Life Insurance, a contract whereby an insurer engages, for a consideration called a premium, to insure a person against a certain amount of pecuniary loss supposed to be consequent upon the decease of a certain life. The personal right of property is the chief spur to human industry, and thus lies at the foundation of civilized society. Yet the isolation which grows out of it results in such evils as to suggest communism as a remedy. Legitimate insurance is a borrowing of communism just enough to cure some of the worst evils of family isolation, without impairing the stimulus to personal exertion arising under it. In a general point of view the most important case of insurance is that which covers, for the benefit of a helpless family, the chief source of its sustenance, the life of its productive head. The history of life insurance shows, however, that an institution which has abundantly justified its existence is still in its infancy, struggling amid very unsettled methods. The doctrine of probabilities developed by Pascal and Iluygens, in regard to games of chance, was first applied by Jan De Witt of Holland, in 1671, to life contingencies, but only to determine the value of life annuities and reversions, with a view to aid the government in raising loans.

Its application to life insurance was not made till nearly 90 years later. Little more than a quarter of a century, however, passed away before the first distinct germs of modern life insurance, as a provision for widows and orphans, made their appearance in the London "Mercers' Widows' Fund" of 1698, the "Society of Assurance of Widows and Orphans " of 1700 in the same city, and the famous "Amicable Society for a Perpetual Assurance Office," also founded there in 1706, which continued in existence till 1867. The first two seem to have passed away without leaving any trace of their plan of operations; but we know that till a very recent period the "Amicable " placed no reliance upon the science of biological contingencies. It was purely mutual; each member, without regard to age, contributed to the common fund a fixed entrance fee, and also a fixed annual payment per share on from one to three shares. At the end of each year a portion of the fund was divided among the heirs of the deceased members in proportion to the shares held by each. Thus the amount insured depended on the number who died, subject to the vote of the members who survived as to the portion of the common fund which should be divided.

At first, for the sake of accumulating a fund, only a small dividend was voted; it was gradually enlarged from £30 to £90 a share. As the annual payment was £5 a share, this at best was very dear insurance, except for bad or old lives. There was no medical selection except so far as the members themselves exercised it in voting in new members. After some experience this was done with considerable caution and judgment; the age of admission was limited to 45, and there were restrictions in regard to dangerous occupations, travel, and military service. After a considerable fund had accumulated, the dividends became larger by reason of the smaller proportion of deaths and the greater liberality in voting the amount to be divided. From 1760 to 1780 it averaged about £174 a share, which would have been a fair amount supposing the members had all entered at the age of 40. It was not till this society had existed more than a century that anything like modern equitable and scientific life insurance was engrafted upon it.

Prof. De Morgan described it in 1838 as "founded rather on the principle of mutual benevolence than mutual insurance." It lived to a very respectable age by the wisdom of accumulating a considerable fund, and not promising a fixed amount of dividend or insurance, but died at last for want of science to graduate the payments according to the risks, and to exclude bad ones. - In 1760 Thomas Simpson, who 20 years earlier had published a valuable work on life contingencies, in connection with Mr. Dodson, another mathematician, applied for a charter of the "Society for Equitable Assurances,1' on the plan of graduating the premium to insure a prescribed amount according to the probabilities of living after the age of entry. But the crown refused a charter, on the ground that it would be unjust to existing companies which had paid large sums for their charters, and because it was an untried speculation depending " on the truth of certain calculations taken upon tables of life and death, whereby the chance of mortality is attempted to be reduced to a certain standard." Mr. Simpson died the next year, but in 1762 the famous "Equitable" was founded, without a charter, by a deed of settlement.

It does not seem to have achieved much success till it had called in the powerful aid of the Rev. Richard Price, the author of " Observations on Reversionary Payments " (1769). He gave the Equitable its Northampton table of premium rates, as well as some excellent advice about the necessity of not being led "to check or stop the increase of its stock too soon" through the encouragement arising from the possession of a large surplus, meaning by this the necessity of keeping an adequate premium reserve. By a fortunate error in the Northampton table, the premiums were so high that the " stock " or reserve increased rapidly, and so much real surplus over the necessary reserve accumulated, that the society began in 1791 to make additions to the policies, which, though small at first, were enlarged every ten years, till one who had entered in 1790, at the age of 30, for £100, in 1849, at the age of 89, was insured for £626, without any increase of the original annual premium, which was £2 13s. 4d. This large addition to the old policies is not so wonderful when we consider that Dr. Price had laid down the maxim that "the plan of a society ought always to be such as that the loss arising from discontinuance of payments should fall on the purchaser, and never on the society." Hence, as any discontinuing member forfeited his share of the society's stock or reserve, the persisting members had the more; and it must be remembered that £1 per annum at 5 Per cent. will amount in 59 years to £353, so that the premium paid would amount to £940. A fair reserve on the increased policy for £626 would be about £556. The Equitable, arising amid a large number of bubbles, which were pricked by Dr. Price, and adopting his principles and precautions, proved a great success.

But whoever reverts to the writings of Dr. Price in regard to the various schemes for the relief of widowhood and orphanage by insurance, and for provision for old age by annuities and endowments, will be struck with the fact that he looked almost exclusively at the security and permanence of the society, and very little at the contingencies of the individual. It does not seem to have occurred to him that provision both for his heirs and for the old age of the insured himself could be secured in the same policy, or that the cessation of the necessity for either provision could be provided for in the policy by a stipulation of terms of surrender. Dr. Price is justly regarded as the father of modern life insurance. What has since been done and what remains to be done are mere corollaries to his general propositions. By the writings of Dr. Price and the solid establishment of the Equitable a large number of ill-advised schemes, possessing the same objects and started about the same time, were swept away before they had done much mischief. But the great success of the Equitable some years later brought forth a new and numerous brood of imitators and rivals. A few of these became strong and healthy institutions, but their history for the most part is one of wreck and disaster.

The "Insurance Handbook," published in 1867 by Mr. Cornelius "Walford, a very able and painstaking writer on insurance, gives a list of the life insurance offices existing in the United Kingdom at that date, comprising 117, of which 3 were "proprietary," 26 "mutual," and 88 "mixed." It also gives a list of 240 companies which had gone out of existence, either by absorption in other companies or by dissolution in the court of chancery, during the previous 23 years. The wrecks within the present century up to this time would doubtless double that list. Of the 240 disappearances recorded by Mr. "Walford, 33 companies died in the year of their birth, 102 died under 5 years of age, 105 died over 5 years of age, 35 over 13 years, 9 over 30 years, and 4 over 50. The oldest had attained the age of 77 years. While half of these defunct corporations may probably be set down as mere abortions, injurious only to subscribers to the stock, and some of the others may have coalesced, or " amalgamated," to use the English term, with other companies, without injury to their policy holders, a considerable number must have perished by grossly incompetent or dishonest management.

Some of these failures doubtless arose from want of care in rejecting bad risks, but the prime cause must have been extravagant expenses of management - the failure to retain and accumulate at interest the excess of the net premiums received over the actual death claims; or, in other words, from regarding any such excess as " surplus." The mischief of these failures is beyond computation. The recent wrecks of the Albert and the European, the former comprising by amalgamation 27 and the latter 40 corporations, have inflicted a blow which no business except one of almost absolute necessity could survive. - This very great difference has existed from the first between the life insurance companies of Great Britain, that what some consider a reserve from past premiums necessary to supply the deficiency of future ones, others consider as surplus or profit, and consequently expend or divide it. Even so late as July, 1874, the officers charged with reporting to the president of the board of trade on this subject say: " It will hardly be believed that the board of trade could have had submitted to them, for acceptance under the life assurance companies' act of 1870, valuations in which the future profit, future expenses, and even future commissions, have been turned into present value, and the whole represented as profit.

These accounts have been rejected as being manifestly incorrect and misleading, and amended returns requested." This distinction between past and future payments, which is one of life and death, will be plain enough when we come to consider the elementary principles of the business. The ease with which life insurance companies have converted probable future profits into assets, and the plausible excuses for doing it, have cost the British parliament very laborious discussion and inquiry, to find some method of shielding the public from its disastrous result. But all investigation and legislation up to the act of 1870 seems to have had an effect exactly the reverse of that intended. That act has obviously checked the formation of new companies by requiring a deposit with the government of £20,000; it has put .an end to fraudulent amalgamations by requiring the terms of any union to be submitted to the court of chancery for approval; and it promotes honesty of management by requiring an annual statement of all details to the officers of the board of trade. These statements are such as to expose extravagance and give fair warning of any tendency to insolvency.

There are said to be 125 companies now existing in the United Kingdom, all but five of which made returns in 1873. The premium income was £10,824,093, amount of insurance outstanding £338,882,752, and the reserve fund £94,260,-592, with an average interest of 4.41 per cent. The Equitable, which was once the largest in point of funds if not of insurance, having an accumulation of more than £10,000,000, and which has still the largest reserve in proportion to its amount, is now the fifteenth in amount of insurance and the fifth in the magnitude of its fund. It may expire, but it will not fail. There were 21 companies having over £5,000,000 each insured, and five having over £10,000,000. The Scottish Widows' had £14,572,154, and the Standard £16,867,-577. The greater part of the companies are ably managed institutions. The strength of our own more recent but not smaller institutions is well known, and it may be interesting to compare the aggregate figures of the two. Referring to the latest official reports on both sides, probably not exhaustive on either, but more nearly so in Great Britain than here, the amounts insured, funds in reserve, and death claims paid within a year, are as follows:

COMPANIES.

Amount insured.

Funds.

Death claims.

British.........

$l.640.192.519

$512,660,011

$38,586,653

America............

2,086,027,178

360,140,684

27,232,435

Considering that the American companies average a little less than 15 years of age and the British over 32, it will be instructive to compare the ratios of funds to amount of insurance; also the ratios of death claims to insurance and to funds:

COMPANIES.

Ratio of funds to insurance.

Ratio of death claims

to insurance.

to funds.

British....

312

per cent.

2.35

per cent.

7.52

per cent.

America......

173

,,

1.30

,,

7.56

,,

This shows how as the companies grow older the reserve fund must bear a greater ratio to the amount of insurance outstanding, because the death claims will bear a greater ratio. The American ratio of funds to insurance is considerably larger than it otherwise would be on account of the greater prevalence here of endowment insurance, which requires a more rapid accumulation of reserve; and for the same reason the American ratio of death claims to funds is a little smaller than it would otherwise be. In a well managed company it decreases a little as the age increases. When the reverse happens, and where for successive years it exceeds 15 per cent., danger arises. The premium income of the British offices was $52,-388,610, while that of the American was $96,-000,088. This large excess of the American premium income in proportion to the insurance is perhaps slightly due to the practice of diminishing the premiums in some British offices by enlarging the reserve, as a mode of returning surplus; but it is chiefly due to the much larger proportion of endowment insurance done by American offices. The distribution of $38,-000,000 a year among families bereaved of their heads by death produces a degree of public satisfaction not to be seriously disturbed by cases of failure or traits of imperfection.

The attending evils have always been keenly felt, but they have been submitted to with little complaint for the sake of such good as could be found nowhere else. - The early abuses of life insurance in England were checked by a statute (14 George III., c. 48) enacting that "no insurance shall be made by any person or persons, bodies politic or corporate, on the life or lives of any person or persons, or on any event or events whatsoever, wherein the person or persons for whose use, benefit, or on whose account such policy or policies shall be made, shall have no interest, or by way of gaming or wagering; and that every assurance made contrary to the true intent and meaning hereof shall be null and void to all intents and purposes whatsoever." This statute has been held to apply only to the inception of policies. It takes no effect when the insurable interest ceases during the term, as it usually does when a person insured for the whole life lives to a great age. To carry out the intent of the statute in regard to such policies is an unsolved problem, which will probably require for its solution a stipulation in the policy of a proper surrender value. - The creation of corporations in America with power to insure lives and grant annuities dates back beyond the revolution.

Dr. Richard Price and his friend Benjamin Franklin interested themselves in prescribing rates and rules for one which was chartered in the province of Pennsylvania as early as 1760, for the benefit of the families of Episcopal clergymen. The "Massachusetts Hospital Life Insurance Company " and the " New York Life and Trust Company " may be mentioned among the pioneers of the early part of the century, none of which have ever obtained much business. Four companies started successively in 1843, 1844, 1845, and 1846, in New York, Massachusetts, New Jersey, and Connecticut, were the first to win success. They now combine almost one third of the insurance and considerably more than one third of the accumulated funds. The existing companies are nearly as numerous as in Great Britain, and perhaps as various in quality; but the number of failures has not been as great nor attended with as much disaster. The rapidity of the growth of life insurance after 1843, and especially since 1858, is remarkable. Thirteen companies, including the four above referred to, reported to the state of Massachusetts in 1858 an aggregate of 42,450 policies, insuring $116,348,995. The same companies in 1869 reported 298,661 policies, insuring $907,187,407, having increased more than seven fold in 11 years.

The increase during the last four years has been less rapid, the same companies reporting in New York, in 1873, 346,884 policies, insuring $985,-752,299. It will be observed here that the number of policies increased faster than the amount insured, which is accounted for by the large number of small "paid-up " policies taken as surrender value of larger annual premium policies. The most striking and significant fact in the history of American life insurance, however, is the 404 fold increase of endowment insurance in those 11 years, coupled with its non-increase, if not decrease, since. The British life insurance companies are remarkable for their great variety of policies; for though ordinary whole-life policies, payable by annual premium during life, together with "paid-up" additions, called " bonuses" or reversionary dividends, constitute the bulk of their business, most of them issue a few joint-life and survivorship policies, ordinary whole-life, payable by single or a limited number of premiums, or by ascending or descending scales of premium, short-term, pure endowment, and endowment insurance policies.

The exact amount of the last class cannot be ascertained from the blue books under the recent act, because the policies are classified in the returns only in valuation years, which occur annually in only a very few companies, but usually in periods of from three to ten years. An examination of the returns for the first two years under the act shows $14,832,698 of endowment insurance out of $652,393,091 of all sorts, or about 2.27 per cent.; and this is probably about its ratio for the whole. These policies are issued in Great Britain for premiums sub-stantiallv the same as in this country, which enhances the interest of the inquiry why they should, for ten years at least, have been so much more abundantly popular here. The following tables from the New York "Insurance Times " of 1873, drawn from the Massachusetts and New York insurance reports, furnish a foundation for the study of a most im-portant phase of this subject. The first gives the amounts outstanding, divided into three classes, of the insurance reported by all the companies in 15 successive years, and the percentage of the endowment insurance to the whole.

The second table gives the annual increase or decrease of this percentage, showing the acceleration, culmination, and incipient relative decline of this branch of the life insurance business:

And Ratio Of Endowment Amounts To The Whole Table I. Number And Amount Of Three Classes Of Policies

YEARS.

WHOLE LIFE.

ENDOWMENT.

SIMPLE TERM.

Per cent. of endowm't to the whole.

Number.

Amount.

Number.

Amount.

Number.

Amount.

1858.....................

38.231

$107,659,465

278

$988,900

3.999

$7,833,830

0.85

1859.....................

44.593

123,913.596

369

1,252,256

3,645

7,574,974

0.94

1860.....................

51,230

142.176,279

668

1,974,437

3,446

7,148,114

1.3

1861.....................

53.348

144.253.449

846

2,417,653

2,945

6,267,475

1.58

1862.....................

71.425

189,494,396

1,567

3,958,437

2.950

5,810,250

1.99

1863.....................

92.083

245,525,537

3.119

8,448,450

2.741

5,751,153

3.25

1864.....................

136.565

357.304.512

7.007

18,833,703

2.990

6,431.974

4.92

1865.....................

190,037

507,168,417

17.705

46,445,160

2.767

7,030,700

8.28

1866.....................

262,354

739,662,035

44,231

119.460,867

3.361

10,990,660

13.78

1867.....................

336.257

967,113.546

91,566

234,695.681

3.132

10,898.910

19.35

1868.....................

409,830

1,194,620.763

132,432

882,728,827

3,557

12.650.340

21.61

1869.....................

475,723

1.379,764,566

165.727

399,855.389

4.692

16,527.480

22.26

1870.....................

538,812

1,510,226.564

183,847

418.331.941

4.438

17.385,119

21.50

1871.....................

543,605

1,515.433.338

169.560

380.011.733

5.552

17.952.459

19.86

1872.....................

570,206

1,574,904,424

178,934

404,258,870

5,535

17,489,763

20.22

And Decline Table II. Acceleration Culmination

TEAKS.

Gain or loss per cent.

1859.....

0.09

1860...........

0.36

1861...........

0.28

1862...........

0.41

1863...........

1.26

1864...........

1.67

1865...........

3.36

TEAKS.

Gain or loss per cent.

1866...........

5.45

1867...........

5.62

1868...........

2.26

1869...........

0.65

1870...........

-0.76

1871...........

-1.64

1872...........

0.36

- State Supervision. The failures of life insurance companies in Great Britain, and the necessity of some governmental safeguard against the peculiar facilities for fraud furnished by this business, as demonstrated by Mr. Wilson's celebrated parliamentary committee in 1853, caused the legislature of Massachusetts in 1855 to establish an insurance commission, one of whose duties was to exact and publish annually detailed returns of the assets and liabilities of all life insurance companies doing business in the commonwealth. Tor some years previous it had been required by law in Massachusetts that every company transacting business there should deposit with the secretary of state an annual statement of its assets and liabilities, including the value of its policies. But these returns in some cases (see eighth life insurance report of the insurance commissioners) were very far from being satisfactory. Hence the commission established in 1855 was authorized, though not imperatively required, to test the accuracy of the returns by a valuation of the policies. The first three reports of the commission were without the application of any such test.

The fact that at least two companies, one of them an English one, were operating extensively in the state with an apparently insufficient reserve fund, induced the legislature in 1858 to make a valuation of the policies of all companies obligatory upon the commissioners. Such valuations of the policy liabilities have been made annually ever since, and are on record in the office of the commissioners. An insurance department with similar powers and duties, except that for several years it made no valuations, was established in the state of New York in 1860, by an act dated in 1859. In consequence of the law making it the duty of the commission-ers in Massachusetts to value the policies, one company immediately ceased to issue new policies in the state, and another, being found to possess only a little over one third of the requisite premium reserve, showing a deficiency of over $1,000,000, was obliged to retire. One consequence of this success in checking fraud was to inspire public confi-dence in the companies that stood the test. Hence many sought to do business within the narrow borders of Massachusetts, not in the hope of gaining much, but for the sake of the credit which their standing in its reports would give them in other and broader fields.

In 1865 the number of companies reported had increased from 13 to 31; in 1870, to 64. Since then the number has considerably decreased. As an offset to any benefits of state supervision, it must undoubtedly be set down that it has inspired too much public confidence in the corporations that have passed its ordeal. Another misfortune is, that what any state does with any appearance of success, especially in the way of increasing offices, every other state must do. Hence state insurance departments have become so multiplied, that the charges on a company whose business extends into many states have become almost insupportable. From the inception of state supervision the danger of this has been felt; and unavailing efforts have been made to substitute national for state supervision, or to constitute a single board of impartial and scientific experts, whose valuations should be accepted by all the states instead of those of state bureaus. In England those officers of the companies who are responsible for the maintenance of the proper reserve fund are generally members of a corporate body entitled the "British Institute of Actuaries," which has power to maintain a high standard of scientific attainment, meets statedly to discuss all mathematical questions pertaining to life insurance, and publishes a journal devoted to the subject.

The conservative influence of this body is very obvious, and the soundness of so large a portion of the British companies is doubtless due in some measure to it and a similar organization in Scotland. But, the members being generally connected with the companies in subordinate rather than commanding positions, it is equally obvious that the institute has no great power of progress or reform. Its labors in developing the law of mortality, as exemplified in the general population, in particular occupations, and in insured lives, have been of great value, and practically conclusive. But beyond the better adjustment of rates, it has not originated many practical improvements, nor eliminated many of the errors and imperfections which time has shown in the work of Dr. Price. There is a marked illustration of this in its relation to Dr. William Farr, a member of the institute and actuary in the registrar general's office. His masterly manipulation of the British census returns has given him the highest place in the world among statisticians.

Twenty-five years ago, in his letter to the registrar general, given in the 12th annual report of that officer (1849), he demonstrated and began to advocate an improved plan of life insurance, founded on a recognition of a more distinct right of the policy holder to a certain portion of the fund arising from the premiums. The scientific and practical merit of the system seems to have been tacitly admitted by the institute; yet it has not been adopted by any of the old companies, and the several new ones that have been started to carry it out have either died of inanition or are in danger thereof. Dr. Price insisted on nothing more strenuously, as essential to safety, than that every life insurance company should be headed by some thoroughly scientific person. The success and permanence of the business depends fully as much on the rarer qualities of medical and mathematical ability as on the more common quality of commercial skill. - Elements of Life Insurance. The principle of equity at the foundation of a mutual life insurance company is, that payments shall be proportional to risks. Each member must pay toward the death claims which may occur in a given time a sum to be determined by the company's risk of having to pay the claim arising from his own death in that time.

The first question is, how to measure this risk. As the probability of dying within a given time is greater, other things being equal, as the age is more advanced, the insurable portion of life is, for simplicity, divided into equal units of time, during each of which the risk is assumed to remain the same, while it differs in successive units, increasing as the age advances more and more rapidly according to a definable law. The unit of time commonly assumed is one year, and there is a great convenience to the calculations in assuming that premiums and interest are payable also by coincident yearly rests. The law or table of mortality deduced by the British actuaries from observations on insured lives, first published in 1843, and amply confirmed by later observations, is given below, with the chances of death each year out of 1,000, and the consequent natural premiums payable at the beginning of each year of age to insure $1,000 payable at the end of the year, provided death should occur within it:

Actuaries Table. From The Combined Experience Of 17 English Companies

AGE.

Living.

Dying.

Chances out of 1,000 of dying in one year.

Natural premium to insure $1,000 for one year.

10....

100.000

676

6.76

$6 50

11....

99.324

674

6.79

6 53

12....

98.650

672

6.81

6 55

18....

97.978

671

6.85

6 59

14....

97.307

671

6.90

6 63

15....

96.636

671

6.94

6 68

16....

95,965

672

7.00

6 73

17....

95,293

673

7.06

6 79

18....

94,620

675

7.13

6 86

19....

93.945

677

7.21

6 93

20....

93.268

680

7.29

7 01

21....

92.588

683

7.38

7 09

22....

91.905

686

7.46

7 18

23....

91,219

690

7.56

7 27

24....

90,529

694

7.67

7 37

25....

89.835

698

7.77

7 47

26....

89,137

703

7.89

7 58

27....

88,434

708

8.01

7 70

28....

87,726

714

8.14

7 S3

29....

87.012

720

8.28

7 96

30....

86,292

727

8.42

8 10

31....

85.565

784

8.58

8 25

32....

84,831

742

8.75

8 41

33....

84.089

750

8.92

8 58

34....

83,339

758

9.10

8 75

35....

82,581

767

9.29

8 93

36....

81,814

776

9.48

9 12

37....

81,038

785

9.69

9 31

38....

80,253

795

9.91

9 53

39....

79,458

805

10.13

9 74

40....

78.653

815

10.36

9 96

41....

77,838

826

10.61

10 20

42...

77,012

839

10.89

10 48

43....

76.173

857

11.25

10 82

44....

75.316

881

11.70

11 25

45....

74.435

909

12.21

11 74

46....

73.526

944

12.84

12 35

47....

72,582

981

13.52

18 00

48....

71.601

1,021

14.26

13 71

49....

70.580

1,063

15.06

14 48

50....

69,517

1,108

15.94

15 83

51....

68.409

1,156

16.90

16 25

52....

67,253

1.207

17.95

17 26

53....

66,046

1.261

19.09

18 86

54....

64.785

1.316

20.31

19 53

55....

63.469

1.375

21.66

20 S3

56....

62.094

1.436

23.13

22 24

57....

60,658

1,497

24.68

23 73

58....

59.161

1,561

26.39

25 37

59....

57.600

1,627

28.25

27 16

60....

55.973

1.698

30.34

29 17

61....

54.275

1,770

32.61

31 36

62....

52.505

1.844

35.12

33 77

63....

50,661

1.917

37.84

36 38

64....

48.744

1.990

40.83

39 26

65....

46,754

2.061

44.08

42 39

66....

44.698

2.128

47.61

45 78

67....

42.565

2.191

51.47

49 49

68....

40.374

2,246

55.63

53 49

69

38.128.

2.291

60.09

57 78

70....

35,837

2,327

64.93

62 44

AGE.

Living.

Dying.

Chances out of

1,000 of dying in one year.

Natural premium to insure $1,000 for one year.

71....

33,510

2.351

70.16

67 46

72....

81,159

2.362

75.80

72 89

73....

28.797

2,353

81.88

78 73

74....

26,439

2.339'

88.47

85 07

75....

24,100

2.303

95.56

91 89

76....

21,797

2,249

103.18

99 21

77....

19.548

2,179

111.47

107 18

78....

17,369

2.092

120.44

115 81

79....

15.277

1,9S7

13006

125 06

80....

13,290

1,866

140.41

135 01

81....

11.424

1,730

151.44

145 61

82....

9,694

1,532

163.19

156 92

83....

8.112

1.427

175.91

169 15

84....

6.685

1,268

189.63

182 33

85....

5,417

1,111

205.10

197 21

86....

4.306

953

222.48

213 92

87...,

3,348

811

242.23

232 92

88....

2.537

673

265.27

255 07

89....

1,864

545

292.38

281 14

90....

1,319

427

323.73

311 28

91....

892

322

360.99

347 10

92....

570

231

405.26

389 68

93....

339

155

457.23

439 64

94....

184

95

516.30

496 45

95....

89

52

584.27

561 80

96....

37

24

648.65

623 70

97....

13

9

692.31

665 63

98....

4

3

75000

721 15

99....

1

1

1000.00

961 54

It is assumed for the sake of simplicity, both in calculation and practice, that insurable lives of the same age, counting always either from the nearest birthday or the next succeeding birthday, are of the same risk. This assumption of course cannot accord with the actual facts, but it accords sufficiently well with our attainable knowledge of the facts; and to attempt a distinct classification on other grounds than age would in some measure defeat the very end of life insurance. The only exception made in practice, to any considerable extent, is, that when individuals are admitted not fairly up to the average standard of health, either an arbitrary extra premium is charged, or the premium is arbitrarily charged which belongs to a more or less advanced age. The natural premiums above given are supposed to be payable at the beginning of the year, and the death claims to be settled at the end of it. Hence the value of the risk, or chance of dying out of a thousand, is discounted a year, and, for the sake of safety, at the low interest of 4 per cent.

The policies being all equal, if the deaths should occur out of the persons insured at each age precisely according to the table, and there were no working expenses, and exactly 4 Per cent. should be realized on the premiums, these natural premiums would exactly settle all the death claims at the end of the year, and there would be nothing left. But supposing the policies unequal, and paid for according to amount as well as age, if the assumed interest is realized, any one of three probable events, in the absence of the other two, may make the natural premiums insufficient. The number of deaths may exceed the tabular expectation; they may not be distributed among the ages according to the tabular expectation; or the average death claim may exceed the average policy. To guard against these adverse contingencies, as well as to provide for the working expenses, besides the precaution of assuming a rate of interest in all the calculations below that which is expected, it is deemed necessary to add to the net natural premiums, as well as to the artificial ones into which they are commuted, what is called a "loading." It is plain that, if we can rely upon the deaths in a very numerous company being distributed among the ages very nearly according to the above table, and upon bad risks being excluded by the medical officers to such an extent that the aggregate mortality shall much oftener fall below than above that expected, with a proper addition for the expenses and the contingencies above named, a mutual insurance company, including all ages and considerable difference in amount of policy, can be safely founded on these natural premiums for one year.

At the end of the year, if the contracts to pay the ascending scale of premiums extended for many years or for life, there would be nothing but a stipulation without penalty to prevent sound lives from discontinuing their policies, while the impaired lives would be pretty sure to continue. Here is a moral hazard too great to be incurred in the present state of society. A company so organized would inevitably become bankrupt, unless at the start it exacted of every policy holder, as security for the continuance of the payments, a deposit, to be forfeited in case of discontinuance, sufficient to make the company whole against the loss of its best life. Other objections to an ascending scale of premiums will readily occur. The impracticability of founding a permanent company on the natural ascending scale of premiums led to commuting them at the start into single premiums, or equal annual premiums, payable for a limited number of years or during the whole term of the policy. This was very naturally done by Mr. Simpson and Dr. Price, because in the old unscientific system which they supplanted the payments were equal. The improvement was to make them different for different ages of entry, allowing them still to remain, as before, equal for the successive years of the same age of entry.

Thus was at once solved the problem of securing against discontinuance, by the forfeiture of the early excess of the level premiums. The security, unfortunately, became, too ample as the policy proceeded, even to the extent of keeping it in force after the cessation of the insurable interest. Time had to reveal this defect, which might have been foreseen at first, but was not; and it will probably take a good deal of time to remove it. Nothing can contribute more to this desirable end than thoroughly to popularize the method of commuting the net natural ascending into the net equal annual premium. Though algebra is very convenient in this process, it is an entire mistake that it cannot be perfectly understood without it. Recurring to the actuaries' table, it will be noticed that the natural premium to insure $1,000 for one year, at the age of 99, is simply the present value of $1,000 certainly due in one year. It is assumed that the insured, at whatever age he entered, will certainly die in that year, if he should live to enter it. Hence, so far as the calculation is concerned, a whole-life policy, payable at death whenever that event may occur, is identical with an endowment policy payable at 100 or on previous death.

Hence, in converting the natural premiums of a whole-life policy, under this table, into a level annual premium, we are doing the same thing as commuting the natural premiums of an endowment insurance payable at 100 or previous death. But if the table had assumed that human life terminates at 40 instead of 100, the mortality of the ages previous to 39 being just the same, then the natural premium of age 39 would be the same as 99, viz. (at 4 per cent.), $961 54 per $1,000; and an endowment insurance policy, at whatever age entered, payable at 40 or previous death, would be identical, under the assumption, with a whole-life policy. Hence the method of commuting must be the same, whether life is supposed to stop at 99 or at 40. The patience of the reader however will be least taxed by selecting a policy only long enough fairly to illustrate the mode of operation. Let the age of entry be 32, and life terminate at 40. Let the natural premiums from the table, with that of the new assumption of no life beyond 40, be placed against the ages in column A. In column B place the present values of $1 payable certainly when the premiums are due, discounting at 4 Per cent. compound interest.

In column C place, in decimal form, the fractions expressing the chance of the insured being alive' to pay each premium when due.

AGE.

A.

B.

C.

D.

E.

32........

8.41

X

1

X

1

=

8.41........

1.0000

33......

8.58

X

•9615

X

•9913

=

8.18........

•9531

34........

8.75

V

•9246

x

•9824

=

7.95.....

•9083

35........

8.93

X

•8890

X

•9735

=

7.73........

•8654

36........

912

X

•8548

X

•9644

=

7.52........

•8244

37........

9.31

X

•8219

X

•9553

=

7.31........

•7852

38........

9.53

X

•7903

X

•9460

=

7.13..........

•7477

39 ....... 9

61.54

X

•7599

X

.9367

=

684.41........

•7118

738.64

6.7959

The first premium, being paid in advance, is a certainty, which is expressed by a unit. The chance of the person being alive to pay the second premium is expressed by the ratio of those living at 33 to those living at 32 (see actuaries' table), or 84089/84831= 9913. So the chance of the person being alive at 34 to pay the third premium is expressed by83339/84831=.9824; and so on. Now the present value of any future payment can only be such part of its present value as discounted at the assumed rate of interest, as those living to that age are of those living at the start. For example, the $961 54 which is payable at the end of seven years would be worth only .7599 x 961.54.= $730 67, if it were payable certainly. But as there are only 9,367 chances out of 10,000 that it will be paid at all, it is really worth only .9367 x 730.67=$684 41. The values of the anterior payments in column D are ascertained in the same way, and their sum, $738 64, is the single premium equivalent, if paid in advance, to all the natural ones. To ascertain the equal annual premium equivalent to this single one, we must first find the value of one dollar payable annually during the term, if the person is alive to pay it.

This is done simply by substituting unity for the natural premiums in column A and placing the products in E; or, to be more particular, the first dollar is payable certainly in advance, and we set that down undiminished in column E. The present value of the dollar payable in one year is given in column B as .9615, and the chance of its being paid in column C as .9913. Hence its value is .9615 x.9913 = .9531 in column E. And in the same way the factors in B and C produce all the present values in E, the sum of which, $6.7959, is the present value at the start of $1 payable annually, subject to the chance of the person being alive to pay it. By rule of three, as this present value, $6.7959, is to the equivalent payment of $1 a year, so is the present value of all the natural premiums, $738 64, to the equivalent level annual premium, $108 69. This may be tedious, but it is plain, and it is absolutely all there is in commuting the natural premiums of the scale into the level net premiums of practice.

No matter what is the length of the policy's term, each possible year of it must be treated separately, as above, in commuting directly from the original scale of living and dying. - The security for the fulfilment of the contract and persistence of the payments, in other words against the deterioration of the average vitality, which arises from the commutation of the natural premiums, has already been remarked. A still more important thing is its effect on the risks assumed by the company. A contract to insure a given sum for life, on the payment yearly in advance of the natural premiums, is a contract to carry a series of risks of ever increasing magnitude. The equivalent level premium has the effect of throwing a portion of those risks from the start, and growing larger and larger to the end, on the insured party himself; and in all cases of endowment insurance, the more so the shorter the term. It in fact converts what was wholly insurance into two complementary processes of insurance and self-insurance, the former (unless the policy extends beyond the age of 75) a constantly decreasing and the latter an increasing series.

The non-recognition of this important fact in the conduct of ordinary whole-life (that is, longest possible) endowment insurance has constituted that most serious defect in British life insurance which Dr. Farr has labored so long to remedy. His remedy is, so to invest the self-insurance or "how much in deposit" part of the funds, that no policy holder's share of it can be used by the company to pay expenses or any death claim but his own. The same is the object of American laws prescribing a fixed standard of reserve and net valuation. But it is in its bearing on short endowment insurance, or that which never extends beyond 75, that the distinction between insurance and self-insurance becomes vitally important; and the present decay and unpopularity of that branch of the business, which flourished so marvellously from 1858 to 1869, must be attributed to its being wholly ignored up to the latter date. This great practical mistake seems to have arisen from an unfortunate, though not incorrect, definition or analysis of the endowment insurance policy, the effect of which is described as follows in the " Insurance Times" for November, 1873:

"Endowment insurance is commonly defined as the union of insurance with endowment in the same policy. If the endowment is of the same amount as the insurance, as is almost invariably the fact, and for the same term, then the whole policy may be and commonly is regarded as the union of a simple term insurance with a pure endowment for the same term. If the life contingency, or risk of death, is considered as a positive quantity in the former, it is a negative quantity in the latter. This means that if the company loses by the death during the term in the former case, it gains by it in the latter. According to this commonly accepted definition, this very useful policy, which provides for one's dependents in case of his own death, and for his own old age in case of his survival, is analyzed into two, both of which are affected by the law of mortality in contrary senses. The more you analyze in this way, the more people not well versed in algebra are mystified; for no other language than algebra has power to deal satisfactorily with positive and negative quantities in the same calculation. By a different analysis the negative quantities will all disappear.

If, instead of regarding the policy as composed of the insurance of a given invariable amount for a term of years, united with an endowment of the same amount at the end of the term in case of survival, we regard it as the insurance of a decreasing series of sums, united to an increasing accumulation, the amount of which latter at any period of the term, added to the sum then insured, shall equal the face of the policy, we shall have precisely the same thing as before, with the contingency, so far as the company is concerned, all on one side. The 'endowment1 in a technical sense is annihilated. We have in its stead a mere series of savings-hank deposits, subject to certain peculiar conditions, or, in other words, a series of self-insurances, supplementary to the series of yearly insurances done by the company. Without affecting the practical results at all. we have pot a new point of view from which the whole matter is as plain as insurance for a single year.11

Had the companies regarded the increase of the net premiums of the endowment insurance policies over those of the ordinary life policies, not as insurance premium at all, but mere self-insurance or savings-bank deposit, they would have abstained from doing two or three very unfortunate things. They would not have added more margin to the net endowment premiums than to the smaller net life premiums, but rather less. They would not, whatever the premium might be, have paid more to procure a given amount of short-term endowment insurance than of long, but rather less. They would not have assessed more for expenses on a given amount of short endowment insurance than of long, if as much. The consequence of paying the agent no more, if not less, for bringing in $100 of endowment insurance premium, than for bringing in $25 of life premium, would doubtless have been a slower growth of this branch of the business. But, if there had been less of it, and less overloading and over-assessment, it would not now be showing signs of wasting away. The force of these remarks cannot be fully appreciated without recurring to the elementary principles, and perceiving how the commuted premium operates from the start.

After once finding it, no matter whether it be single, limited annual, or annual during the term, the effect on the company's risk, and the reserve that must be on hand at the end of each succeeding year, can be very readily ascertained by means of the tables already given. Take for example the net annual premium for 32, death or 40, to insure $1,000, which we find to be $108 69. The claim being payable at the end of the year, if only the natural premium is paid at 32 for $1,000, and a claim occurs on the policy the first year, the co-insurers will have to pay $991 25; if $108 69 is paid, they will have to pay only $886 96. Hence, in this latter case the company insures only 886.96/991.25 of the face of the policy; the rest the person insures himself, and it should therefore cost him normally, in advance, only 886.96/991.25 X $8 41, to pay for carrying the risk, or $7 52. (See table No. 1.) Deducting this from the net premium, we have $101 17 for deposit, which at the end of the year will amount to $105 21. This is the first year's self-insurance. It will go to make up the $1,000 if the policy turns up a claim; otherwise it must be on hand, for a reason that will be plain enough at the end of eight years.

All that this policy contributes the first year to death claims, if the person does not die himself, is $7 52 (or $7 52 1/2, to be exact), instead of the natural premium of $8 41. The other 88 1/2 cents is accounted for as the normal cost of the self-insurance, at the rate of $8 41 per $1,000. In the same way, for the next year, adding the net premium to the reserve and accumulating at 4 per cent., we find the co-insurers will pay in case of death $777 54, instead of the $991 08 they would have paid if the natural premium only had been paid. Hence the year's risk costs 777.54/991.28 x $8 58=$6 73; and the deposit is $101 96, which added to $105 21, and increased by the interest, makes the self-insurance of the second year $215 45. In this way columns B, E, and F, in table No. 1, are completed, columns B and E being simply the analysis of the net premium. The same is true of the same columns in No. 2, where the first eight years of a long endowment insurance, entered at the same age, are given.

It is plain that if a dollar were borrowed out of the deposits, or reserve, in columns E and F (No. 1), it must be returned with interest, or the company would not be able to pay the $1,000 to the person himself on his reaching 40. The only insurance resources are columns A and B, and these ought to be abundantly sufficient both for the claims and expenses of that branch of the business. The extra interest over 4 Per cent. of the self-insurance part will suffice for its own expenses, and should generally return some surplus. But the company must be ill managed or ill constructed which draws upon it for the expenses and claims of the insurance part.

No. l.-Death Or 40. Gross Premium, $132 60. Net Premium, $108 69.

AGE.

INSURANCE.

SELF-INSURANCE.

A

Margin, or "loading."

B

Normal cost of insurance.

C

. Risk.

D

Insurance value.

E

Deposits.

F Reserve at end of each year.

32......................................

$23 91

$7 52

$894 79

$29 80

$101 17

33......................................

23 91

6 73

784 55

23 37

101 96

$105 21

34.....................................

23 91

5 85

668 98

17 47

102 84

215 45

35......................................

23 91

4 89

547 79

12 18

103 80

331 02

36......................................

23 91

3 84

420 66

7 66

104 85

452 21

37......................................

23 91

2 67

287 22

4 01

106 02

579 34

38......................................

23 91

1 40

147 15

1 40

107 29

712 78

39......................................

23 91

0 00

0 00

0 00

108 69

852 85

40.....................................

...

-----

.......

........

......

1000 00

No. 2.-DEATII OR 75. Gross Premium, $26 67. Net Premium, $19 05.

32......................................

$7 62

$8 32

$988 84

$174 70

$10 73

........

33.....

7 62

8 38

977 30

174 60

10 67

$11 16

34......

7 62

8 44

965 34

174 40

10 61

22 70

35......................................

7 62

8 52

952 99

174 15

10 53

34 66

36.....................................

7 62

8 58

940 21

173 88

10 47

47 01

37......................................

7 62

8 64

927 01

173 59

10 41

59 79

38......................................

7 62

8 70

913 32

173 20

10 35

72 99

39......................................

7 62

8 76

899 16

172 79

10 29

86 68

40......................................

-----

-----

.....

.....

.....

100 84

The "margins" of these two policies (column A) are those usually applied, the first being 22 Per cent. of the net premium, and the second 40 per cent. Expenses are usually assessed according to these margins, with what effect will appear presently. Let it be observed that the insurance done by the company (column C) is always the face of the policy less the " self-insurance " of the year. Let us suppose that the holders of No. 1 and No. 2 have lived through eight years. The insurance which the company has done for each is the sum of the numbers in column 0 against the eight years. For No. 1 it is $3,751 14; for No. 2 it is $7,564 17, a little more than double. Supposing the death claims to have been according to the table, and that the expenses have consumed half the margins (not an unusual experience), the insurance enjoyed by No. 1 has cost him the sum of column B plus half that of A= $128 54, and that by No. 2, $08 82. That is, at No. 2's rate, No. l's insurance ought to have cost him only $49. If No. 2 paid enough, No. 1 paid at least $79 54 too much.

As the policy No. 2 that was to extend beyond the eight years had a much greater interest than the other in having the company enlarged, in proportion to the insurance it enjoyed during the eight years, it would seem it ought to have been assessed for the expenditures devoted to that object in a higher ratio. - This brings us to the question, What is the measure of a member's interest in the company, as an insurance company ? Plainly it is not the face of the policy or the premium, one or both, alone. A person who has a series of larger risks to be carried through 40 years, sick or well, if he should live so long, must have a larger interest than one who has a series of smaller risks to be carried only eight years, though the premium of the latter should be larger and the face of the policy the same. He may have a greater interest in it as a savings bank, and this is measured by the deposits. It is difficult to discover any nearer measure of the interest of a member in the insurance, than the present value of all the insurance contracted to be done under the policy, and this is found by discounting both by interest and mortality all the normal costs in column B. This process, already explained, gives column D, in which is placed against each age, under the head of "Insurance Value," the present value of all the future normal costs, including that just due.

The insurance values given in No. 2 include, of course, the discounted normal costs of the 59 years of possible insurance not included in the table. - If the self-insurance fund accumulated on a policy can never be used properly by the company for any purpose but to pay the claim arising on the policy itself, it becomes an important question how far the company can justly appropriate it as a penalty for the non-fulfilment of the contract. The loss which the company will sustain by the non-performance of the contract can have no appreciable relation to the self-insurance or accumulated deposits, but only to the insurance that remains to be done, that is, to the present value of it. This grows less while the self-insurance grows greater. Manifestly, then, the penalty for breach of contract should not increase with the age of the policy. It cannot therefore be a fixed percentage of the self-insurance fund, but it may perhaps justly equal or exceed it at first. There is therefore nothing to which it can to any appreciable extent have any just relation but the " insurance value." This principle is just beginning to be recognized by some of the largest offices.

The "insurance value" of the policy is also beginning to be recognized as the proper basis for determining the addition to be made to the net premiums for expenses and adverse contingencies. This will have the effect to reduce the premiums on the shorter endowments, if not to increase those on the longer ones. It is also beginning to be seen that the expenses, so far as they exceed those of ordinary trust institutions, should be assessed upon the members, not according to the premiums they pay, or their self-insurance, but according to the value of their interest in the company as an insurance company. Nothing can be more certain than that, as the business has hitherto been managed, it is better to put the difference between the premiums of an endowment insurance policy and a term policy for the same term into an ordinary savings bank, and take only the term policy of the life insurance company. It can only be politic to take the endowment insurance policy when the company's expenses in excess of one half of one Per cent. on its investments are assessed on the policy holders according to the then present insurance values of their policies, discounted at an interest as low as 4 per cent.

In that case, no one who needs insurance at all can afford to deposit in an ordinary savings bank, but will find it profitable to employ the life insurance office both for insurance and accumulation. Nor, in that case, will the redundancy of the premium be any objection, because it will be sure to return annually with interest. If three things, to wit - 1, the normal or tabular cost of carrying the risk of each year; 2, the addition to the net premium made to meet the working expenses and to provide against the possible excess of death claims in any year over the amount expected by the table; and 3, the self-insurance of each year with that part of the net premium devoted to its increase - were all stated distinctly in the policy itself, and also kept distinct in the books of the company, it would probably dispel most of the mystery which has so much bewildered policy holders, and remove the necessity of any more elaborate governmental supervision than that which is exercised over other fiduciary institutions. - The following are the kinds of policies usually issued by life insurance companies.

It is to be understood that a claim said to be payable " on the death of the insured " is payable according to the calculation at the end of the policy year in which he dies; but when the claim is known to be valid, it is usually paid within from GO to 90 days. A whole-life policy is an agreement on the part of the company to pay a certain sum to those representatives of the insured mentioned therein on his death. About three fourths of all the policies issued are of this kind. A term policy is an agreement to pay to the representatives of the insured a certain sum on his death, provided that event happens within a certain fixed term. A simple endowment policy is an agreement to pay a certain sum to the insured at the end of a fixed term if he be then alive. The insured himself takes the risk of living till the end of the term. Such policies are seldom taken out in this country. An endowment insurance policy is an agreement to pay a certain sum to the insured at the end of a fixed term, or to his representatives on his death should that happen before the end of the term. when " endowment policies " are spoken of, it is this kind which is usually meant. A joint-life policy is an agreement to pay a certain sum on the death of one of two or more persons named.

In this and the following kind of policy usually only two persons are named, upon the death of cither of whom the policy becomes payable; but three or more may be. A survivorship policy is an agreement to pay a certain sum to the survivor of two persons named on the death of the other. Various other kinds of policies are sometimes issued, especially by English companies; but those mentioned are the only ones issued in this country to any considerable extent. (See Annuities.) - Life insurance is governed by the same legal principles, so far as they are applicable, as other kinds of insurance. (See Insurance.) Any fraud or deceit in obtaining a policy, or misrepresentation of essential facts, even innocently made, will render it void. Any person can insure the life of another upon whom he or she is dependent for support, or in the continuance of whose life he has an adequate pecuniary interest; and a wife is always held to have an insurable interest in the life of her husband. At present the policies of companies make specific provision in regard to most points which would be likely to give rise to disputes.

As these provisions vary somewhat in different companies, they should be carefully examined and strictly complied with. - Some idea of the magnitude of the business of life insurance may be formed from the following statistics of the New York state companies for the year 1873:

Number of companies.............................. 27

Number of policies in force..................... 385,781

Amount insured........................ $1,051,099,364

Cross assets............................. 180,895,403

Gross liabilities except capital............. 158.516,342

Surplus as regards policy holders.......... 22,379,061

If to these amounts we add those of the companies of other states doing business in the state of New York, they will be almost exactly doubled.