If the reader has followed the discussion carefully from the 
 first page to the current one, he will readily understand that 
 the amount of contribution to the reserve by those who have 
 died will vary very largely with the form of policy and the 
 length of time during which the insurance has been in force, 
 being in some cases of considerable, and in others of incon- 
 siderable, importance. But that any such contribution, of 
 greater or of less amount, has been made, is sufficient to 
 nuUify the alleged ** ownership " of the reserve. The fact 
 is that the insured agrees to pay so much a year for so much 
 insurance ; as a rule he knows little of the theory or practice 
 of the business, and concerns himself less. He has a very 
 hazy idea of a ''reserve," and wouldn't know what was 
 meant if he should be told that he " owned " it ; he does 
 not buy a reserve nor stipulate for such a purchase ; he ex- 
 pects the company to live up to its contract and to treat 
 him fairly ; and, even if he expected or desired it, the com- 
 pany could not sell him the ownership of his reserve unre- 
 stricted by conditions and enforceable at any time. Conse- 
 
46 The A B C of Life Insurance, 
 
 quently what shall be done with the reserve under a lapsed 
 policy is, apart from legislative interference, purely a ques- 
 tion of equity between the two parties to the contract. 
 
 In determining what is equity, the company on its sirle 
 must at least consider another question in some respects far 
 more important than the loss of income and profit in case 
 of lapse. The man who is in sound health will be likelier 
 to surrender his insurance than the man who has reason to 
 believe that his health is impaired and his chance of life 
 diminished. This is simply human nature, and in this re- 
 spect the " selection," as it is termed, is always against the 
 company. By this it is not meant that none but '* good risks '* 
 will allow their insurance to terminate, Financial difficul- 
 ties, altered circumstances, the death of beneficiaries for 
 whom consequently the provision of insurance is no longer 
 needed, a multitude of reasons for discontinuing insurance 
 affect alike the. good and the poor risks, and in many cases 
 are imperative. But where there is any choice in the mat- 
 ter, the man of impaired health, because he values his insur- 
 ance the more, will make the greater effort to continue it. 
 The consequent result of a high rate of lapse is to reduce 
 the average standard of the risks which remain, and thus to 
 increase the death rate, a consideration of the utmost im- 
 portance. 
 
 There are other questions which might be considered if 
 this little book were intended as an exhaustive discussion of 
 the topics presented, but for its less ambitious purpose it is 
 not necessary to take them up. Enough has been said to 
 make it evident that, as a matter of self-protection to the 
 company, and, in fact, of equity between the retiring 
 policyholder, the company and those who remain, a reason- 
 able forfeit might well be demanded by the company from 
 the man who lapses his policy. This forfeit is known as a 
 
■ 
 
 7 he A B C of Life Insurance, 47 
 
 surrender charge." What should be the amount of this 
 charge is a vexed question. Eminent actuaries differ in 
 regard to it, the practice of the companies is not uniform, 
 £,nd the laws of such States as attempt to regulate the mat- 
 ter by statute are widely apart in their provisions. Without 
 a.ttempting to decide or even to suggest where doctors fail 
 jto agree, let us consider for a moment in what form that 
 portion of the reserve which remains after deducting the 
 surrender charge, shall be available. 
 
 It has been said that life insurance companies exist for 
 , the purpose of selling life insurance and not of buying it. 
 Tliat used to be true, but the modern surrender-value sys- 
 jtem has largely modified the actual functions of an insurance 
 company. Theoretically, if A has purchased a policy of life 
 insurance, and B an endowment, and C an annuity, they 
 would be entitled, in the event of lapse, to receive as a con- 
 sideration for their respective reserve equities an equivalent 
 amount of their respective forms of insurance upon which 
 no further payment of premium would be necessary. Thus 
 iVs reserve equity would be applied as a single premium to 
 purchase insurance payable at his death, B's would be 
 i applied as a single premium to buy an endowment payable 
 at the same date at which his original endowment would 
 have been payable, and C's to purchase an annuity payable 
 [It the same time and under the same conditions with his 
 original annuity. All of these policies would be known as 
 ** paid-up" policies. Their amount would necessarily be 
 less than the amount of the originals. 
 
 Example. — A took a whole life policy of $5000 at age 
 40, carried it ten years and lapsed. To what amount of 
 paid-up insurance would he be entitled as a surrender 
 value ? 
 
4^ The A B C of Life Insurance. 
 
 Reserve on such a policy (see table on page 75) 
 would be 5 X $162.97 or $814.85 
 
 Surrender charge, say 10 per cent 81.49 
 
 ' — -^— ^^— — — 
 
 Net equity in reserve $7 3336 
 
 A at the time of lapse is, of course, 50 years old. Single 
 premium for insurance at that age is $481.92 for each $1000 
 (see table on page 75). Consequently A's equity would 
 
 purchase ^^^^ of $1000, which would be $1520. 
 48162 
 
 In this case, then, instead of having a policy of $5000 
 on which he must pay a premium every year, A would have 
 a policy of $1520 on which he would have to pay no more 
 premiums. 
 
 There is another way in which the reserve equity might 
 be appHed to the purchase of insurance. Instead of issu- 
 ing a paid-up policy for a less amount but in force until 
 terminated by the death of the insured, the company might 
 continue the full amount of the insurance (in the example, 
 $5000,) in force during such a term as the reserve equity 
 would pay for. If the insured should die during that term 
 his beneficiaries would be paid the full amount of the policy, 
 but if he should outlive the term, the policy would ter- 
 minate by expiry and the insurance would cease. An 
 arrangement of this description is called "extended'' 
 insurance. 
 
 It is also evident that any person's reserve equity under 
 one form of insurance might be used to purchase an equiv- 
 alent amount of paid-up or extended insurance of another 
 form. Thus B might have the reserve equity under his 
 endowment policy applied to the purchase of paid-up 
 whole-life insurance. 
 
 The above surrender values which, not so very many 
 
The A B C of Life Insurance, 49 
 
 years ago, were about all that were offered or allowed by 
 the majority of companies — unless in exceptional instances 
 or under very special forms of policies — have in recent times 
 been supplemented and largely superseded by the popular 
 cash surrender value. Practically there are many cases in 
 which the insured, when he lapses his policy, has no further 
 need for insurance, but has urgent need for money, and in 
 which to insist upon applying his reserve equity to the pur- 
 chase of any form of insurance, and to refuse to give it to 
 him in cash, works a hardship. Consequently a policy 
 which provides for a cash value is attractive to anyone who 
 thinks he may sometime need the cash more than the insur- 
 ance, and would rather have a contract right to call for the 
 cash than to be obliged to negotiate for it and perhaps find 
 the company unwiUing to pay it. Partly as a concession to 
 possible necessity on the part of the insured and partly as 
 an effective method of competing for business, the com- 
 pany began to make cash surrender values a feature of more 
 and more of their policies until at the present time a policy 
 without such provision is rather the exception than the rule. 
 In the beginning a good deal of caution was exercised on 
 the theory that it might not always be convenient for a com- 
 pany to pay the reserve equity in cash. It is necessary that 
 a company should obtain a certain rate of interest on its 
 assets, and it cannot afford to keep on hand too large an 
 amount of uninvested money. Investments must also be 
 made in the best class of securities and in those having a 
 long time to run. A life insurance company must also pro- 
 tect itself against the results of a financial panic and must 
 not open the way for a possible " run " upon itself by treat- 
 ing its reserves practically like individual deposits in a bank. 
 These and other similar arguments seemed to have great 
 weight at first, and in consequence cash values were not 
 
50 The A B C of Life Insurance, 
 
 allowed whenever the policies might lapse, but only at stated 
 intervals, five, ten, fifteen years, and so on. Moreover, the 
 portion of the reserve which would be paid in cash was 
 smaller than the amount which would be applied to pur- 
 chase insurance, in other words, when cash was paid the 
 surrender charge was increased. But gradually all this has 
 been done away with. This may be partly due to the fact 
 that the evil effects which were anticipated from the free use 
 of cash surrender values, were not realized, and partly to the 
 efforts of the different companies to outdo each other in 
 competition for patronage, but, whatever the reason, cash 
 values are to-day the rule among the '^ options " given by 
 policy contracts whenever the policy lapses, and surrender 
 charges have diminished in proportion. Practice in this 
 case, as in many others, does not conform to theory. It is 
 the aim of this discussion to present the latter clearly. He 
 who seeks an exemplification of the former by examining 
 the current forms of policies issued by the several com-^ 
 panics will find that the reserve equity — pretty nearly the 
 entire reserve, for that matter — and the contingent interest 
 of the insured, if any, in dividends are made the foundation 
 upon which is reared a structure of numerous options avail- 
 able in the settlement of lapsed policies. The relative 
 value and equity of these options in any particular case 
 cannot be determined by one who has no knowledge of the 
 elementary principles of life insurance. The man who 
 decided to patronize one company rather than another be- 
 cause the surrender values of the former were based upon 
 " the reserve with ^ per cent interest," while those of the 
 latter were based upon " the reserve with 4 per cent inter- 
 est," made a mistake due to his ignorant belief that the 4^ 
 per cent reserve was the larger. 
 
 p'or information in regard to surrender values actually 
 
 i 
 
The A B C of Life Insurance, 5 1 
 
 allowed, the reader is referred to the published literature of 
 the companies. .« 
 
 The most elaborate statutory provisions are contained in 
 the so-called "Non-forfeiture Law" of Massachusetts. 
 This, with its accompanying tables, constitutes quite a for- 
 midable document. At the present time the law is under 
 criticism by the Massachusetts companies, the Insurance 
 Commissioner of that State and the majority of American 
 actuaries for the alleged reason that it is based upon an 
 erroneous and inequitable theory of surrender values. 
 
52 The A B C of Life Insurance, 
 
 CHAPTER VIII. 
 
 FLANS OF INSURANCE, 
 
 The words " insurance " and *' policy " are often usee 
 interchangeably, thus : " An insurance of five thousanc] 
 dollars," or " A policy of five thousand dollars." 
 
 Life Policies. • 
 
 A policy payable only upon the death of the insured is 
 known as a life policy. When the premiums are paid an- 
 nually (or in semi-annual or quarterly installments) during ; 
 the lifetime of the insured, the policy is called an ordinary, 
 whole-life policy. 
 
 When the payments are to be completed in a given num- 
 ber of years, the term limited-payment life policy is used. 
 Or, the exact term is mentioned, as " ten-payment Hfe," 
 ^* fifteen-payment life," etc. The payment of a single pre- 
 mium constitutes a single-payment life policy. Of course, \ 
 all limited-payment premiums are higher than ordinary pre- ■ 
 miums, since the equivalent of payments during a lifetime 
 must be contained in the limited number of payments made. \ 
 Consequently, the reserve or self-insurance element is also 
 larger. 
 
 On all limited payment policies it is customary to give 
 paid-up insurance for as many proportionate parts of the 
 original amount as there have been premiums paid. Thus 4 
 premiums paid on a ten-payment life policy of $1000 would 
 secure paid-up insurance of $400 payable at death ; 7 pre^ 
 miums paid on a len-payment endowment of $1000 at 6c 
 would secure a paid-up endowment of $700 payable at 60. 
 
I UNIVERSITY ) 
 The A B C of Lg%Jns^r,^nf^^^ 53 
 
 Joint-life policies are contingent upon two lives (some- 
 times more than two), both of which are insured under one 
 policy, the insurance being payable to !he survivor upon the 
 death of either. The premium is higher than that upon a 
 single life, but is not equal to the sum of the full premiums 
 on both lives. Policies of this form are not in favor with 
 American companies at the present time. Very intricate 
 calculations are involved in the computation of joint-life 
 premium rates. 
 
 Term insurance is insurance covering a specified term. 
 This provides for payment on account of such deaths only 
 as occur during the term. The example on page 23 is an 
 illustration of a five-year, term insurance. As will be seen 
 by examination, out of 78,106 persons living at age 40, 
 only 3933 will die during the succeeding five years. If the 
 term of the insurance, then, is limited to five years, the pre- 
 mium need be only large enough to provide for 3933 deaths, 
 while a whole-life insurance would require provision for 
 78,106 deaths. The term premium is consequently lower. 
 When the policy provides for insurance for a specified term, 
 with the privilege of renewing the insurance at the end of 
 that term for another similar term, upon payment of a pre- 
 mium adjusted to the cost of each successive term, it is 
 called a renewable term policv. The length of the term is 
 indicated by such nomenclature as "yearly renewable term,'* 
 or " ten-year renewable term." 
 
 Annuities. 
 These policies provide for the payment of a certain 
 yearly sum to the insured, or to the beneficiary named in 
 the policy, during the life-time of the annuitant The 
 premium may be paid in one payment, or in annual pay- 
 ments for a given number of years. Its amount depends 
 
54 -^^ A B C of Life Insurance, 
 
 upon the relative ages of the insured and the annuitant. 
 Thus if A, being 25 years old, insures his life for the bene- 
 fit of his mother, 60 years old, with the understanding that 
 the insurance is to be an annuity, payable, in the event of 
 his death, during the remainder of his mother's life, the 
 premium would be very small. For the probability is chat 
 A will survive his mother — in which case the company 
 would have to pay nothing — or, in any event, that he will 
 pay a considerable number of premiums to the company, 
 while his mother will not live many years after his death 
 to receive her annuity. On the contrary, if B, the insured, 
 were an old man, and his daughter, the beneficiary, were 
 young, the chance would be that B would pay comparatively 
 few premiums, while the daughter would survive him many 
 years to receive her annual stipend. In such a case, the 
 premium would be very high. Annuities, while quite pop- 
 ular in Europe, are Httle sought after in this country. 
 Endowments. 
 A pure endowment, as has already been explained, is an 
 agreement to pay a certain sum of money when the insured 
 shall have reached a certain age, but nothing if he shall die 
 before reaching that age. Although a few policies of this 
 description have • been issued in this country, this form, 
 unmodified, is almost never used, but there is added to it 
 an agreement to pay the sum insured if the person insured 
 shall die before reaching the specified age. Thus, an endow- 
 ment assurance of $1000 at 60 means that the company 
 will pay $1000 if the insured reaches the age of 60, or upon 
 his death at any time before that. The premium, therefore, 
 must be the sum of two premiums, one covering the insur- 
 ance for the term, and the other providing for the endow- 
 ment at the end of the term. This has been fully ex- 
 plained and illustrated in Chapter III. 
 
The A B C of Life Insurance. 55 
 
 Endowments are sometimes classified by the age which 
 the insured must attain in order to receive the amount of 
 the poHcy; thus, an "endowment at 60," an ** endowment 
 at 70." They are more commonly classified by the term 
 covered. Thus, an endowment on a hfe, age 40, payable 
 ^t age 55, would be called a *' 15 -year endowment." If 
 a premium was to be paid each year during this term, the 
 policy would be called an " ordinary 15-year endowment/' 
 If, however, the premiums were to be paid in 10 years, the 
 policy would be called a ^^ten-payment, 15-year endow- 
 ment." 
 
 The rate of premium depends upon the age of the in- 
 sured, the length of the endowment term and the number 
 of payments. 
 
 Return-premium Policies, Instalment Policies, 
 Bonds, Etc., Etc. 
 
 The preceding policies, three only in number, include just 
 about everything, in principle^ which is possible in life insur- 
 ance. And since annuities are so little in vogue in this 
 country, it is within the truth to say that the life policy and 
 the endowment are the principal part of the seventy- five or 
 more differently named policies which are to-day offered to 
 the public. To describe any considerable number of these 
 would not be worth the space which it would require. We 
 mention two or three. 
 
 Some policies, either life or endowment, stipulate that 
 upon the death of the insured, within a specified number of 
 years, the amount of the premiums paid by him shall be 
 returned in addition to the amount named in the policy. 
 Other policies guarantee the payment of the amount of the 
 insurance with 6 per cent interest thereon. Of course, in 
 either case and in all similar cases, the addition to the 
 
56 The A B C of Life Insurance. 
 
 amount named in the policy is just so much additional 
 insurance, and an additional premium must be, and always 
 is, charged therefor. 
 
 The instalment principle has been widely applied to both 
 life and endowment policies. Thus the contract of a whole- 
 life insurance may stipulate that, whenever the policy 
 matures as a death claim, the amount of the insurance shall 
 be paid in a specified number of equal annual instalments. 
 The premium for this would be less than for the same form 
 and amount of insurance payable in one sum at the death 
 of the insured, for the very obvious reason that the risk is 
 not at any time the full aggregate amount of the instalments, 
 but only the present value of those instalments. Thus if a 
 policy which nominally insures for ^20,000 stipulates that 
 that amount shall be paid in twenty equal annual instal- 
 ments, the measure of the risk actually assumed by the com- 
 pany under that policy is the present value of twenty instal- 
 ments of ^1000 each, the first payable at once, the second 
 at the end of one year, the third at the end of two years, 
 and so on, the last one being payable at the end of nineteen 
 years. From the table of present values, page 76, we find 
 this to be $14,138, or a little more than seven- tenths of the 
 nominal insurance. 
 
 The foregoing will serve as examples. A most admirable 
 ingenuity has been displayed in the numerous combinations 
 of life and endowment insurance with the return of all pre- 
 miums, or a portion of them, with the payment of interest, 
 at different rates and for longer or shorter terms, and with 
 the payment of the principal sum insured in instalments 
 covering any number of years desired, and themselves of 
 uniform or varying amounts. In the keen competition for 
 business almost every possible wish or necessity of the in- 
 suring public has been met by one or another of the com- 
 
The A B C of Life Insurance. 57 
 
 panics. The nomenclature by which these different forms 
 are known is equally ingenious and sometimes decidedly 
 picturesque. "* 
 
 Tontines. 
 
 In 1648, Lorenzi Tonti organized a fund in Naples, the 
 conditions of which were as follows : Each subscriber paid 
 a certain sum of money into the fund. The total fund was 
 invested, and the interest on the amount of each subscrip- 
 tion was paid, during the lifetime of the subscriber, to such 
 person as he named. At the death of a subscriber his sub- 
 scription was forfeited to the fund, and the interest thereon 
 was divided among the subscribers, who, for this purpose, 
 were divided into classes according to age. At the death 
 of the last subscriber the entire capital subscribed reverted 
 to the crown. 
 
 It will be seen that this is the converse of life insurance, 
 since those who live longest receive the greatest benefits. 
 The principle of forfeiture on the part of those who die and 
 of accumulation for those who live is known as the " Ton- 
 tine " principle, and is perfectly illustrated in the pure en- 
 dowment, page 26. That application of this principle to 
 life and endov/ment insurance policies which has given to 
 such policies, as a cluss, the name *' Tontines," is as follows : 
 
 As has already been explained, a policyholder who has 
 paid premiums for several years and then given up his in- 
 surance, paying no further premiums, leaves in the hands 
 of the company the reserve credited to his policy, and also 
 any share in the surplus which might fairly be considered 
 his, but which has not been actually paid to him in the 
 form of dividends. Under the early Tontine practice the 
 entire amount of this reserve and of this surplus was credited 
 by the company to the other policies of the same form and 
 class. If any policy became a death claim the face of the 
 
58 The A B C of Life Insurance, 
 
 policy only was paid, and any accrued but undivided sur- 
 plus thereunder was credited in like manner. Finally, at 
 the end of a specified number of years, known as the Tontine 
 period, the gains from these sources were divided among the 
 policies of the same form and class which then remained in 
 force. 
 
 This practice has been modified so that in many cases 
 the Tontine principle is now applied, after the policy has 
 been in force three years, to surplus only, the retiring 
 policyholder receiving an equitable consideration in paid-up 
 insurance (see page 47) for his reserve. The Tontine 
 principle is applicable to any form of policy written upon 
 mutual or participating premiums. The methods of ap- 
 plication are quite numerous, and the policies are variously 
 designated as Semi-Tontine, Free Tontine, Five, Ten, Fif- 
 teen or Twenty-year Distribution policies, etc. The extent 
 to which the principle is applied can be determined only 
 from a knowledge of the terms and conditions of the policy 
 in each case. The different companies writing this kind of 
 policies furnish estimates of the probable results. 
 
The A B C of Life Insurance^ 59 
 
 CHAPTER IX. 
 
 CERTAIN CONDITIONS IN POLICY 
 CONTRACTS. 
 
 Payments of Premiums, — Premiums are always payable 
 at the home office of the company, but, for the convenience 
 of the policyholder, are allowed to be paid at some bank or 
 agency near him. Prompt payment of premiums is also re- 
 quired. In actual practice, this is often waived, although 
 there would seem to be no good reason why the insured 
 should not pay his premiums with the same promptness 
 which he expects and demands from the company in the 
 payment of its losses. 
 
 Residence and Occupation, — The conditions of policies in 
 regard to these matters are usually exceedingly liberal. ' 
 Residents in notoriously unhealthy localities, or persons en- 
 gaged in extra-hazardous occupations, would not be 
 insured by any company at the usual rates of premium. 
 Policies provide that, after being insured at the usual rate, 
 the policyholder shall not reside in such localities or engage 
 in such occupations without first obtaining the company's 
 consent and paying an extra premium therefore. The 
 written consent of the company is called a " permit." 
 
 Use of Stimulants and Narcotics, — Some policies provide 
 that the insured shall not indulge in the use of stimulants 
 or narcotics to such an extent as to impair his health or 
 shorten his life. 
 
 Suicide, — The practice of different companies differs as 
 to suicide. Some policies provide that death by suicide, 
 whether the insured be sane or insane, shall not constitute 
 
6o The A B C of Life Insurance, 
 
 a claim against the company. In others, death by suicide 
 from insanity is treated as the natural termination of the dis- 
 ease. In others, no reference is made to suicide. 
 
 Non- Forfeiture, — As already stated, every company now 
 allows some equitable return, in the way of paid-up or ex-^ 
 tended insurance, and most likely in cash, for the reserve 
 left in its hands by the lapse of a policy. Provision for this 
 is made by the terms of the poHcy, and consequently the; 
 reserve equity is not forfeited by failure to pay a stipulated 
 premium. 
 
 Incontestability. — Most policies provide that, subject to 
 the conditions of the policy in regard to residence, occu- 
 pation, and the payment of premiums, the insurance shall be 
 incontestable after a certain number of years (two or three). 
 The exact phraseology of this provision differs with dif- 
 ferent companies and policies. The general effect of the pro- 
 vision, however worded, is to waive, in case of claim against 
 the company after the specified term, all defenses of a merely • 
 technical nature, or such as might be based upon misstate- 
 ments in the application, made without fraudulent intent. 
 No company ought, perhaps, to waive its right to contest a 
 fraud, or to be estopped from making such defense if good 
 grounds for it exist. The sensible man will undoubtedly admit 
 that there is no more reason why attempted fraud upon an ; 
 insurance company should not be resisted, than there is for 
 non-resistance to any other form of fraud. Attempts of this 
 sort sometimes occur, and are either fought out in the courts 
 or settled by compromise as a matter of expediency. Resist- 
 ance to such claims is always creditable to a company, and 
 should have the support of agents and policyholders. On 
 the other hand, the fact that a company frequently resists 
 the payment of claims or forces compromises, may be ac- 
 cepted without hesitation as proof that something is wrong 
 in the management. 
 
The A B C of Life Insurance, 6i 
 
 In general, there are two things which should be said 
 in regard to the conditions of the later .^policy contracts. 
 
 No one can determine what are all the conditions of any 
 policy by an examination of the policy only. Every con- 
 tract of insurance consists of two parts, the request for the 
 insurance known as the '* application/' and the policy, and 
 these two are in legal effect one. Consequently any stipu- 
 lations or conditions recited in the application and consented 
 to by the applicant, as witnessed by his signature thereto, 
 are as much a part of the contract as they would be if 
 printed in the policy. The practice of the companies is not 
 uniform in this respect, and in one case the majority of the 
 conditions appear in the policy, while in another they are to 
 be found in the application. 
 
 The general tendency in late years has been toward 
 fewer conditions and restrictions, and greater liberality. 
 Certain rights and obligations of both parties have been 
 definitely established in practice and by legal decisions, 
 while others have been made matters of statutory pro- 
 vision. The supposed necessity for some restrictions has 
 not been demonstrated by experience to be a real necessity, 
 and in the case of some others where it cannot fairly be 
 said that experience has demonstrated anything, thus leav- 
 ing the matter in doubt, the companies have given their 
 patrons the benefit of the doubt. The life insurance 
 manager of fifty years ago, comparing a "latter day" 
 policy with one of his own lengthv, verbose and minutely 
 restricted contracts, would be more than likely to mistake 
 the former for a promissory note. 
 
62 2"he A B C of Life Insurance. 
 
 CHAPTER X. 
 
 APPLICATIONS; RISKS; MEDICAL 
 EXAMINERS. 
 
 When a person desires insurance, he makes application 
 therefor upon printed forms furnished by the company. It 
 is intended that this form, when properly filled out and 
 accompanied by the report of the Medical Examiner, shall 
 furnish the company with information which will enable it 
 to decide whether or not the applicant is a desirable risk. 
 His family history as to longevity, existence of hereditary 
 diseases, etc. ; his own personal history as to health or 
 disease, residence, occupation, etc.; his present residence 
 and occupation, and, last but not least, his present physical 
 condition, must all be taken into the account. 
 
 It is here that the Medical Examiner plays a most 
 important part. It is his duty to ascertain the present 
 physical condition of the applicant, and from the results of 
 his examination, together with the personal and family 
 history of the appHcant, to determine the probability of a 
 long or short life, and consequently to recommend or reject 
 the risk. No one performs a more important duty in 
 connection with the whole business of life insurance. If 
 Medical Examiners are incompetent or careless, the best 
 plans of insurance and the ablest management will end in 
 nothing but disaster. The fact that not one of the import- 
 ant failures of life insurance companies in this country has 
 
The A B C of Life Insurance, 63 
 
 been due primarily to excessive mortality, speaks volumes 
 for the skill and fidelity of the MedicaUExaminers. 
 
 It might appear, at first sight, that a rigid medical exam- 
 ination should result in a large saving to the companies by 
 securing for them an exceedingly row rate of mortality. It 
 is true that the rate is generally very low for a year or two 
 among newly selected risks, but the effect of the medical 
 selection disappears more rapidly than is usually supposed, 
 and but a comparatively short time elapses before the aver- 
 age normal rate is experienced. The very low cost of 
 insurance in assessment organizations, newly organized, is 
 due to the fact that the risks are newly selected, but it is 
 idle to expect that the cost can be kept down to that point 
 by the infusion of "new blood," or by any other process. 
 
 If impaired or doubtful risks were not summarily rejected, 
 the selection against the company, already alluded to, would 
 assert itself at the very outset. The better class of lives 
 would drop out, and the company would find itself over- 
 whelmed by the mortality among the poorer risks remaining. 
 
 Companies have been formed for the insurance of im- 
 paired lives at an adequate rate of premium. It has been 
 found very difficult to determine what premiums are ade- 
 quate, but some of the later experiments in this direction 
 are giving promise of a successful solution of the problem 
 of insuring "sub-standard" risks. 
 
 If sufficient space were available, it would be interesting 
 to note the variations between the standards which the dif- 
 ferent companies make in the matter of risks. Probably 
 it would be correct to say that, in a very general way, 
 all Medical Directors agree as to what constitutes a desir- 
 able, and what an undesirable, risk, but within the lines of 
 this general agreement there is plenty of disagreement on 
 minor points. 
 
64 The A B C of Life Insurance, 
 
 Beside its presentation of the applicant as a risk, the 
 application has another purpose which has already been 
 mentioned — it forms the basis of the insurance contract. 
 The applicant asks for the insurance, declares such and such 
 things to be true in regard to his age, place of birth, per- 
 sonal history, present residence, occupation, etc., and agrees 
 that the policy may be issued to him upon certain con- 
 ditions. In all of this he acts as agent for the bene- 
 ficiary named in the policy and for any and all other 
 persons who may in the future acquire any interest in the 
 insurance. It is not necessary to suggest that an applica- 
 tion should be prepared with care, and that the applicant 
 ought to acquaint himself with all its terms before signing it. 
 
 /* 
 
The A B C of Life Insurance, 65 
 
 CHAPTER XI. 
 ANNUAL STATEMENTS; RATIOS, 
 
 The laws of the different States require companies to file 
 annually statements of their transactions during the pre- 
 ceding year, and of their financial condition at the close of 
 the year. The forms prescribed by the Insurance Depart- 
 ments of the various States are very complete. The results 
 in detail are published in the annual reports of the Depart- 
 ments, and are frequently accompanied by tables of per- 
 centages and ratios. In determining the value of these, 
 some knowledge of the business of life insurance, and more 
 common sense, are necessary. For instance : 
 
 Percentage of expenses to income is not always a reliable 
 standard by which to judge economy of management. 
 Premiums may be very heavily loaded for certain forms of 
 insurance, and the current year's expenses may exhaust but 
 a small part of that loading. Or the investment part of the 
 premiums may be very large, and the premiums, con- 
 sequently, very high. The amount used for expenses 
 would, in either case, constitute but a comparatively small 
 percentage of the gross premiums. On the other hand, the 
 loading, or the investment part, or both, of premiums may 
 be very small, in which case, although expenses may be 
 kept within the loading, they may still constitute a com- 
 paratively large percentage of the premiums. Consequently 
 
66 The A B C of Life Insurance. 
 
 equal economy of management will not necessarily result in 
 the same, or even nearly the same, percentage of expense 
 to premium income. 
 
 The ratio of assets to liabilities is of little consequence 
 until both assets and liabilities have reached respectable 
 proportions. If A has but one dollar in the world, and 
 owes nothing, the ratio of his assets to his liabihties is 
 infinity. If B, however, is worth $200,000, and owes 
 $100,000, the ratio of his assets to his HabiHties is only two 
 to one. Of course, after a company has been in business 
 for a number of years and has placed a large amount oi 
 insurance on its books, the percentage of its assets to its 
 liabilities is a question of the highest importance. 
 
 The percentage of death losses to the mean amount in- 
 sured during the year affords the basis of a fairly close esti- 
 mate of a company's mortality experience. But an exact 
 determination of that experience cannot be made without a 
 knowledge of the ages of all the persons insured, and conse- 
 quently of the percentage of mortality expected by the com- 
 pany and provided for in the premium charges. 
 
 The percentage of interest {including rents and profits on 
 sales of stocks^ bonds and real estate) to mean amount of 
 assets, is important. If premiums are calculated and 
 reserves held upon a basis of 4 per cent, that rate, at least, 
 ought actually to be reaHzed. 
 
 The ratio of expenses to a^nount of new business secured 
 may be of much or little importance, depending entirely 
 upon the proportion of expense fairly chargeable to the 
 securing of new business, as well as upon the provision for 
 that expense made in the premiums charged. 
 
 The ratio of assets to amount of insurance in force 
 is of Uttle value, the main question always being whether 
 present accumulations, together with future premiums, 
 
^e 
 
 The A B C of Life Insurance, 
 
 67 
 
 'e sufficient to provide for future claims. If future pre 
 miums alone are sufficient, the question of present accumu- 
 lation is of less consequence. 
 
 And so on. Persons of a statistical turn of mind are 
 constantly furnishing tables of ratios and percentages, com- 
 parative tables, etc., etc. Most of the statistics thus compiled 
 are interesting, many of them are valuable, a few are vital. 
 Anyone well grounded in the elementary principles of life 
 insurance, and fairly familiar with the practical workings of 
 the business, can decide for himself to which class belong 
 such statistics as come under his observation. 
 
 "Expectation" Table. — Assured Lives. 
 
 (Constructed from the American Experience Table of Mortality.) 
 
 Age. 
 
 10 
 II 
 12, 
 
 13 
 14, 
 
 IS 
 16 
 17 
 18, 
 
 19 
 20 
 21 
 22. 
 
 23 
 24 
 
 25 
 
 26 
 27 
 28 
 
 29 
 30 
 31 
 32 
 33 
 34 
 35 
 36 
 
 Expecta- 
 tion, 
 Years. 
 
 48.7 
 48.1 
 
 47-4 
 46.8 
 46.2 
 455 
 44-9 
 44.2 
 
 43-5 
 42.9 
 42.2 
 
 41.5 
 40.9 
 40.2 
 39 5 
 38.8 
 38.1 
 37.4 
 367 
 36.0 
 
 35 3 
 34-6 
 33 9 
 332 
 325 
 31.8 
 311 
 
 Age. 
 
 37... 
 38--. 
 39--- 
 40... 
 41... 
 42... 
 
 43- •• 
 44... 
 
 45... 
 46... 
 47... 
 48... 
 49--- 
 50... 
 51... 
 52... 
 53... 
 54... 
 55... 
 56... 
 57... 
 58... 
 59-.. 
 60... 
 61;.. 
 62... 
 63... 
 
 Expecta- 
 tion, 
 Years. 
 
 304 
 29 6 
 28.9 
 28 2 
 
 27.5 
 26.7 
 26.0 
 25.3 
 245 
 23.8 
 23.1 
 22.4 
 21.6 
 20.9 
 20.2 
 
 19.'; 
 18.8 
 18.1 
 17.4 
 16.7 
 16. 1 
 
 154 
 14.7 
 14. 1 
 
 135 
 12.9 
 12.3 
 
 Age. 
 
 64 
 
 65 
 66 
 67 
 68 
 69 
 70 
 
 71 
 72, 
 
 73 
 
 74 
 75 
 76 
 
 77 
 78 
 
 80 
 81 
 82 
 83 
 84 
 85 
 86, 
 
 87 
 88 
 
 89 
 90 
 
 Expecta- 
 tion, 
 Years. 
 
 2 5 
 
 2 2 
 
 1.9 
 
 1-7 
 1.4 
 
68 The A B C of Life Insurance. 
 
 American Experience Table of Mortality. 
 
 c 
 
 bXI 
 
 u 
 
 G O 
 
 B 
 
 0,; 
 
 
 .^^ 
 
 H 
 
 .2 h-^ bo 
 
 ^1 
 
 o.S 
 
 r 
 
 
 ^ W) 
 
 
 
 Ho^ 
 
 M 
 
 ;z; 
 
 5-PQ 
 
 ICO.OCO 
 
 749 
 
 .007490 
 
 99.251 
 
 746 
 
 007516 
 
 98.505 
 
 743 
 
 •037543 
 
 97,762 
 
 740 
 
 .007569 
 
 97,022 
 
 737 
 
 .007596 
 
 96,285 
 
 735 
 
 .007634 
 
 95.550 
 
 732 
 
 .007661 
 
 94,818 
 
 729 
 
 .007688 
 
 94.089 
 
 727 
 
 .007727 
 
 93,362 
 
 725 
 
 .007765 
 
 92,637 
 
 723 
 
 .007805 
 
 91,914 
 
 722 
 
 .007855 
 
 91.192 
 
 721 
 
 .007906 
 
 90471 
 
 720 
 
 •007958 
 
 89.751 
 
 719 
 
 .008011 
 
 89 032 
 
 718 
 
 .008065 
 
 88314 
 
 718 
 
 .0 8130 
 
 87596 
 
 718 
 
 .008197 
 
 86,878 
 
 718 
 
 .008264 
 
 86,160 
 
 719 
 
 .008345 
 
 85,441 
 
 720 
 
 .0 8427 
 
 84.721 
 
 721 
 
 .008510 
 
 84.000 
 
 723 
 
 .008607 
 
 83.277 
 
 726 
 
 .008718 
 
 82.551 
 
 729 
 
 .008831 
 
 81,822 
 
 732 
 
 .008946 
 
 81,090 
 
 737 
 
 .009089 
 
 80.353 
 
 742 
 
 .OC9234 
 
 79.611 
 
 749 
 
 .009408 
 
 78,862 
 
 756 
 
 .009586 
 
 78 106 
 
 765 
 
 .009794 
 
 77.341 
 
 774 
 
 .010008 
 
 76.567 
 
 785 
 
 .010252 
 
 75.782 
 
 797 
 
 .010517 
 
 74.985 
 
 812 
 
 .010829 
 
 74.173 
 
 828 
 
 .011163 
 
 73.345 
 
 848 
 
 .011562 
 
 72497 
 
 870 
 
 .012000 
 
 71,627 
 
 896 
 
 .012509 
 
 70,731 
 
 927 
 
 .013106 
 
 69,804 
 
 962 
 
 .013781 
 
 68,842 
 
 1,001 
 
 .014541 
 
 67,841 
 
 1,044 
 
 .015389 
 
 Age. 
 
 53 
 54 
 55. 
 56^ 
 57- 
 58. 
 59- 
 60, 
 61. 
 62. 
 
 63. 
 64, 
 
 65 
 66, 
 
 67. 
 68. 
 69. 
 70 
 71 
 72 
 
 73 ■ 
 74 
 75 
 76 
 77 
 78 
 79 
 80 
 81 
 82. 
 83 
 84 
 85 
 86 
 
 87 
 88 
 
 89 
 90 
 91 
 92 
 93 
 94 
 95 
 
 l4 
 
 hfl 
 
 ^ * 
 
 C 
 
 l> 
 
 
 c 
 
 ^u 
 
 .t wi 
 
 ^f> 
 
 hJ.S 
 
 •>•> 
 
 a 
 
 Pi 
 
 ^•^ 
 
 
 
 PQ 
 
 ^ 
 
 66.797 
 
 i,c9i 
 
 65.706 
 
 1. 143 
 
 64563 
 
 1,199 
 
 63.364 
 
 1,260 
 
 62,104 
 
 1325 
 
 60.779 
 
 1.394 
 
 59.385 
 
 1,468 
 
 57,917 
 
 1,546 
 
 56.371 
 
 1,628 
 
 54.743 
 
 1. 713 
 
 53.030 
 
 1.800 
 
 51.230 
 
 1,889 
 
 49341 
 
 1,980 
 
 47.361 
 
 2,070 
 
 45.291 
 
 2,158 
 
 43.133 
 
 2243 
 
 40,8qO 
 
 2 321 
 
 38,569 
 
 2,391 
 
 36,178 
 
 2,448 
 
 33.730 
 
 2,487 
 
 3^243 
 
 2505 
 
 28,738 
 
 2.501 
 
 C6237 
 
 2,476 
 
 23,761 
 
 2431 
 
 21,330 
 
 2369 
 
 i8,q6i 
 
 2 291 
 
 16,670 
 
 2,196 
 
 14.474 
 
 2,091 
 
 12,383 
 
 1,964 
 
 10,419 
 
 I 816 
 
 8603 
 
 1,648 
 
 6.955 
 
 1,470 
 
 5,485 
 
 1,292 
 
 4,193 
 
 1,114 
 
 3.079 
 
 933 
 
 2,146 
 
 744 
 
 1,402 
 
 555 
 
 847 
 
 385 
 
 462 
 
 246 
 
 216 
 
 137 
 
 79 
 
 58 
 
 21 
 
 18 
 
 3 
 
 3 
 
The A B C of Life Insurance, 
 
 69 
 
 Net Premiums for a Whole- Life Insurance of $1000. 
 
 Based upon the American Experience Table of Mortality, with 4 per ceilt interest. 
 
 Age. 
 
 20 
 21 
 22 
 
 23 
 24 
 
 25 
 26 
 
 27 
 28 
 
 29 
 30 
 31 
 32 
 33 
 34 
 
 ^i 
 
 36. 
 
 38 
 39 
 40 
 41, 
 42 
 43 
 44. 
 
 45' 
 46 
 
 47 
 48, 
 
 49 
 SO. 
 51 
 
 52. 
 S3 
 S4. 
 
 56. 
 57 
 58 
 59 
 60 
 61 
 62 
 
 64 
 65 
 
 Single Pre- 
 miums 
 which are 
 also Net 
 Reserves 
 on Paid-up 
 Policies, 
 
 $247.77 
 251-85 
 256.08 
 260.47 
 265.04 
 269.79 
 27474 
 279.87 
 285 21 
 29075 
 296.51 
 302 50 
 308 71 
 315 17 
 321.86 
 328.81 
 33602 
 34850 
 35124 
 359-27 
 367-57 
 376.17 
 385.06 
 394-25 
 403-75 
 41355 
 423 66 
 434.06 
 444.76 
 
 455-74 
 466.99 
 47848 
 490.21 
 502.15 
 514.31 
 526.65 
 
 539.15 
 551 81 
 564.59 
 577.48 
 590.46 
 
 603.49 
 616.56 
 629.63 
 642.69 
 655.70 
 
 Annual 
 
 Premiums 
 
 During 
 
 Life. 
 
 $12 67 
 
 ^2.95 
 13.24 
 
 13-54 
 13-87 
 14.21 
 
 14.57 
 14-95 
 15-35 
 1577 
 
 16 21 
 f6.68 
 
 17 18 
 17.70 
 18.25 
 18.84 
 19.46 
 20.12 
 20 82 
 
 21.57 
 22.35 
 23.19 
 24 08 
 2503 
 26.04 
 27.12 
 28 27 
 29.50 
 30. 8 E 
 32.21 
 3370 
 3529 
 36.98 
 
 3879 
 40.73 
 42.79 
 45.00 
 
 47-35 
 49.87 
 
 5257 
 55-45 
 58.54 
 6t 84 
 
 65 39 
 69 18 
 7325 
 
 Annual 
 
 Premiums 
 
 for 
 
 Twenty 
 
 Years. 
 
 $18.73 
 19.05 
 19-38 
 19.72 
 20.08 
 20.46 
 20.85 
 21.26 
 21.68 
 22.13 
 
 22.59 
 23.08 
 
 23.59 
 24.12 
 
 24-67 
 25.26 
 2587 
 26.51 
 27.18 
 27.88 
 28.68 
 29.41 
 30.24 
 31 II 
 32.03 
 33.00 
 3404 
 35.14 
 3630 
 37.55 
 38.86 
 4027 
 41.76 
 43.36 
 4506 
 46.88 
 48.84 
 50.93 
 53-17 
 55-59 
 58.18 
 60.98 
 
 63-99 
 67.24 
 
 7075 
 74 54 
 
 Annual 
 
 Premiums 
 
 for 
 
 Fifteen 
 
 Years. 
 
 SP22.53 
 22.91 
 23.30 
 23.71 
 24.14 
 24.58 
 25.05 
 25-53 
 26.03 
 26.56 
 27.10 
 27.67 
 28 27 
 28.89 
 
 29-53 
 30.20 
 30.91 
 3164 
 32-41 
 33-21 
 34.05 
 34-93 
 35-85 
 36.82 
 
 37.83 
 38.90 
 40.02 
 41.21 
 42.45 
 43.76 
 45 14 
 46.60 
 
 48-13 
 49.76 
 
 51.47 
 53-29 
 55.21 
 57.26 
 
 59-44 
 61.76 
 64.25 
 66.90 
 
 69.74 
 72.79 
 76.07 
 7959 
 
70 
 
 The A B C of Life Insurance. 
 
 Annual Premiums— Analysis of First Year's Premium, 
 Different Ages, $icxx) Whole-Life Insurance. 
 Participating Rate. 
 
 AGE. 
 
 Net Premiums, American Ex- 
 perience Table of Mortality, 
 with 4 Per Cent Interest. 
 
 Portion 
 for Death 
 Claims. 
 
 $7-71 
 7.76 
 7.Z2, 
 7.88 
 7.96 
 803 
 8.11 
 8.20 
 830 
 8.40 
 8.51 
 8.64 
 
 877 
 8-93 
 
 9 TO 
 
 9.29 
 9.49 
 9.71 
 
 9-95 
 10.24 
 
 10.5s 
 10 92 
 11.32 
 
 11.79 
 12.34 
 12.97 
 13.67 
 1445 
 15.33 
 16 30 
 
 17-38 
 18.60 
 
 1993 
 21.40 
 23.10 
 24.85 
 
 Portion 
 
 for 
 Reserve. 
 
 $650 
 6.81 
 7- 13 
 7-47 
 7.8r 
 8.18 
 
 8.57 
 8.98 
 9.40 
 986 
 
 IO-33 
 10.82 
 
 11-35 
 11.89 
 12.47 
 1306 
 13.70 
 1437 
 15.08 
 15.80 
 16.57 
 17.35 
 18.18 
 19 02 
 1987 
 2073 
 21.62 
 
 22.53 
 23.46 
 
 24-43 
 25.41 
 26.40 
 27.42 
 28.67 
 
 2953 
 30.60 
 
 Total 
 
 Net 
 Premiums 
 
 $14.21 
 1457 
 149s 
 15-35 
 1577 
 
 16 21 
 16.68 
 
 17 18 
 17.70 
 18.25 
 18.84 
 19.46 
 20.12 
 20.82 
 21.57 
 22.35 
 23.19 
 24 08 
 2503 
 26.04 
 27.12 
 28.27 
 2950 
 30.81 
 32.21 
 3370 
 3529 
 36.98 
 3879 
 40.73 
 42.79 
 4500 
 
 47.3s 
 49.87 
 
 52.57 
 55-45 
 
 Loading. 
 
 $5-63 
 583 
 5.98 
 6.13 
 6.30 
 649 
 6.67 
 6.87 
 7.08 
 7-30 
 7-54 
 7 79 
 8.05 
 
 8.33 
 
 8.62 
 
 8.9s 
 
 9.28 
 
 9.64 
 
 10.02 
 
 10.42 
 
 10.85 
 
 IT. 31 
 11.80 
 12.32 
 
 12 88 
 1348 
 
 14 IT 
 14.80 
 15.52 
 16.29 
 17 12 
 18.00 
 18.94 
 
 1995 
 21.03 
 22.18 
 
 See Explanatory Notes on Page 77. 
 
The A B C of Life Insurance. 
 
 71 
 
 ^^K Actuaries' or Combined Experience Table 
 
 ^^ OF MORTALfTY. 
 
 The following table was prepared by a committee of 
 eminent actuaries on the data afforded by the combined 
 experience of seventeen of the principal life insurance offices 
 in England. It was deduced from 62,537 assurances. Some 
 of the objections advanced against it are that certain lives 
 have been more than once assured, have appeared twice or 
 oftener as elements of the calculation, and that the data for 
 the older ages were insufficient. The average duration of all 
 the policies was a little less than eight and a half years. The 
 later Actuaries' or H. M. (healthy males) Table is now more 
 generally used in England. The American Experience Table 
 furnishes a better standard than either for American lives. 
 
 Age. 
 
 
 |i 
 
 3 
 
 Ratio of Deaths 
 
 During the Year to 
 
 Number Living at the 
 
 Beginning of the Year. 
 
 Age. 
 
 :>o 
 
 ►J bJO 
 
 is 
 
 I 
 
 3 
 
 3 
 
 10 
 
 IT 
 
 12 
 
 13 
 
 14 
 
 15 
 
 16 
 
 17 
 
 18 
 
 19 
 
 20 
 
 21 
 
 22 
 
 23 
 
 24 
 
 100,000 
 
 99.324 
 98,650 
 97.978 
 97.307 
 
 96,636 
 95.965 
 95.293 
 94,620 
 
 93.945 
 
 93.268 
 92,588 
 
 91.905 
 91,219 
 90,529 
 
 676 
 
 674 
 672 
 671 
 671 
 
 671 
 672 
 673 
 675 
 677 
 
 680 
 683 
 
 686 
 
 S^ 
 694 
 
 .006760 
 
 .006786 
 .006812 
 .006848 
 .C06896 
 
 .006944 
 .007003 
 .007062 
 .007134 
 .007206 
 
 .007291 
 .007377 
 .007464 
 .007564 
 .007666 
 
 25 
 
 26 
 
 27 
 
 28 
 
 29 
 
 30 
 
 31 
 
 32 
 
 33 
 
 34 
 
 p::::::: 
 P::::::: 
 
 39 
 
 89.835 
 89.137 
 
 ^7,726 
 87,012 
 
 86,292 
 85.565 
 84.831 
 84,089 
 
 83.339 
 
 82,581 
 81,814 
 81,038 
 80.253 
 79.458 
 
 698 
 
 703 
 708 
 
 714 
 720 
 
 72.7 
 
 734 
 742 
 750 
 758 
 
 767 
 776 
 785 
 
 
 Q S ** 
 
 fi3^ 
 
 .007770 
 .007887 
 .008006 
 .008139 
 .008275 
 
 .008425 
 .008578 
 .C08747 
 .008919 
 .009095 
 
 .009288 
 .009485 
 .009687 
 .009906 
 .010131 
 
72 
 
 The A B C of Life Insurance, 
 
 Actuaries' or Combined Experience Table 
 OF Mortality. 
 
 {Continued front preceding ^age^ 
 
 •r 5 ^ 
 
 1) 4) « 
 
 5 « 
 
 78,653 
 77.838 
 77,012 
 76.173 
 75.316 
 
 74.435 
 73.526 
 72,582 
 71,601 
 70.580 
 
 69.517 
 68,409 
 67.253 
 66,046 
 64,785 
 
 63,469 
 62,094 
 60658 
 59.161 
 57.600 
 
 55.973 
 
 54.275 
 52,505 
 50,661 
 
 48,744 
 
 46,754 
 44.693 
 42.565 
 40.374 
 38,128 
 
 ^2 
 
 815 
 826 
 
 839 
 857 
 881 
 
 909 
 
 944 
 
 981 
 
 1,021 
 
 1,063 
 
 1,108 
 1. 156 
 1,207 
 1,261 
 1,316 
 
 1.375 
 1.436 
 1.497 
 1,561 
 1,627 
 
 1,698 
 1,770 
 1,844 
 
 1.917 
 1,990 
 
 2,061 
 2,128 
 2,191 
 2,246 
 2,291 
 
 •5 rt rt*^ 
 
 .0 10362 
 .010612 
 .010894 
 .011251 
 .011697 
 
 .012212 
 .012839 
 
 .013517 
 
 .014260 
 .015061 
 
 •OI593Q 
 .0^6898 
 .017947 
 .019093 
 .020313 
 
 .021664 
 .023126 
 .024679 
 .026386 
 .028247 
 
 .030336 
 
 .032612 
 .035120 
 .037840 
 .040826 
 
 .044082 
 .047614 
 
 .051474 
 .055630 
 
 .060087 
 
 70 
 
 71 
 72 
 
 73 
 74 
 
 75 
 1^ 
 77 
 78 
 79 
 
 80 
 8i 
 82 
 83 
 84 
 
 85 
 
 86 
 
 87 
 88 
 
 89 
 
 90 
 
 9C 
 92 
 
 93 
 94 
 
 96 
 97 
 98 
 99 
 
 4> U 
 
 
 ,£i OS 
 
 i!< 
 
 
 
 t> 
 
 «.• 
 
 ^^ 
 
 ^2 
 
 
 'l> 
 
 
 
 1^ 
 
 %-i 
 
 9 
 
 ^^ 
 
 55 
 
 35.837 
 
 2.327 
 
 33.510 
 
 2,351 
 
 31.159 
 
 2,362 
 
 28,797 
 
 2.358 
 
 20,439 
 
 2.339 
 
 24,100 
 
 2,303 
 
 21,797 
 
 2,249 
 
 19.548 
 
 2,179 
 
 17.369 
 
 2,092 
 
 ^S^277 
 
 1,987 
 
 13.290 
 
 1,866 
 
 11,424 
 
 1.730 
 
 9.^94 
 
 1,582 
 
 8,112 
 
 1.427 
 
 6,685 
 
 1,268 
 
 5.417 
 
 1,111 
 
 4.306 
 
 958 
 
 3.348 
 
 81E 
 
 2,537 
 
 673 
 
 1,864 
 
 545 
 
 1.3^9 
 
 427 
 
 892 
 
 322 
 
 570 
 
 231 
 
 339 
 
 155 
 
 184 
 
 95 
 
 89 
 
 52 
 
 37 
 
 24 
 
 13 
 
 9 
 
 4 
 
 3 
 
 I 
 
 I 
 
The A B C of Life Insurance, 
 
 73 
 
 Net Premiums for a Whole-Life Insurance of $1000. 
 
 Based upon the Combined Experience Table of Mortality, with 4 percent interest. 
 
 20 
 21 
 22 
 
 23 
 24 
 25 
 26 
 27 
 28 
 29 
 30 
 31 
 32 
 
 33 
 34 
 35 
 36. 
 
 37 
 38. 
 39 
 40. 
 41. 
 42. 
 
 43- 
 44. 
 
 45- 
 46. 
 
 48. 
 49. 
 50- 
 51- 
 52. 
 53- 
 54. 
 55. 
 56. 
 57. 
 58. 
 59. 
 60. 
 61. 
 62. 
 63. 
 64, 
 65. 
 
 $251.88 
 256.57 
 261.38 
 266.34 
 271.49 
 276.80 
 282.29 
 287.98 
 293.84 
 299.91 
 306.14 
 312.61 
 
 319-31 
 326.15 
 33327 
 340.61 
 348.16 
 356.00 
 364.08 
 372.42 
 381.04 
 38996 
 399- 18 
 408.69 
 418.49 
 
 42857 
 438.84 
 
 449-34 
 460.04 
 470.88 
 481.92 
 493" 
 504.46 
 515-97 
 527-59 
 539-32 
 551-15 
 563-12 
 
 57515 
 587.27 
 599-43 
 611.62 
 62385 
 636 00 
 648.11 
 660.19 
 
 $12.95 
 
 ' 13.27 
 
 13.61 
 
 13.96 
 
 M-33 
 14.72 
 
 15 13 
 
 1556 
 
 16. OT 
 16.48 
 16.97 
 
 1749 
 18.04 
 18.62 
 19.23 
 19.87 
 20.54 
 21.26 
 22 02 
 22.82 
 23.68 
 2459 
 
 25-55 
 26.58 
 27.68 
 28.85 
 30.08 
 31-39 
 32.77 
 3423 
 35-78 
 37.42 
 39-15 
 41.00 
 
 42.95 
 4503 
 47-23 
 4957 
 5207 
 5472 
 5756 
 60.57 
 6378 
 67.20 
 70.84 
 74.72 
 
 Annual 
 
 Annual 
 
 Premiums 
 
 Premiums 
 
 for 
 
 , for 
 
 Twenty 
 
 Fifteen 
 
 Years. 
 
 Years. 
 
 $19.00 
 
 $22.86 
 
 ' 19-37 
 
 23.29 
 
 1976 
 
 23-75 
 
 20.15 
 
 24.22 
 
 20.57 
 
 2471 
 
 21.00 
 
 25 21 
 
 21.44 
 
 25-74 
 
 21.90 
 
 26.28 
 
 2238 
 
 26.84 
 
 22.88 
 
 27-43 
 
 23-39 
 
 28.03 
 
 2393 
 
 28.65 
 
 24.49 
 
 29.30 
 
 25.07 
 
 29-97 
 
 25.68 
 
 30.67 
 
 26.32 
 
 31.40 
 
 26.98 
 
 32.15 
 
 27.67 
 
 32.94 
 
 28.40 
 
 33-76 
 
 29.17 
 
 3462 
 
 29.98 
 
 35-53 
 
 30.83 
 
 3647 
 
 31-74 
 
 37-47 
 
 32.69 
 
 3852 
 
 3371 
 
 39-63 
 
 34-77 
 
 40.78 
 
 3590 
 
 41.99 
 
 37.08 
 
 ^53-25 
 
 38.32 
 
 44.57 
 
 39-63 
 
 45-95 
 
 41 02 
 
 47-38 
 
 42.48 
 
 48.89 
 
 4402 
 
 5046 
 
 45-66 
 
 52.12 
 
 47-39 
 
 53.86 
 
 4924 
 
 5569 
 
 51.20 
 
 57.63 
 
 5329 
 
 59.67 
 
 55 53 
 
 61.84 
 
 57-92 
 
 64.15 
 
 60.49 
 
 6660 
 
 63.24 
 
 69.21 
 
 66.18 
 
 71.99 
 
 69-33 
 
 74.96 
 
 72.71 
 
 78.12 
 
 7634 
 
 81.50 
 
74 
 
 The A B C of Life Insurance, 
 
 Ordinary, Continued-Payment, Whole-Life. 
 
 net value, or reserve of a premium-paying policy of 
 
 $1000, at the end of various years, actuaries* 
 
 table, 4 per cent 
 
 ist 
 Year. 
 
 7.60 
 7.91 
 8.24 
 8.58 
 8.93 
 
 9-31 
 970 
 
 lO.II 
 
 10.54 
 11.00 
 
 II 48 
 11.99 
 
 12.55 
 13 12 
 
 1374 
 
 14.41 
 15 12 
 15.85 
 1659 
 17.30 
 
 18.01 
 18.69 
 
 1939 
 20.10 
 20.86 
 
 21.62 
 22.39 
 23.19 
 24.00 
 24.85 
 
 25.72 
 26.61 
 27.56 
 28.52 
 29.50 
 3045 
 
 ad 
 Year. 
 
 15-45 
 16.09 
 
 1675 
 17.43 
 18.16 
 
 18.91 
 19.70 
 2054 
 21 42 
 22.35 
 
 23.33 
 24.39 
 2551 
 26.69 
 27.96 
 
 29.31 
 
 30.73 
 32.18 
 
 33-59 
 34.99 
 
 3636 
 37.71 
 39.10 
 
 40.54 
 42.02 
 
 43-52 
 4506 
 46.63 
 48.26 
 49.94 
 
 51.65 
 53.43 
 55-29 
 57.18 
 5905 
 60.90 
 
 3d 
 
 4th 
 
 5th 
 
 6th 
 
 7th 
 
 Year. 
 
 Year. 
 
 Year. 
 
 Year. 
 
 Year. 
 
 $ 
 
 $ 
 
 $ 
 
 $ 
 
 $ 
 
 2356 
 
 31.94 
 
 40.58 
 
 49-51 
 
 58.73 
 
 24.52 
 
 3324 
 
 42.24 
 
 51-52 
 
 61. II 
 
 2553 
 
 34.60 
 
 4396 
 
 53.62 
 
 6359 
 
 26.58 
 
 36.02 
 
 4576 
 
 5581 
 
 6620 
 
 27.68 
 
 37.50 
 
 47.64 
 
 58.12 
 
 68.93 
 
 28.83 
 
 3906 
 
 49.63 
 
 60.54 
 
 71.80 
 
 30.03 
 
 40.70 
 
 51 71 
 
 63.08 
 
 74.84 
 
 31.31 
 
 42-43 
 
 53.91 
 
 65.78 
 
 7804 
 
 32.65 
 
 44-25 
 
 56.25 
 
 68.63 
 
 81.43 
 
 34.07 
 
 46.20 
 
 58.71 
 
 71.65 
 
 85.03 
 
 35.59 
 
 48.25 
 
 61.34 
 
 74-86 
 
 88.84 
 
 37.19 
 
 50.43 
 
 64.11 
 
 78.26 
 
 92.87 
 
 38.90 
 
 52.75 
 
 67.08 
 
 81.87 
 
 97.09 
 
 40.72 
 
 55-22 
 
 70.20 
 
 85.62 
 
 101.43 
 
 4^.65 
 
 57.83 
 
 73.46 
 
 8948 
 
 105.88 
 
 44.70 
 
 60.55 
 
 76.79 
 
 93-42 
 
 110.36 
 
 46 81 
 
 6329 
 
 80.16 
 
 97-35 
 
 114.85 
 
 4891 
 
 66.04 
 
 83-49 
 
 101.26 
 
 119.32 
 
 5100 
 
 68.73 
 
 8678 
 
 105.13 
 
 123 80 
 
 53.02 
 
 71.38 
 
 90.04 
 
 109.02 
 
 128.28 
 
 55.04 
 
 7403 
 
 .93 34 
 
 11294 
 
 13280 
 
 57.05 
 
 76.72 
 
 96.67 
 
 116.90 
 
 137.38 
 
 59.14 
 
 79.47 
 
 100.09 
 
 120.95 
 
 142.05 
 
 6128 
 
 82.30 
 
 103-57 
 
 125.09 
 
 146.83 
 
 63.47 
 
 85.19 
 
 107.14 
 
 129.34 
 
 151-73 
 
 65.70 
 
 88.13 
 
 110.79 
 
 133.67 
 
 15672 
 
 67.98 
 
 91.14 
 
 114-53 
 
 138.09 
 
 161.84 
 
 70.33 
 
 94-24 
 
 118.34 
 
 142.64 
 
 167.09 
 
 72.74 
 
 97.42 
 
 122 29 
 
 147.32 
 
 172.47 
 
 75.22 
 
 100.70 
 
 12635 
 
 152.12 
 
 177-93 
 
 77.78 
 
 10408 
 
 130.51 
 
 156.98 
 
 183.46 
 
 80.42 
 
 107.55 
 
 134-72 
 
 161.90 
 
 189.01 
 
 83-15 
 
 III. 07 
 
 138-99 
 
 166.84 
 
 194-59 
 
 85.88 
 
 114 59 
 
 14323 
 
 171.76 
 
 200.14 
 
 88.60 
 
 118 08 
 
 147 46 
 
 176.66 
 
 20563 
 
 91.28 
 
 121 54 
 
 151-63 
 
 181.49 
 
 2ir.02 
 
 See Explanatory Notes on Page 77. 
 
The A B C of Life Insurance. 75 
 
 Ordinary, Continued-Payment, Whole-Life. 
 
 net value, or reserve of a ^remium-paying policy of 
 
 $1000, at the end of various years, actuaries' 
 
 table, 4 per cent. 
 
 ( Continued from preceding page. ) 
 
 gth 
 Year. 
 
 $ 
 7806 
 
 8452 
 87.99 
 91.64 
 
 95-48 
 
 99-53 
 103.82 
 108.36 
 11315 
 
 118. 16 
 
 12335 
 128.69 
 134.10 
 139.60 
 
 145-14 
 150.73 
 156.33 
 161.94 
 167.56 
 
 17324 
 179.12 
 184.90 
 190.90 
 197.06 
 
 203.34 
 209.76 
 216.27 
 222.86 
 229.51 
 
 236. 19 
 242.87 
 
 249-54 
 256.13 
 262 63 
 269.02 
 
 loth 
 Year. 
 
 $ 
 88.20 
 91.76 
 95-50 
 99-43 
 103.56 
 
 107.91 
 112.51 
 
 117-37 
 122.50 
 127.86 
 
 133-41 
 139-13 
 144.97 
 150 89 
 15689 
 
 162.97 
 169.09 
 175.22 
 181.37 
 187.54 
 
 193-79 
 2C0.13 
 206.59 
 213.19 
 21995 
 
 226.84 
 233.82 
 240.88 
 248.00 
 255.18 
 
 262.35 
 269.52 
 276.63 
 283.65 
 290.58 
 297.42 
 
 iSth 
 Year. 
 
 $ 
 144.12 
 149.99 
 156.17 
 162.65 
 169.41 
 
 176.42 
 
 183.65 
 191.06 
 198.65 
 206.39 
 
 214.30 
 222.36 
 
 230.54 
 238.83 
 247.22 
 
 255-70 
 264.25 
 272.83 
 281.47 
 290. 19 
 
 299.01 
 307.89 
 316.86 
 325-89 
 33498 
 
 344-07 
 353-18 
 362.24 
 37^-25 
 380.21 
 
 389.11 
 397.92 
 406.65 
 415.26 
 
 423-74 
 432.09 
 
 20th 
 Year. 
 
 $ 
 209.84 
 218.13 
 226.62 
 
 23531 
 244.20 
 
 25329 
 262.57 
 272,02 
 281.64 
 291.42 
 
 301-35 
 311.42 
 321.60 
 331 91 
 342.33 
 
 35284 
 363-37 
 37390 
 38439 
 394.86 
 
 40530 
 415-71 
 426.07 
 
 43637 
 446.62 
 
 45679 
 466.88 
 476.87 
 48676 
 496-55 
 
 506.21 
 
 515.79 
 525-16 
 534-43 
 543.52 
 552.49 
 
 25th 
 Year. 
 
 $ 
 283 60 
 29372 
 30403 
 314-51 
 325.18 
 
 336.02 
 347.02 
 358-17 
 36949 
 380.94 
 
 392.53 
 404.18 
 
 41589 
 427.60 
 
 439-31 
 
 450.97 
 462.54 
 
 47398 
 485-29 
 496.45 
 
 507-49 
 518.41 
 52923 
 53992 
 55049 
 
 560.91 
 571 20 
 581.36 
 591-36 
 601.20 
 
 610 89 
 620.47 
 630.03 
 639 68 
 649.52 
 659.75 
 
 ^oth 
 Year. 
 
 $ 
 362.97 
 374.60 
 386.39 
 398.34 
 410.44 
 
 422 68 
 434.90 
 447.38 
 459.80 
 472.23 
 
 484.64 
 497.00 
 50927 
 52142 
 533 44 
 
 545-32 
 55702 
 568.53 
 57985 
 59097 
 
 601 90 
 612 65 
 623.26 
 633.69 
 64393 
 
 654.00 
 663.94 
 673.82 
 68374 
 693-81 
 
 70415 
 714-83 
 72588 
 737.37 
 749.24 
 761.42 
 
 35th 
 iTear. 
 
 446. IT 
 458.86 
 471.67 
 48452 
 497.38 
 
 510.21 
 52301 
 
 535-72 
 548.34 
 560.83 
 
 57320 
 58542 
 597-47 
 609.34 
 621 01 
 
 63247 
 644.11 
 
 654-71 
 665.47 
 
 67599 
 
 686.30 
 696.43 
 706.46 
 716.50 
 726.61 
 
 73693 
 747-48 
 758.32 
 769.48 
 780.92 
 
 79251 
 804 24 
 815.99 
 827.41 
 838.15 
 847-87 
 
 See Explanatory Notes on Page 77. 
 
76 
 
 The A B C of Life Insurance. 
 
 Present Value of $i Due at End of Year in from 
 One to Forty Years from the Present Time. 
 
 No. OF Years. 
 
 3 
 
 4 
 
 c 
 
 6 
 
 7 
 8 
 
 9 
 
 lO 
 
 TI 
 12 
 13 
 
 14 
 15 
 i6 
 
 17 
 i8 
 
 19 
 
 20 
 
 21 
 22 
 23 
 24 
 25 
 26 
 
 27 
 
 28 
 29 
 
 30 
 
 31 
 32 
 
 33 
 34 
 35 
 36 
 37 
 38 
 39 
 40 
 
 Four Per 
 Cent. 
 
 ,961538 
 924556 
 888996 
 854804 
 821927 
 790315 
 759918 
 730690 
 702587 
 675564 
 
 649581 
 624597 
 600574 
 577475 
 555265 
 533908 
 513373 
 493628 
 474642 
 456387 
 
 438834 
 421955 
 405726 
 3901 2 I 
 
 3751 17 
 360689 
 
 346817 
 333477 
 320651 
 308319 
 
 296460 
 285058 
 274094 
 263552 
 
 253415 
 243669 
 234297 
 225285 
 216621 
 208289 
 
 Four and 
 One-Half 
 Per Cent. 
 
 956938 
 915730 
 876297 
 838561 
 802451 
 767896 
 734828 
 703185 
 672904 
 643928 
 
 616199 
 589664 
 564272 
 
 539973 
 516720 
 
 494469 
 473176 
 452800 
 433302 
 414643 
 
 396787 
 379701 
 363350 
 347703 
 332731 
 318402 
 304691 
 291571 
 279015 
 267000 
 
 255502 
 244500 
 
 233971 
 223896 
 214254 
 
 164525 
 196199 
 877501 
 179665 
 I 71929 
 
 Five Per 
 Cent. 
 
 952381 
 907029 
 863838 
 822702 
 783526 
 746215 
 710681 
 676839 
 644609 
 613913 
 
 584679 
 556837 
 530321 
 505068 
 481017 
 458112 
 436297 
 415521 
 395734 
 376889 
 
 358942 
 341850 
 325571 
 310068 
 
 295303 
 281241 
 
 267848 
 
 255094 
 242946 
 
 231377 
 
 220359 
 209866 
 199873 
 
 190355 
 181290 
 135282 
 164436 
 156605 
 149148 
 142046 
 
 Six Per 
 Cent. 
 
The A B C of Life Insurance. 77 
 
 EXP LAN A TOR*y NO TES. 
 
 Pages 74 and 75. — Reserves are calculated upon the basis qj net pre- , 
 miums. The amount of loading, added to the net premium to make the'^ 
 gross premium, does not aftect the reserve. Upon the same kind of a 
 policy, issued at the same age and with the same number of premiums 
 paid, the reserve would be the same, no matter what amount of annual 
 premium might be charged for the insurance. 
 
 Under premium-paying policies, the amount of the reserve depends 
 upon the age of the insured at the time the policy was issued, and 
 the number of premiums paid. Under paid-up insurance, the amount of 
 the reserve depends entirely upon the age of the insured at the date 
 for which the reserve is computed. 
 
 The reserves given are based upon the Actuaries' Table of Mortality, 
 with 4 per cent interest. See pages 33 and 34. For the sake of exactness 
 it should be said that, while these reserves are for the most part greater 
 than those based upon the American Experience Table, with 4^ per cent 
 interest, the latter are the greater at the very highest ages. The reason 
 for this is that according to the American Table the term of life ends with 
 age 95, while according to the Actuaries' it continues to age 100. 
 
 Page 73. — The net single premiums given are also the net values 
 or reserves of a paid-up pohcy of $1000 at the different ages. To esti- 
 mate pretty nearly the amount of paid-up insurance which a company 
 would allow for the surrender of an ordinary whole life policy with pre- 
 miums payable annually, ascertain the reserve on that policy according to 
 the table of reserves on pages 74 and 75, and divide 90 per cent of it by 
 the single premium given for the age actually attained by the policyholder 
 at the time of surrendering his original pohcy for paid-up insurance. 
 
 Page 70.— This table shows the component parts of both the net and the 
 gross (or office) premiums at different ages, for an insurance of $1000, 
 payable at death. This analysis, however, is correct for ihejftrst year of 
 the insurance at each age only. Each subsequent year the portion of the 
 premium used for death claims is greater, and the portion used for reserve 
 is smaller than these respective portions for the first year. The accumu- 
 lated reserve incre^ises each year by the addition of that year's reserve 
 portion of the premium and of interest, as is shown in table on page 36. 
 The "loading" remains the same theoretically for each year of the insur- 
 ance, although the amount actually collected by the company will vary 
 wirh the amount of dividend allowed on that account. 
 
WH/T IS THOUGHT OF THE/ B C OF LIFE INSURAp. 
 
 OPINIONS OF EXPERTS. 
 
 COL. J A COB L» GREENE, President Connecticut Mutual Life Insurance 
 Company y Hartford^ Conn. 
 *' I find it, as I expected from its authorship, to be a clear and concise statement 
 of the matters therein treated, and I should think that it would be useful for the 
 purpose which I presume it is intended to serve — the instruction of new agents. 
 It has the advantage of some other elementary works which I have seen, of much 
 greater brevity." 
 
 HON. JAMES G. BATTERSON^ President Travelers Insurance Company., 
 Hartford^ Conn. 
 " It is a very plain and intelligent statement of the case. I am glad that you 
 have kept out of the actuarial field. The various propositions stated arithmetic^ 
 ally can be easily comprehended. Clear away mysteries from life insurance and 
 the people will take it. You have done a good and useful work." 
 
 DAVID PARKS FACKLER, Consulting Actuary, New York. 
 
 *' I have endeavored to read through your little treatise with the attention due 
 
 to its compact and masterly style For the purpose it has in view it 
 
 seems to excel anything I have seen, and I hope it will have the wide circulation 
 it merits." 
 
 SHEPPARD HOMANS, Consulting Actuary, New York, 
 
 " The ' A B C ' is the modest title of a manual of life insurance which should 
 •be studied by every canvassing agent. It is not ©nly full of valuable information 
 relating to the fundamental principles of the business, couched in language free 
 from algebraic formulas, but it contains information concerning the practicdl 
 application of these principles which is of great value to the student," 
 
 OPINIONS OF PRACTICAL FIELD MEN. 
 
 SUDLOW &> MARSH, Indianapolis, Ind. 
 
 ** We have looked it over very carefully, and are very glad to say that we think 
 it will subserve a most desirable purpose in the education of agents. Further, the 
 tables contained therein are very simple, decidedly good, and will prove of great 
 assistance in soliciting business. It meets our hearty commendation." 
 
 R. L. DOUGLAS, Philadelphia, Pa, 
 
 *' It is an exceedingly instructive and enjoyable production. What a contrast 
 between to-day and twenty years ago ! Then, and even at a much later period, it 
 was generally supposed that the subject of life insurance was a mystery beyond 
 the reach of ordmary intellects. Mr. Elizur Wright and Mr. Sheppard Homans 
 punctured that illusion. This book of yours is another long stride in advance 
 You take the bed rock and build from it " 
 
The A B C of Life Insurance, 79 
 
 WHAT IS THOUGHT OF THE A B C OF LIFE INSDRANCE.-c.«/.««.rf. 
 
 HON. JOHN A. FINCH, the well-known insurance lawyer of Indianapolis, 
 in a recent lecture before the senior class of the Medical College of Indiana of the 
 University of Indianapolis, commended A B C OF LIFE INSURANCE as 
 follows: 
 
 If your interest should be general in the subject (of life insurance), so that you 
 wish to know something of the principle or principles which underlie the business 
 of life insurance, I know of no better work to recommend you to than a little book 
 called A B C OF LIFE INSURANCE, published by The Spectator Company, 
 New York. There is also a book by M. M. Dawson, entitled ELEMENTS OF 
 LIFE INSURANCE; also THREE SYSTEMS OF LIFE INSURANCE, 
 both by the same publishers, all of which you will find profitable. 
 
 Mr. Finch has also given the following endorsement of A B C OF LIFE 
 INSURANCE : 
 
 I believe I have in my office as nearly a complete set of books on the subject of 
 life insurance as can be collected, and I am free to say that I think there is more 
 meat in A B C OF LIFE INSURANCE than in any single book for the 
 beginner in the study of the principles of life insurance. I think the insurance 
 companies would do themselves and the public service if they would buy this 
 little book and give a copy to each student in the law schools of the country. I am, 
 perhaps, a little over hopeful, but I believe the popular impression of life insurance 
 as reflected in the decisions of the courts and the acts of our legislatures is very 
 largely attributable to ignorance ; and I believe this could be removed by proper 
 missionary work. 
 
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