shows the percentage of annuity contributed by the employee and the percentage gained through the increment of interest:

TABLE VIII.-Showing percentage of annuity contributed by employee and percentage gained through increment of interest.

Table IX shows the amount returned to the employee in cash, after various periods of service, for each dollar deposited.

TABLE IX.-Showing amount returned to the employee in cash, after various periods of service, for each dollar deposited.

The rapidity with which a fund increases at compound interest after the lapse of a few years is graphically illustrated in the accompanying chart by the curves representing the amount resulting from a deposit of $1 a year compounded at various rates of interest from 1 to 50 years, and Table X, which follows, shows the same thing in numbers. It will be noted that during the first years of accumulation the amount of interest is insignificant, and the curves representing it are slight, but that after about 20 years' accumulation the amount of interest increases very rapidly, approaching and passing

CHART SHOWING THE AMOUNT OF A DEPOSIT OF $1 PER ANNUM FROM ONE TO FIFTY YEARS AT VARIOUS RATES

the amount of the principal itself. In other words, the interest. accumulation on shorter periods is vastly less than on the longer periods of service. To illustrate: The interest on $1 per annum compounded for 40 years, at 4 per cent, amounts to $58.83, while for 50 years, an accumulation period of only 10 years more, or but one-fifth of the whole period, it amounts to $108.77, or nearly twice the interest of the shorter period.

TABLE X.-Showing the amount of a deposit of $1 per annum from 1 to 50 years at various rates of interest.

The cumulative power of compound interest being so great, the rate at which the interest is compounded is important, since even slight variations in the rate cause considerable differences in results. (See chart, p. 102.)

The rate of interest that money will earn is important in connection with this plan in two respects. It has to be considered with reference to the payment of interest on the accumulated savings of the employees, and also in connection with the computation of the annuity that these savings will buy. The bill provides, in the first sentence of the first section, that interest at 3 per cent compounded annually shall be added to the savings of the employees. It likewise provides in the last sentence of the same section that the deductions from the employees' salaries shall be based on the proper mortality table, with interest at 3 per cent compounded annually. In other words, no specific amount or uniform percentage of salary is stated as the proper rate of deduction from salaries, but a sum which, on two assumptions, will at the retirement age yield the amount necessary to buy the desired annuity. The two assumptions are the rate of mortality and the rate of interest. The latter is fixed by the proposed law at 3 per cent, but the right to change the mortality basis is left to the Secretary of the Treasury, so that, in case the experience among the Government annuitants should make it desirable to use a table showing a higher or a lower rate of mortality, the change can be made. The table recommended for the present is the British Offices' Select Annuitants' Table. For both purposes, the accumulation of interest on the employees' savings and the computation of annuities to be bought with them, the rate of interest proposed is 3 per cent.

RATE OF 3 PER CENT PROPOSED IN BILL.

The rate of 3 per cent was adopted in drafting the proposed bill as the desirable rate to be allowed the employees on their money held by the Government, since, in the opinion of some who have considered the subject, it is the maximum rate that can be safely guaranteed by the Government; while, on the other hand, a lower rate than 3 per cent would require the deductions from salaries to be unduly high in order to create the fund from which to pay the annuities provided in the bill. It was also thought to be about as low a rate as the Government could consistently ask its employees to accept on enforced savings, since that rate or a higher one is offered them by the majority of outside savings institutions.

OBJECTION TO LOW INTEREST RATE.

The most practical objection to too low a rate of interest is the fact that it necessitates too high a deduction from the employee's salary, a factor in the problem that is not very flexible. The higher interest rate would undoubtedly create a better feeling among the

employees also, some of the more thrifty of whom object to a compulsory savings plan solely on the ground that they can find more remunerative investments for their savings than the Government would guarantee under this bill.

The improvident, too, who never have any money to invest would be less likely to complain about a compulsory savings plan characterized by low rather than high deductions from salary. In the opinion of the author, therefore, 3 per cent is altogether too low an interest rate on enforced savings, and the Government should be willing to guarantee at least 4 per cent. It is very improbable that a guarantee of that rate would put a burden on the Government, for it would undoubtedly often be able to earn more than 4 per cent, which would offset the times when it would earn less. As explained on page 77 also, the safest and wisest way for the Government to lend its aid to the retirement project, far better than by any direct contribution, is through grant of a liberal rate of interest, since encouragement of that kind from the Government would offer no temptation to the introduction of abuses which invariably creep in under a system supported wholly or in part by contributions from the Government. The payment of a liberal rate of interest would operate chiefly as a reward of merit for the benefit of the longservice employee, for it is not until after a long period of years that the difference of a point or two in the rate of compound interest begins to show to any considerable extent, so that, while it would not make much difference to the employee who left the service after 10 years whether the interest rate allowed on his savings was 31 or 4 per cent, it would make a very great difference to the employee who had been in the service 40 or 50 years. Reference to the interest chart on page 102 will show how much more interest at 4 and 5 per cent will amount to on a long period of years than on a short term.

ADVANTAGE OF LOW INTEREST RATE.

On the other hand, the assumption of a low interest rate is not without its advantages. The lower the rate of interest the less probable, of course, that the Government would ever fail to realize the rate guaranteed. The bill provides that whatever is carried above the guaranteed interest rate should be returned to the employees, and it is proposed (see p. 110) that this surplus earning should be divided among the annuitants in order to make the annuity settlement as attractive as possible and to discourage employees from taking their money in cash. Naturally, the lower the rate of interest guaranteed, the more there will be to divide among annuitants and the greater the advantage given them over those who take a cash settlement on retirement.