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ILLUSTRATION. Suppose the dues to be 50 cents a share per month; the rate of interest paid by borrowers, 8 per cent; maturing value of shares, $100; the rate of earnings, 7 per cent; and profits divided annually.

Von-borrower's account.

$6.00

.21

6.21 3.00

9.21

First year's dues on one share.....
First year's dividend at 7 per cent on half the dues
Value of a free share at end of first year.,
Add half the dues paid the second year..
Amount on which dividend is reckoned the second year.
Second year's dividend.....
Valuo at end of first year..
Second year's dues....
Value of a free share at end of second year.....

Borrower's account-Loan of $100.
First year's dues on one share..
First year's interest on loan...

$0.64
6.21
6.00

12.85

$6.00 8.00

14.00

Total payments of dues and interest......
First year's dividend at 7 per cent on half of dues and interest
First year's dues .....

$0.49
6.00

Value of a share borrowed on at end of first year.
Add the interest paid the first year.......
Add one-half the dues and interest paid the second year.

6. 49 8.00 7.00

21. 49

Amount on which dividend is reckoned the second year.
Second year's dividend at 7 per cent...
Value at end of first year...
Second year's dues....

$1.50
6.49
6.00

Value of a share borrowed on at end of second year....

13.99 The number of associations operating under this plan is as follows: LOCAL.-Missouri, 1; total local associations, 1.

PLAN 19.

1. Give a fixed rate of interest to the various series in proportion to the amount of invested capital as determined at the previous month's apportionment.

2. Give the profits from withdrawals, premiums, and fines, etc., to the series which have furnished the money from which the profits have been made, taking into consideration, with each item of profit, the amount of money furnished by each series and the length of time for which it is furnished.

This rule is applicable only to associatious organized on the serial plan, time limit of series, gross premium fully earned, and monthly

3, 320

175

40

ILLUSTRATION,
Let there be three series of 1,000 shares each, series A being 24 months old, series
B 12 months old, and series C just issued. Let the invested capital at the beginning
of the month be $33,000 for series A and $15,000 for series B.

Let 108 months be the length of time each series is to run.
Fines on interest in arrears are counted as interest.

Fines on dues in arrears are credited to the respective series in which the dues were in arrears, as dues. Let the interest paid at end of month on invested capital, together with fines paid on interest in arrears, be......

$320 Let dues and fines paid on dues in arrears in series A at end of month be....

1,000 Let dues and fines paid on dues in arrears in series B at end of month bo.... 1,000 Let dues and fines paid on dues in arrears in series C at end of month be...

1,000 Total cash paid during the month (including interest on capital) Let $850 of this cash be used in withdrawing stock, as follows: Book value of 25 shares withdrawn from series A, at $33=$825; 16 shares from serios B, at $15=$240 Cash paid for the same by the association, at $26= 650; for withdrawals from series B at $12.50=200 The profit made from withdrawals

+ er $215 in all.

At the end of the month series A has yet to run 83 months; series B, 95 months; and series C, 107 months. Earned gross premium for loan of 83 months, stock of series A borrowed on, loan of

$1,000 =$210. Earned gross premium for loan of 95 months, stock of series B borrowed on, loan of

$1,000 = $240. Earned gross premium for loan of 107 months, stock of series C borrowed on, loan of

$1,000 = $270.

For simplicity of illustration, the matter of expense is not considered, but the expense is distributed in proportion to the total cash received during the month.

The interest and fines on interest in arrears received during tho month, and amounting to $320, are distributed to series A and B in proportion to tho invested capital of each series at the beginning of the month, series A thus receiving $220, and series B, $100. The cash contributions during the month were, therefore, as follows:

By series A $1,000 + $220 = $1,220.
By series B $1,000 + $100 = $1,100.

By series C $1,000.
The withdrawal profit, amounting to $215, is then divided in proportion to the
monthly contributions of each series, which gives a withdrawal profit of $79 to series
A, $71 to series B, and $65 to series C.

Profits arising from premiums are distributed thus:

1. For the loan of $1,000 for 83 months with stock borrowed on from series A, a gross premium of $210 was paid. The money furnished for this loan by the various series all remains for 83 months, so that in this case the question of time is eliminated and the distribution of the premium is the same as for profits on withdrawals. This gives $77, as series A's share of series A's premium; $70, as series B's share of series A's premium; and $63, as series C's share of series A's premium.

2. For the loan of $1,000 for 95 months with stock borrowed on from series B, a gross premium of $240 was paid. The money furnished by series A for this loan remaias only 83 months (as series A matures then), while the money furnished by series B and C remains for 95 months; therefore,

$1,220 for 83 months =$101,260, series A’s investment for one month.
$1,100 for 95 months=$104,500, series B's investment for ono month,
$1,000 for 95 months = $95,000, series C's investment for one month.

$300,760, total investment for one month.

The premium of $240 is then apportioned as follows:

$300,760 : $101,260 :: $240 : $81, series A's share of B's premium.
$300,760 : $104,500 :: $240 : $83, series B's share of B's premium.

$300,760 : $95,000 :: $240 : $76, series C's share of B's premium. 3. For the loan of $1,000 for 107 months with stock borrowed on from series (.. gross premium of $270 was paid. The money furnished by series A remains only 3 months, that furnished by series B, 95 months, and that by series C, 107 months: then, as before,

$1,220 for 83 months =$101,260, series A's investment for one month.
$1,100 for 95 months=$104,500, series B's investment for one month.
$1,000 for 107 months = $107,000, series C's investment for one month.

$312,760, total investment for one mouth. The premium of $270 is then apportioned as follows:

$312,760 : $101,260 :: $270 : $88, series A's share of C's premium.
$312,760 : $101,500 :: $270 : $90, series B's share of C's premium.
$312,760 : $107,000 :: $270 : $92, series C's share of C's premiam.

Series A. Series B. Series (". Value of series at, beginning of month.

$33,000 $15, 000 nothing Less book value of withdrawals ...

825

240 nothing

32, 175 14,760 nothing Amount of interest to each series ....

220 100 nothing Dues paid and fines on dues in arrears

1,000

1,00 Profits from withdrawals .....

79 Profits from premiums on loans of series A, 83 months...

70 Profits from premiums on loans of series B, 95 months ... 81 83 Profits from premiums on loans of series C, 107 months.. 88 90 Value of series at end of month

33, 720 16, 174 1.25 Number of shares in force at end of month

975 984 Valuo per share

34.58 16.43 1. The number of associations operating under this plan is as follows: LOCAL.-Colorado, 1; total local associations, 1.

1,000

PLAN 20.

From the net receipts for each series from the beginning, as shown at the previous apportionment, deduct the amount of withdrawals from the series during the term, and to this remainder add dues and entrance fees received for the series during the term. To find each series' share of interest and interest share of premium: First, find the dues' share of premium, or what profit has been made on loaning out dnes at a premium; and, second, the interest share of premium, or what profit has been made by loaning out interest received at a premium, by the following proportions: The amount of dues and interest received during the term is to the premium received during the term, as the amount of dues received during the term is to the dues' share of the premium; the amount of dues and interest received during the term is to the premium received during the term, as the interest received during the term is to the interest share of the premium.

Add the interest share of the premium to the interest received dur

the series: The amount of total receipts since beginning is to the amount of interest received and interest share of premium for the term, as the amount of A's receipts since beginning is to A's share of interest and interest premium; treating each series, B, C, etc., in the same way, to find their respective shares.

Add dues' share of premium and fines received during the term and divide among the series, as follows: The amount of dues received by all series during term is to the dues' share of premium and fines received during the term, as the amount of A's dues received during the term is to A's share; treating each series, B, O, etc., in the same way, to find their respective shares.

Expenses are divided among the series by the following proportions: The amount of total receipts from dues, interest, and interest share of premium during the term is to the total expense during the term, as the amount of A's receipts from dues, interest, and interest share of premium for the term is to A's share of expense; treating each series, B, C, etc., in the same manner.

Each series' net gain since last apportionment of profits is found by adding their respective shares of interest and interest share of premium and their dues share of premium and fines together, and taking from this result their share of expense and whatever incidentals there inay be, such as interest on withdrawals, etc. To this remainder add dues and entrance fees received during the term and each series' share of the profits for the value of the series.

The number of associations operating under this plan is as follows: LOCAL.-Colorado, 1; total local associations, 1.

PLAN 21.

1. A fixed rate of interest is given upon the value of the shares as declared by the last report plus the equated amount of dues paid during the term.

2. Profits arising from withdrawals are divided equally among the shares of the respective series from which the withdrawals took place.

3. The remainder of the profits is divided equally among all the shares.

To illustrate the rule, suppose that at the end of the second year of the existence of an association there were two series in force; first series, 100 shares, present value, $26; second series, 200 shares, present value, $12.40. At the beginning of the third year another series of 150 shares was issued. During the year a general profit of $569.50 was made, and, in addition, a withdrawal profit of $15 in the first series and 812 in the second series.

ILLUSTRATION.

$32.50, amount per

$26.00, previous value, + $6.50, equated amount of dues, share of first series entitled to interest.

$12.40, previous value, + $6.50, equated amount of dues, = $18.90, amount per share of second series entitled to interest.

$6.50, equated amount of dues, = amount per share of third series entitled to interest.

$32.50 x .06 = $1.95, interest on one share of the first series.
$18.90 x .06 = $1.13, interest on ono share of the second series.

$6.50 x .06 = $0.39, interest on ono share of the third series.
$1.95 x 100 = $195.00, interest belonging to the first series.
$1.13 X 200 $226.00, interest belonging to the second series.
$0.39 X 150 $58.50, interest belonging to the third series.

$479.50, interest belonging to all the series. $569.50 - $179.50 = $90.00, net profits due all the series. $90.00 - 450, shares in all series, = $0.20, profit per share. $15.00 --- 100, shares in first series, = $0.15, withdrawal profit per sharo in first series, $12.00 -- 200, shares in second series = $0.06, withdrawal profit per share in second

series. $26.00 + $1.95 + $0.20 + $0.15 + $12.00 = $40.30, value of a share in first series. $12.40 + $1.13 + $0.20 + $0.06 + $12.00 = $25.79, value of a share in second series. $0.39 + $0.20 + $12.00 = $12.59, value of a share in third series. The number of associations operating under this plan is as follows: LOCAL.-Louisiana, 1; total local associations, 1.

PLAN 22.

1. Multiply the total amount of interest collected by the average rate paid for premiums during the year and add the product to the interest collected.

2. Divide this sum among the shares in force in proportion to their previous values and the average amount of dues paid in during the year.

3. Deduct the premiums already apportioned from the total amount of premiums collected during the year and divide the remainder in proportion to the dues paid in during the year.

4. Divide the gross losses in proportion to the previous values of the shares and the average amount of dues paid in during the year.

5. From the sum of the profits gained on one share deduct the loss on the share for the net profits of one share.

The number of associations operating under this plan is as follows: LOCAL-California, 1; total local associations, 1.

PLAN 23.

This rule applies to some associations whose various series are divided into separate classes. For instance, the monthly series issued during the first year form class A; the monthly series issued during the seeond year form class B, etc.

The rule is as follows:

1. Profits arising from fines and transfer fees are credited to the shares in the class in which they occur.

2. Interest and premiums are distributed to the different classes in

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