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Def. Fellowship is the Rule, by which the gain, loss, or liability in a joint concern may be equitably apportioned to each of the partners, according to the amount of their contributions to the general stock, or the advantages reaped by each from the concern. It is called Simple or Compound Fellowship, according as the times for which each partner has been engaged are the same or not.

I. TO DETERMINE THE AMOUNT OF GAIN OR LOSS BELONGING TO EACH

PARTNER IN A JOINT CONCERN, THE TIMES OF ENGAGEMENT OF ALL BEING THE SAME.

Rule. Find the ratio of the whole gain or loss to the whole stock and multiply by it each partner's stock. The result will be each partner's share.

EXAMPLE. A and B trade together, A puts into the general fund £1450 10s. Od. B puts in £2560 15s. Od.; they gain £1050 13s. Od. ; what is the share of each? A's stock... = £1450.5

4011,25)1050.650(.261926 B's stock...... = £2560.75

802250 Whole stock.. = £4011.25

248400 240675

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II. TO DETERMINE THE SHARE OF GAIN OR LIABILITY OF EACH PARTNER IN A CONCERN, ACCORDING TO THE NUMBER OF SHARES HELD BY EACH.

Rule. Divide the whole liability by the whole number of shares, and multiply the result by the number of shares, which each partner holds. The results are the liabilities or gains of each partner.

EXAMPLES. 1. A, B, C, purchase shares in a concern ; A pays for 8 shares, B for 12, C for 15; they gain £735 : 15:0; determine each partner's share of the gain.

Whole No. of shares = 8 + 12 + 15 = 35.

£. d.
17)735 15 0 = whole gain
35

2 15

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2. A and B rent a pasture for £70; A puts in 150 sheep, B 200 sheep, how much ought each to pay towards the rent?

No. of shares = 150 + 200 = 350
70

1
£

ニーよ = Rent belonging to 1 share 350

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111. TO DETERMINE THE SHARE OF GAIN OR LOSS BELONGING TO EACH

PARTNER IN A CONCERN, THE TIMES FOR WHICH EACH HAS BEEN ENGAGED NOT BEING THE SAME.

Rule. Express all the times and stocks in terms of the same unit, multiply each partner's stock by the units in the time; add the products ; divide the whole gain or loss by the sum, and multiply by each product separately. The results will be the shares required.

EXAMPLES 1. A, B, and C trade together; A advanced £850 for 12 months, B £1000 for 9 months, C £1500 for 6 months; they gain £1250; what is the share of each?

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IV. TO DETERMINE THE LIABILITY OF EACH PARTNER IN A CONCERN,

ACCORDING TO THE NUMBER OF SHARES HELD BY EACH, AND THE TIME FOR WHICH HE HAS HELD THEM.

Rule. Multiply the number of shares held by each, by the number of units in the time, (all the times being expressed in terms of the same unit;) add the products, and divide the whole liability by the sum; multiply the quotient by each product; the results will be the shares of each partner.

EXAMPLES. 1. Three persons rented a field for £68 : 10:0. A puts in 140 sheep for 14 days; B 160 sheep for 12 days; C 200 sheep for 8 days; what should each pay?

£. £. 140 X 14 = 1960

548,0)68.56.0125 160 x 12 = 1920

548 200 X 8=1600

1370 5480

1096

2740
2740

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TO FIND THE EQUITABLE TIME AT WHICH SEVERAL PAYMENTS DUE AT

DIFFERENT TIMES MAY BE ALL PAID AT ONCE.

Rule. Multiply each sum due (expressed in the same unit) by the number of units in the respective times (all expressed in the same unit), add the products, and divide by the sum of all the debts. The result will be the number of units in the equated time, the unit being that in which the times were expressed.

EXAMPLES. 1. Find the equated time at which the following debts may be paid : viz. £250 due in 7 months; £500 in 9 months; £250 in 12 months.

250 X 7=1750 £250
500 X 9= 4500 £500
250 X 12 = 3000 £250

Sum of products

=9250 £1000

- Sum of debts.

9250

=91. .: Equated time = 91 months.

1000 2. Find the equated time at which the following sums may be paid : viz. £347 : 11 : 6 due now, and £72: 5:6 to be paid every month for the next 12 months.

£347:11:6 = £347.575 £72: 5:6 = £72.275 12 X £72: 5:6 = £867.300

Sum of debts =£1214.875
Sum of products = (1+2+3+ &c. to 12 terms) X 72.275

= 78 x 72.275 = 5637.450.
1214.875)5637.450(4.648

4859 500

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Def. 1. Any income payable at stated periods is called an annuity.

Def. 2. Annuities to continue a fixed number of years are called annuities certain.

Def. 3. Annuities depending on the life or lives of individuals are called contingent or life annuities.

Def. 4. Annuities, to commence after the lapse of a certain time, are called deferred or reversionary annuities.

Def. 5. If the payment of an annuity is forborne for a certain number of years, the sum of the amounts of the payments at compound interest is the amount of the annuity.

Def. 6. The present value of an annuity is that sum, which put out at compound interest, would be sufficient to pay the annuity as it becomes due.

I.

TO FIND THE AMOUNT OF AN ANNUITY FORBORNE FOR ANY

NUMBER OF TERMS.

Rule. Find the ratio of the Compound Interest on £l for the given time to the interest for 1 term, and by it multiply the given annuity.

EXAMPLE Find the amount of an annuity of £50 : 10 : 6 forborne for 4 years at 5 per cent.

(1.05)4 – 1 Amount =

x 50.525 £.

.05 1.05

.05).2155963 = (Int. of £1.) 1.05

4.310126 525

52505 1050

21550630 1.1025000

215506 52011

8620

2155
11025000
1102500

£217.76911 = Amt. of annuity.
22050
5513

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II.

TO DETERMINE THE PRESENT VALUE OF AN ANNUITY TO LAST A

GIVEN NUMBER OF TERMS.

Rule. Find the compound interest of £l for the given time; divide this by the product of the amount of £l and the interest for 1 year; multiply the annuity by the quotient.

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