are accumulating in the same way the sums necessary to purchase their own annuities, and have no need of his help.

HOW TO DETERMINE THE AMOUNT OF DEDUCTIONS FROM SALARIES.

To determine the amounts that must be deducted from any salary at any entrance age, all that is necessary, in addition to the data already secured, in computing the cost of the employee's annuity is Table XVIII, which shows the amount to which a deposit of $1 a month, first payment immediate, will accumulate at 33 per cent per annum, compound interest, at the end of the number of years which the employee will have to serve before reaching the age of retirement. TABLE XVIII.-Showing the amount to which a deposit of $1 per month (first payment immediate) will accumulate at 3 per cent per annum compound interest at the end of a given term of years.

By dividing the sum which has been previously ascertained as the cost of the annuity by the amount shown in the above table (Table XVIII) which a deposit of $1 per month will accumulate in the given number of years, the amount of the monthly deduction required from the monthly salary during all the years of service to accumulate the price of the annuity is obtained. Table XIX, which follows, shows the per cent required to be deducted monthly from any salary at different entrance ages to provide an annuity for a male at age 70 equal to 1 per cent of the annual salary for each year of service.

TABLE XIX.-Showing amount required to be deducted from a monthly salary of $100 (per cent of other salaries) to provide an annuity at age 70 equal to 1 per cent of annual salary for each year of service.

To determine the amount of deduction required from any salary at any age, multiply the amount shown as required from a salary of $100 at the age desired by the ratio of the salary for which the deduction is desired to 100. In other words, the deduction required from a salary of $100 for an employee entering the service at age 30 is shown in the table as $5.289. For a salary of $150 for an employee entering the service at age 30 the deduction required is determined as follows: 150

= $7.933.

As a concrete illustration of the amount of salary to be deducted for the creation of an annuity payable quarterly from age 70, of 1 per cent of salary for each year of service, take the case of the employee mentioned in the illustration on pages 113, 114. It was ascertained that he would have to accumulate the sum of $7.595 times 900, or $6,835.50, in order to obtain a life annuity of $900, which would be an annuity of 1 per cent of his salary of $1,200 for 50 years, he having entered the service at age 20. To ascertain what his monthly deductions from salary would be, divide $6,835.50 by the amount which a deposit of $1 per month will accumulate at 31 per cent per annum, compounded annually, at the end of 50 years. According to the interest table that is $1,601.78. The amount of his monthly deduction from salary is therefore $6,835.50 divided by $1,601.78, equaling 4.267, and that it remains until he receives a promotion in salary.

PERCENTAGE OF SALARY DEDUCTED VARIES WITH RETIREMENT AGE.

The percentage of salary to be deducted must necessarily be larger when retirement is contemplated at the ages of 65 and 60 than it is when retirement takes place at the age of 70, since the time during which contributions for the purchase of annuities are accumulated at compound interest is 5 years shorter in one case and 10 years shorter in the other. In addition to this, the time during which the annuities will be payable is 5 years longer in one case and 10 years longer in the other. The deductions from salaries for retirement at age 65 are shown in Table XX; for retirement at age 60 in Table XXI.

TABLE XX.-Showing amount required to be deducted from a monthly salary of $100 (per cent of other salaries) to provide an annuity at age 65 equal to 1 per cent of annual salary for each year of service.

TABLE XXI.-Showing amount required to be deducted from a monthly salary of $100 (per cent of other salaries) to provide an annuity at age 60 equal to 1 per cent of annual salary for each year of service

WITH SALARY.

It will be seen that for the younger ages, when retirement at age 70 is contemplated, less than 5 per cent of salary-the percentage most often suggested in the schemes proposing a uniform rate of deduction from salaries will be sufficient, but for the older ages more than 5 per cent will be necessary. Those entering the service late in life and having but a short period of accumulation must set aside a larger sum each month in proportion to their salaries than those entering early, who have a longer period of accumulation. This puts a premium on the early entrance ages, which is as it should be. On the other hand, it is wholly fair to the elderly person who enters the service, the deductions from his salary being in no case excessive, his savings being accumulated for him at compound interest and some provision thus assured him for his old age. It is important to remember, too, that after the age of 70 the accumulations increase very rapidly, and that the price of the annuity, on the other hand, decreases very fast, so that an employee who entered the service late in life and would have a very small annuity to his credit at 70, by remaining a few years after reaching that age, under the provisions of the bill (see sec. 4, p. 211), would retire on a very comfortable annuity. For instance, as is shown by Table XXII, an employee entering the service at age 50, on a salary of $100 a month would, on reaching the age of 70, have to his credit $2,734, which would then buy him an annuity of but $360 a year. By remaining in the service until he reached the age of 75 his accumulations would have increased to $3,903, which would then purchase an