rather than to take an annuity which would cease with his death or run on after his death for the benefit of some one else.

It seems certain at least that any average human being would object, and be justified in objecting, if his employer, whether the same were the Government, a corporation, or an individual, should withhold part of his earnings and reserve the right to return them at some remote date in the form of an annuity only, regardless of the employee's circumstances at that time or his wishes in the matter. In the opinion of most people that would be carrying the element of compulsion farther than necessary. It is unfortunate that it should ever be necessary to force people to take any step for their own good, and, theoretically, there is only one thing to be said in favor of compelling a person, whether a Government employee or not, to save his money, and that is that, since he is a member of society, the possibility is recognized of his making a claim on society, and society is right in protecting itself by prescribing what his conduct shall be. Undoubtedly, the ideal plan of retirement would be no retirement plan at all, but a government willing to pay salaries large enough to support its employees in dignity and comfort and a body of employees so thrifty as voluntarily to lay aside a competence for the rainy days of old age. There would be no problem then of superannuation in the public service, but such a condition can not be expected before the millennium, and in the meantime the Government must deal with the situation, in justice to itself and the employees, in such a practical way as to get beneficial results, regardless of any theory that it is tyranny for a government to require an individual to include thrift among the virtues he must cultivate in order to be held law-abiding. The Government is commonly held to be justified in protecting itself against the possibility of dishonesty on the part of its employees by requiring those holding offices of trust to give bond for the faithful performance of duty, and it is difficult to see why the Government is not equally justified in protecting itself against the evil consequences of improvidence on the part of its employees by requiring them to make such regular deposits of money as may guarantee their ability to retire when the interests of the Government so demand. A compulsory retirement law, such as that here proposed, is indeed much less paternalistic than a law requiring employees to give bond, because under this retirement system every contributor recovers his contributions with interest, whereas under the bonding system of the Government nine hundred and ninety-nine honest officials contribute to reimburse the Government against loss at the hands of one dishonest employee. At the same time there is surely a limit to the extent the Government is justified in interfering with the individual's liberty or assuming responsibility for his welfare, and that point would seem to be reached in a retirement plan

when the Government has arranged the employee's affairs so that it can without injustice dismiss him from the service, leaving him. thereafter to his own devices.

ANNUITY RATES USED IN PROPOSED PLAN.

The next thing to consider is what price the Government should charge for these annuities. In determining what the rate should be for an annuity of $1, beginning at various ages, the first step is to select a mortality table that most accurately represents the particular body of lives on which the annuities are to be granted. The table recommended, for reasons given on page 95, is the British Offices' Select Annuitants' Table. The next step is to decide upon a rate of interest which the funds received in payment for the annuity contracts may reasonably be expected to earn. The rate of interest proposed, for reasons given on page 104, is 3 per cent. With these two fundamentals established, Table XIV has been prepared, which shows the present value of a life annuity of $1 for a male at age 70, first payment in one year to be $7.2205. Briefly stated, the price of an annuity is the present worth of a series of payments to be made to a person for a stated period or until the happening of some event, such as death.

TABLE XIV.-Showing how the value of an annuity is determined.

PRESENT VALUE OF AN ANNUITY OF $1 FOR A MALE, BEGINNING AT AGE 70, It will be observed that, according to the above table (Table XIV), the number living at the beginning of age 70 is 38,991. At the beginning of the second year there will be, according to the same table, only 37,573 living, and consequently as the first annuity payment under our calculation is to be made at the beginning of the second year the payment will amount to only $37,573. If an adjustment were made at the beginning of the first year, the Government would have to pay such a sum as would with compound interest amount to $37,573 at the end of the year. Since each one of the annuitants has an equal claim upon this sum, it must be divided by 38,991, the number living at the beginning of the first year. The share of each annuitant, 3 per cent interest being assumed, is therefore the present value of 3:33 of $1, or 33:53 0.96618357, or $0.93104601. The present value of all payments commuted in this manner constitutes the value of a life annuity at the age given. The present value of a life annuity of $1 for a male at age 70 (first payment in one year) is therefore the sum of the present values of all commuted payments from the age of 70 to 103, the oldest age contemplated under the British Offices' Select Annuitants' Table. This sum equals $7.22. To buy an annuity of $1, therefore, payable at the end of age 70 and every year thereafter until the end of life, the annuitant must pay a sum (or numerous sums at stated intervals) which, with interest compounded annually at 3 per cent, will amount, when he reaches the age of 70, to $7.22 for every dollar of the life annuity that he desires to buy.

99

ILLUSTRATION.

37,573

As a concrete illustration, take the case of an employee entering the Government service at the age of 20, expecting to retire under the plan at the age of 70 on an annuity equal to 12 per cent of his salary for each year of service. For the sake of simplicity, let us assume that his salary is $100 a month, and continues at that rate throughout the entire period of his service. An annuity at age 70 equal to 11 per cent of $1,200 a year for 50 years would amount to $900. To ascertain the price of that annuity it is necessary then to multiply $7.22, the present value of a life annuity of $1 beginning at age 70, by 900. This amounts to $6,498, and is the sum which he will have to accumulate by means of his savings and with the help of compound interest.

As a matter of fact, however, the present value of a life annuity of $1 beginning at age 70 will be $7.595, rather than $7.22, because the bill provides for the payment of the annuities quarterly rather than at the end of the year. Since all persons of a given group who 74196°-S. Doc. 745, 61-3---8

are expected, under a given table, to die during a year will not be dead at the end of three months when the first payment is due, it is manifest that annuities payable quarterly require somewhat larger premiums than do those payable annually, when the first payment is due at the end of the first year.

The sum, therefore, which he will have to accumulate will be $7.595X900 $6,835.50.

PRESENT VALUE OF AN ANNUITY OF $1 FOR A FEMALE BEGINNING At age 70.

It is the practice of life-insurance companies to charge women higher rates for annuities than men. This is because of their greater longevity. According to the British Offices' Select Annuitants' Mortality Table, the complete expectation of life for a female at age 70 is 10.884 years, as against 9.537 years for a male at the same age. The greater longevity among female annuitants may be attributed in some degree to the greater "self-selection " exercised by them.1

If the practice of the insurance companies is followed in the matter of rates charged women annuitants, and if the rate charged a male for an annuity of $1, payable quarterly, beginning at age 70, is $7.595, the corresponding rate charged a female for a similar annuity of $1, beginning at the same age, must be, according to Table XV, $8.512.

There are several reasons, however, for suggesting that the annuity rates charged by the Government might properly be made the same for women as for men. In the first place, outside of the District of Columbia, there are comparatively few women in the service. Table 2 in Census Bulletin 94 (p. 10) shows that only 7.4 per cent of the employees in the entire civil service are women. In the District of Columbia women constitute 29 per cent of the employees. In the civil service elsewhere than in the District of Columbia women form only 4 per cent of the total number.

In the second place, the "self-selection" exercised by women annuitants would probably be less severe against the Government than that exercised against the insurance companies. Annuities issued by the Government would probably be more attractive because they are issued by the Government without loading for expense, and because a surplus derived either from interest earned or from excessive mortality among annuitants would be distributed among the survivors, whereas annuities issued by insurance companies are generally on the nonparticipating plan.

In the third place, the Government might properly follow the example of other nations in this respect and make some concession to women in the matter of conditions under which they are retired.

1 See Journal of the Institute of Actuaries, vol. 39, pp. 2, 3.

It is customary in other countries which have a system of retiring civil employees to retire women at a younger age than men. In New Zealand, for instance, the retirement age for women is 55, as against 65 for men. The proposed plan makes no similar provision, but in view of the fact that the annuity rates, even for women, have been constructed on the most conservative basis, it seems fair to charge them no more than men for their annuities.

A fourth consideration lies in the fact that a uniform rate for both sexes would avoid the complexity incident to the use of two sets of deductions and would simplify the matter of accounting.

TABLE XV.-Showing the present value of a life annuity of $1, for males and females, beginning at various ages, first payment in three months (British Offices' Select Annuitants' Mortality Experience; interest 3 per cent, compounded annually).

THESE RATES CONSERVATIVE, AS SHOWN BY COMPARISON WITH CANADIAN

GOVERNMENT RATES.

The fact that these rates are conservative is brought out by comparison with the rates offered to the public generally by the Canadian Government. A system of Government annuities was recently established by Canada, which enables any citizen to purchase from the Government an annuity, which may be either immediate or deferred, but can not be payable before the age of 55. The rates at which.