these annuities are thus sold are less, as will be seen from Table XVI, than the rates here recommended.

TABLE XVI.-Showing immediate annuity rates of Canadian Government, annuities payable quarterly, first installment three months after purchase.

Furthermore, deposits made in payment of deferred annuities are credited with interest at 4 per cent, whereas the rate of interest proposed here is 3 per cent. It should be added, however, that under the Canadian plan the depositor is paid but 3 per cent if he elects to receive cash instead of an annuity or dies before his annuity begins.1

INFLUENCE OF INCREASED LONGEVITY ON ANNUITY RATES.

It is important that there be no confusion in the minds of those considering the basis of this plan in regard to the relation between the average length of life and the total span of life. The statement is frequently made that, owing to general improvements in the conditions under which life is maintained, the span of human life is lengthening. If this is so, then objection might be made to using mortality tables as the basis for annuity rates which were made on the assumption that out of 100,000 individuals living at a given age, all will be dead at the age of 104, as is the case with the British Offices' Select Annuitants' Mortality Table, or that they will be dead at the age of 96, as shown in the American Experience Table of Mortality, or at some other age as shown in some other table. It might be argued that, since the duration of life seems to be longer than in former years, it is not safe to use a table made on any of the present assumptions as to length of life.

Even though this contention were true, it does not follow that the mortality table that runs to the greatest age is the safest. Several tables run to 104 or more, but they are not as safe as the tables used, because they do not contemplate so many payments in the aggregate from the ages of 60, 65, and 70-the retirement ages under this plan. That the span of life is lengthening is, however, doubted by many

1 See Canadian Government Annuities, Ottawa (1908), p. 24.

actuaries. Mr. Henry Cockburn, president of the British Institute of Actuaries, discussing the British Offices' Tables, in his opening address on November 28, 1904, said:

The new tables exhibit also a continued improvement in the value of annuitant life, especially among females, which must be attributed in some degree to the "self-selection" exercised by the purchasers. * * As regards the

*

larger question of a general improvement in the value of human life in this country, and apart from the experience in any special class, there is no doubt that advances in matters relating to sanitary science, the care of disease, more healthful ways of living, have diminished at most ages the chances of death, and, indeed, the remark is not unusual that "people live longer than formerly." This improvement in vitality takes the form of, at each age, a greater average number of years lived by those born into the world, constituting, in actuarial parlance, a greater "expectation of life." A larger number than formerly reach adult age and usefulness, though without materially increasing the small proportion who will as heretofore attain to the highest ages; and one distinguishes between this position and longevity in its usual meaning the prolongation of life to advanced ages. In that matter it is difficult to say or to determine that among the population as a whole there is any appreciable increase.1

The subject was very thoroughly discussed at the Fourth International Congress of Actuaries held in New York in September, 1903. Papers on the improvement in longevity during the nineteenth century were presented by Mr. Samuel George Warner, of Great Britain, and Mr. John K. Gore, of the United States, and numerous members of the congress took part in the discussion. The general consensus of opinion seems to have been that the average length of life may be increasing but that the total span of life is not, or, if at all, at an imperceptible rate.

To quote Mr. Warner:

We have the growth of our great hospitals, the various organizations which care for the poor and the suffering, and especially for the children. Contemporarily with this we have also the great advance of science, its increased ability to cope with disease, its triumphs in surgery, its development of sanitation. If we carefully consider these various "streams of tendency," I think we shall not find it difficult to understand how the added length of years which they have combined to bring have come as a gift to childhood and youth rather than to old or middle age."

The conclusions of Mr. Gore were to the same effect. Said he:

In the absence of more complete data, we may conclude from the evidence available that during the last 30 years our urban population has experienced a rapidly decreasing death rate from phthisis, but that at the same time there has been a decided increase in the rate from diseases of the heart, kidneys, and lungs, from cancer and from violence. Among children, on the other hand, the mortality from all the diseases named, except measles, has greatly diminished.

On the assumption that the general tendency of the rate of mortality of our urban population has been the same as that of the whole country, it may be concluded from the data presented in these pages that the gross death rate was

1 See Journal of the Institute of Actuaries, vol. 39, p. 4.

2 Documents Fourth International Congress of Actuaries, p. 62.

lower at the end than at the beginning of the nineteenth century; that there was a decided decline in the rate during the last 50 years; that the greatest decline was at the youngest ages; that there was a considerable decline in the rate at the so-called producing ages of life, and that there was an increase in the death rate at the older ages, the increase being greatest at the most advanced period of life.1

In the discussion which followed the presentation of these papers, Dr. Alfred Manes, of Germany, said:

It may with certainty be surmised only that a much larger percentage of newborn children live longer to-day than a hundred years ago; that, therefore, the mortality among children has diminished, and this circumstance is undoubtedly due to progress in medicine and social politics. On the other hand, there is nothing to prove that to-day a larger percentage than, for instance, a hundred years ago, reaches the highest stages of life—that is, over 60 to 70 years._ On the contrary, these cases seem to occur less frequently to-day, and that is not to be wondered at in view of the change that has taken place in our circumstances of life. If we are indebted to the progress in medicine for the fact that nowadays more children are alive, it seems to me doubtful whether this is an advantage from the standpoint of political economy; for it means that to-day many more delicate children, whom nature had condemned to death at the outset, are kept alive artificially; but this progress is scarcely conducive to the improvement of our race.2

Corroborative of this general view is Table XVII, taken from the report of the Twelfth Census, which shows that in 1900, in comparison with 1890, there was a very regular decrease in the death rate at all ages up to 60 years, and an increase in the rates at each age above 60 years.

TABLE XVII.-Showing for the registration area the death rates at each age per 1,000 of population in 1890 and 1900 and the decreases and increases in the rates.

1 Documents Fourth International Congress of Actuaries, p. 615.

2 See Proceedings Fourth International Congress of Actuaries, vol. 2, pp. 111, 112.

Investigation of the cases of centenarians seems to bear out the statement that the limit of human life is about 100 years. Mr. T. E. Young, late president of the Institute of Actuaries, and author of a work On Centenarians and the Duration of the Human Race, finds that the majority of reputed cases of centenarians in modern times are not authentic, and he proves that evidence of extreme longevity in the past is deficient. Bulletin 13 of the Bureau of the Census contains the statement that the number of centenarians in 100,000 population of known ages at the last six censuses has been as follows: 1850, 11; 1860, 10; 1870, 9; 1880, 8; 1890, 6; 1900, 5. This regular diminution indicates, not that the longevity of the population has been decreasing, but that in this, as in other particulars the accuracy of the age statistics of the censuses has been improving.1

The same bulletin contains a quoted statement to the effect that "in Prussia the number of persons (in a total population of 30,000,000) declared to be more than 100 years old in 1890 was 149, of whom more than one-half were discovered upon investigation to be of less age; and of these 8.8 per cent were found to be from 95 to 100, 14.3 per cent were between 90 and 95, and the rest not yet 90 years old."?

It does not, therefore, seem likely that increased longevity of the race will ever make the annuity rates suggested here inadequate. Provision for that contingency has, however, been made in the bill, and another table can, if necessary, be adopted by order of the Secretary of the Treasury.

A LIFE ANNUITY CONTRACT IS THE CONVERSE OF A LIFE INSURANCE CON

TRACT.

Since the purchase of annuities is not very common in the United States and the question under discussion is how to determine the value of annuities on the lives of Government employees, it may be well to point out the principles underlying the computation. They are precisely the opposite of those employed in the computation of life insurance premiums, with which the American public is more familiar. This is so admirably explained by William Alexander that his statement is given in full:

In calculating annuities a mortality table must be employed and a rate of interest assumed, as in calculating the premiums on life-insurance policies. In fact, investigation will show that a life annuity is simply the opposite of a policy of life insurance. In the case of the policy, a man pays the company a small sum annually as long as he lives, in consideration of which the company agrees 1 See Census Bulletin 13, entitled "A Discussion of Age Statistics," by Allyn A. Young, p. 20.

2 See Mayo-Smith, Statistics and Sociology, p. 61. See last sentence of sec. 1 of the proposed bill.

See Life Insurance Company, by William Alexander, p. 47.

to pay a large sum at his death. In the case of the annuity, a man sinks in the beginning a large sum, in consideration of which the company agrees to pay him a small sum annually as long as he lives.

In view of the fact that the conditions are reversed, and for other reasons, it is usual in calculating annuities to adopt, on the one hand, a mortality table framed on a somewhat more rigid basis than that employed in calculating insurance premiums; and, on the other hand, to assume a somewhat more liberal rate of interest, such, for example, as 3 per cent.

The younger a man is the less it costs to obtain a policy of life insurance. In the case of an annuity the reverse is true. If a man is old, a given sum will yield a large annuity; if he is young, the same sum will yield but a small annuity.

In the case of life insurance the longer the policy holder lives the greater the advantage to the company; hence the company insists upon medical examinations in order that it shall not assume risks on impaired lives. In the case of the annuity, on the other hand, no examination is required, because the sooner the annuitant dies the less the company will have to pay. Hence there is no need for the company to protect itself by an examination. As the annuitant is well aware of this fact, there is no danger that he will sink his capital unless he believes himself to be in good health.

The man who has the greatest need of life insurance is the one who has a family dependent upon him; the man who invests in an annuity is usually one who has no dependents.

DEDUCTIONS FROM SALARIES.

After deciding on the mortality table and the rate of interest proper for the purpose, and by means of them constructing the rates which the Government should charge for the annuities granted its employees, the fourth step in working out the proposed plan is to determine what amount will have to be deducted from the employees' salaries to create the sums necessary for the purchase of the annuities. It has been pointed out that this plan differs essentially from all the plans previously laid before Congress, in that it discards as unfair to the employees of different ages the idea of deducting from all salaries a uniform percentage of salary, large or small.

The problem then under this plan is to determine what percentage of salary must be deducted at each age of entrance into the service for each grade of salary. Each class of cases must be treated individually. Each employee must set aside that percentage of his salary necessary, with the help of compound interest, to accumulate a sum sufficient to buy him at the age of retirement an annuity equal to 1 per cent of his salary for each year he has served. If he should set aside too small a percentage of his salary, then the sum to his credit on reaching the retirement age would be insufficient for the purchase of the annuity desired. On the other hand, there is no need to set aside a larger percentage of his salary than that actually required for the purchase of his annuity, for all his fellow employees