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square of the time of investment expressed in terms or periods corre sponding to the intervals between the series.

2. Divide the sum of these products into the results obtained by multiplying the total net profit by the square of the time of investment expressed as above.

The total of the products as in the last illustration is 15,500; then

$5,325, total profits, ×4×4-15,500 $5,325, total profits, x3x3-15,500

$5.50, profit of a share of the first series. $3.09, profit of a share of the second series.

$5,325, total profits, ×2×2-15,500-$1.37, profit of a share of the third series. $5,325, total profits, x1x1-15,500-$0.34, profit of a share of the fourth series. A share of the first series receives 16 times as much profit as a share of the fourth series; a share of the second series, 9 times as much; and a share of the third series, 4 times as much. This method, therefore, reveals the fact that, by multiplying the number of shares in force in each series by the square of the time each series has been invested, expressed in years, half years, quarter years, etc., corresponding to the intervals between the series, a correct basis of calculation is reached. These simplifications, however, are practicable only where series are issued at regular intervals, as fractions complicate the operation. This simplification is known as Rice's rule.

A few associations arrive at the same results by dividing the total investment for one month into the profits, for a rate per cent of profit, and then applying the rate to each series' investment for one month for each series' share of the profits. The process is also varied in the fol lowing manner: Find what annual rate of interest the profits are equiv alent to on the amount of dues paid for one-half the time that all the dues have been invested, and apply this rate on the dues paid per share for one-half the time of investment, for the profit of a share in any series.

Other variations are the following:

1. The profits are distributed on the amount of dues actually paid in on the shares in force in each series (not what the regular payments should have amounted to), multiplied by one-half the time of investment.

2. The profits are distributed on the total amount of dues standing to the credit of the shareholders in the loan fund multiplied by onehalf the time of investment.

3. The series are not allowed to participate in the profits for the term in which they were issued.

4. The profits are distributed on the amount of dues actually paid in on all shares in force that are three months old or over, multiplied by one-half the time of investment, shares less than three months old not participating.

5. The profits are distributed to the free shares only, dues on shares borrowed on being credited on loans.

6. Profits arising from withdrawals are divided equally among the

7. Profits arising from entrance fees are divided equally among the shares of the respective series in which the shares are taken.

8. A profit of $1 is given to all shares six months old or over. The remainder of the profits is distributed on the dues paid in on the shares in force six months old or over multiplied by one-half the time of investment.

9. Profits arising from premiums are divided equally among all the shares in force at the end of the period during which the loans were made. Profits from all other sources are distributed in accordance with the modified rule.

10. A fixed rate of interest is given on the total amount of dues paid on the shares in force at each apportionment. This interest is deducted from the profits for the term and the remainder distributed according to the modified rule.

11. A fixed rate of interest is given on the value of the shares in force as declared by the last report. This interest is deducted from the profits for the term and the remainder is distributed according to the modified rule.

12. A portion of the total amount of premiums received by and due the association is arbitrarily determined upon, and held in reserve to be applied in future dividends; the amount thus determined upon is deducted from the total profits, and the remainder of the profits is distributed as follows: The interest and dividends allowed on free shares withdrawn are added to the dues paid in on such shares, and the sum total of said interest and dividends is deducted from the amount of distributable profits; the balance is distributed among all the shares in accordance with the foregoing modified rule.

There is still another modification of plan 1, as follows: Multiply each series' investment (that is, the dues paid in on the shares in force) by one-half the number of months invested plus one and apportion the profits in proportion to these products.

Using the same data as before we proceed as follows:

ILLUSTRATION.

$48 × 500 × 25 = $600,000, first series' investment for one month.
$36 × 600 × 19$410,400, second series' investment for one month.
$24 × 400 × 13=$124,800, third series' investment for one month.
$12 × 500 × 7= $42,000, fourth series' investment for one month.
$1,177,200, total investment for one month.

=

Then, proceeding as before, we find that

600000

410400 1177200

124800 1177200

2 or 1 of $5,325 $2,714.07, the first series' share of the profits. or 344 of $5,325 $1,856.42, the second series' share of the profits. 1% or 9 of $5,325 = $564.53, the third series' share of the profits. 1149280 or 3 of $5,325 $189.98, the fourth series' share of the profits. $48, dues, + ($2,714.07500) = $53.43, value of a share of the first series. $36, dues, + ($1,856.42 — 600) $39.09, value of a share of the second series. $24, dues, + ($564.53400) = $25.41, value of a share of the third series. $12, dues, + ( $189.98500) = $12.38, value of a share of the fourth series.

The number of associations operating under this plan and its modifications is as follows:

LOCAL.-Alabama, 11; Arizona, 3; Arkansas, 9; California, 45; Colorado, 14; Connecticut, 4; Delaware, 2; District of Columbia, 13; Georgia, 7; Illinois, 248; Indiana, 63; Iowa, 24; Kansas, 22; Kentucky, 13; Louisiana, 1; Maryland, 1; Massachusetts, 1; Michigan, 9; Minnesota, 38; Mississippi, 11; Missouri, 149; Montana, 1; Nebraska, 14; New Hampshire, 2; New Jersey, 100; New Mexico, 2; New York, 24; North Carolina, 3; North Dakota, 3; Ohio, 20; Oregon, 8; Pennsylvania, 338; Rhode Island, 1; South Carolina, 6; South Dakota, 10; Tennessee, 24; Texas, 12; Utah, 1; Virginia, 2; Washington, 2; West Virginia, 12; Wisconsin, 6; Wyoming, 1; total local associations, 1,280. NATIONAL.-Colorado, 2; District of Columbia, 1; Georgia, 6; Illinois, 19; Indiana, 1; Iowa, 1; Kentucky, 11; Maryland, 2; Minnesota, 4; Missouri, 7; Montana, 1; Nebraska, 1; New York, 2; North Da kota, 1; Oregon, 1; Pennsylvania, 1; South Dakota, 1; Tennessee, 12; Texas, 2; Utah, 1; Virginia, 2; Washington, 1; West Virginia, 1; total national associations, 81.

PLAN 2.

1. Give to each series, except the last, interest at the legal rate upon the value of the shares in force as declared at the last report.

2. Deduct this interest from the profits for the term and divide the remainder equally among all the shares.

Assuming that 6 per cent is the legal rate, and using the same data as in the illustration of plan 1, the plan is worked out as follows:

ILLUSTRATION,

$38.87 × .06== $2.33, interest on one share of the first series.

$25.27 X .06.

$12.32 x .06
$2.33 × 500
$1.52 x 600-

$0.74 × 400=

$1.52, interest on one share of the second series.
$0.74, interest on one share of the third series.

$1,165, interest belonging to the first series.

$912, interest belonging to the second series.
$296, interest belonging to the third series.

$2,373, total interest belonging to the old series.

$3,000, the profits for the term,

- $2,373 = $627, profits remaining to be divided. $6272,000, total shares in force,=$0.31, profit of each share.

$38.87, previous value, +$2.33, interest, + $0.31, profit, + $12, dues, = $53.51, value

of a share of the first series.

$25.27, previous value, +$1.52, interest, + $0.31, profit, +$12, dues, = $39.10, value of a share of the second series.

$12.32, previous value, $0.74, interest, + $0.31, profit, + $12, dues, ==

of a share of the third series.

$0.31, profit, +$12, dues, $12.31, value of a share of the fourth series. Undivided profits, $7.

This is known as Wrigley's rule.

$25.37, value

Many associations using this plan of distributing profits allow a higher or a lower rate of interest than the legal rate, but no separate

The above plan is varied by different associations in the following

manner:

1. Interest is allowed on all the series except the last.

2. Interest is allowed on the dues paid in up to the last report on the shares in force.

3. Interest is allowed on the withdrawal value of the shares in force. 4. Interest is allowed on the value of the shares in force as declared by the last report, plus all the dues paid in during the term.

5. Shares less than six months old do not participate in the profits. 6. Interest is allowed on the value of the shares in force as declared by the last report plus one-half the dues paid in during the term.

7. Interest is allowed on all the dues paid in on the shares in force for one-half the time they have been invested.

S. After the legal rate of interest has been deducted from the total profits, the remainder of the profits is divided in proportion to the amount of dues paid in during the term.

9. Profits arising from withdrawals are divided equally among the shares of the respective series from which the shares were withdrawn. 10. After the legal rate of interest has been deducted from the total profits the remainder of the profits is divided as follows: All shares in force at last report receive an equal part, while shares three months old receive one-fourth as much as shares one year old, shares six months old receive one-half as much as shares one year old, etc.

11. Shares less than three months old are not allowed any part of the profits.

12. This variation of the rule is made by some national associations: After the interest has been deducted from the total profits the remainder of the profits is divided among all the shares in force, in proportion to the amount of dues paid into the loan fund during the term. 13. Each series except the last is given interest at the legal rate upon the value of the shares in force as declared by the last report; the first series is then given credit for all the interest paid during the term on loans made prior to the issuing of the second series. The first and second series together are given credit for all the interest paid during the term on loans made during the existence of the second series and prior to the issuing of the third series, the apportionment being made. equally to the shares in each; and so on for any number of series. The remainder of the profits is divided equally among all the shares in force.

14. A fixed rate of interest is allowed on the value of all shares in force as declared at the last report. This interest is deducted from the profits and the remainder divided among all shares three months old or over, in proportion to the amount of dues paid in during the term.

The number of associations operating under this plan and its variations is as follows:

LOCAL.-Arkansas, 1; California, 32; Colorado, 4; Delaware, 6;

Florida, 3; Georgia, 1; Illinois, 34; Indiana, 4; Iowa, 1; Kansas, 6; Kentucky, 5; Louisiana, 8; Michigan, 1; Minnesota, 2; Mississippi, 2; Missouri, 9; Montana, 3; Nebraska, 5; New Jersey, 41; New York, 8; Pennsylvania, 63; Tennessee, 15; Virginia, 1; West Virginia, 1; total local associations, 256.

NATIONAL.-Kentucky, 1; total national associations, 1.

PLAN 3.

1. To the value of all the shares in force as declared by the last report add one-half the dues paid in during the term.

2. Divide the profits for the term by this sum for the rate per cent of profit.

3. To the value of each share as declared by the last report add onehalf the dues paid in during the term and multiply the sum by the rate per cent of profit, for the profit of each share.

4. To the value of each share as declared by the last report add the dues paid in on the same during the term and the profit of each share, for the present value.

Using the same data as in the previous illustrations the result is as follows:

$38.87 x 500
$25.27 × 600
$12.32 x 400-

ILLUSTRATION.

$19, 435, value of first series at last report.
$15, 162, value of second series at last report.
$4,928, value of third series at last report.

$39, 525, value of all series at last report.
$12 2 × 2,000 $12,000, one-half the dues paid during the year.
$39,525+ $12,000 $51, 525, total dividend bearing capital.
$3,000, the profits for the term, $51, 525
($38.87 + $6) × .058224 = $2. 61, profit of a
($25.27 + $6) × .058224=$1. 82, profit of a share of the second series.
($12.32 + $6) × .058224 = $1. 07, profit of a share of the third series.
$6 × .058224= $0. 35, profit of a share of the fourth series.

5.8224, the rate per cent of profit. share of the first series.

$38. 87, previous value, + $2. 61, profit for term, + $12, dues, = $53. 48, present value of a share of the first series.

$25. 27, previous value, +$1. 82, profit for term, + $12, dues, = $39. 09, present value of a share of the second series.

$12. 32, previous value, + $1. 07, profit for term, +$12, dues, = $25. 39, present value of a share of the third series.

$0.35, profit for term, + $12, dues, $12.35, present value of a share of the fourth

series.

The above rule is known in some sections of the country as the third dividend rule. It is varied by different associations in the following

manner:

1. To the value of all the shares in force as declared by the last report add one-third of the dues paid in during the term for the dividend bearing capital.

2. To the value of all the shares in force as declared by the last report add two-thirds of the dues paid in during the term for the dividend

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