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The interest on all the sums, to the times of payment, is equal to the interest of $1 for 48 months. But 48 is equal to the sum of all the products which arise from multiplying each sum by the time at which it becomes due: hence, the sum of the products is equal to the time which would be necessary for $1 to produce the same interest as would be produced by all the sums.

Now, if $1 will produce a certain interest in 48 months, in what time will $6 (or the sum of the payments) produce the same interest

. The time is obviously found by dividing 48, (the sum of the products,) by $6, (the sum of the payments.)

Hence, we have the following

RULE.

Multiply each payment by the time before it becomes due, and divide the sum of the products by the sum of the payments : the quotient will be the mean time.

2. B owes A $600: $200 is to be paid in two months, $200 in four months, and $200 in six months : what is the mean time for the payment of the whole ?

We here multiply each sum by the time at which it becomes due, and divide the sum of the products by the sum of the payments.

OPERATION. 200x2= 400 200 X4= 800 200x6=1200 600 )24|00

4 Ans. 4 months.

3. A merchant owes $600, of which $100 is to be paid in 4 months, $200 in 10 months, and the remainder in 16 months : if he pays the whole at once, at what time must he make the payment?

Ans. months. 4. A merchant owes $600 to be paid in 12 months, $800 to be paid in 6 months, and $900 to be paid in 9 months : what is the equated time of payment.

Ans. 8mo. 22 Ada.

5. A owes B $600; one-third is to be paid in 6 months, one-fourth in 8 months, and the remainder in 12 months : what is the mean time of payment? Ans. 9 months.

6. A merchant has due him $300 to be paid in 60 days, $500 to be paid in 120 days, and $750 to be paid in 180 days: what is the equated time for the payment of the whole ?

Ans. 1371 days. 7. A merchant has due him $1500; one-sixth is to be paid in 2 months; one-third in 3 months; and the rest in 6 months: what is the equated time for the payment of the whole ?

Ans. 4 months. Note. If one of the payments is due on the day from which the equated time is reckoned, its corresponding product will be nothing, but the payment must still be added in finding the sum of the payments.

8. I owe $1000 to be paid on the 1st of January, $1500 on the 1st of February, $3000 on 1st of March, and $4000 on the 15th of April : reckoning from the 1st of January, and calling February 28 days, on what day must the inoney be paid ?

Ans. Payment in 671% days, or on the 8th March. Q. What is Equation of Payments? What is the sum of the products which arise from multiplying each payment by the time to which it becomes due equal to? How do you find the mean time of pay. ment? When you reckon the time from the date at which the first payment becomes due, do you include the first payment ?

FELLOWSHIP.

$ 167. Fellowship is the joining together of several persons in trade with an agreement to share the losses and profits according to the amount which each one puts into the partnership. The money employed is called the Capital Stock.

The gain or loss to be shared is called the Dividend.

It is plain that the whole stock which suffers the gain or loss must be to gain or loss, as the stock of any individual to his part of the gain or loss.

Hence, we have the following

RULE.

As the whole stock is to each man's share, so is the whole gain or loss to each man's share of the gain or loss.

Q. What is Fellowship? What is the gain or loss called ? What is the rule for finding each one's share ?

EXAMPLES.

{0}:

}:: £32 :

{ flå B's share:

1. A and B buy certain merchandise amounting to £160, of which A pays £90, and B £70: they gain by the purchase £32: what is each one's share of the profits?

A.. £90
B.. £70

£18 A's share.
£160 :

70 2. A and B have a joint stock of $2100, of which A owns $1800 and B $300: they gain in a year $1000: what is each one's share of the profits ?

Ans. A's=$857,14+; B's=$142,85+. 3. A, B, C and D have £20,000 in trade: at the end of a year their profits amount to £16,000: what is each one's share, supposing A to receive £50 and D £30 out of the profits for extra services?

A's=£4030; B's =£3980;

C's=£3980; D's=£4010. 4. Five persons, A, B, C, D and E have to share between them an estate of $10,000: A is to have onefourth; B one-eighth; C one-sixth; Done-eighth; and E what is left: what will be the share of each? Ans. A's=$2500; B's=$1250; C's=$1666,66+;

D's=$1250; E's=#3333,34.

Ans. { Cs=£3980

PROOF.

Add all the separate profits or shares together, their sum should be equal to the gross profit or stock.

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DOUBLE FELLOWSHIP. $ 168. When several persons who are joined together in trade employ their capital for different periods of time, the partnership is called Double Fellowship.

For example, suppose A puts $100 in trade for 5 years; B $200 for 2 years, and C $300 for 1 year: this would make a case of double fellowship.

Now it is plain that there are two circumstances which should determine each one's share of the profits: 1st, the amount of capital he puts in ; and 2ndly, the time which it is continued in the business.

Hence each one's share should be proportional to the capital he puts in, multiplied by the time it is continued in trade. Therefore we have the following

RULE. Multiply each man's stock by the time he continues it in trade : then say, as the sum of the products is to each particular product, so is the whole gain or loss to each man's share of the gain or loss.

Q. What is Double Fellowship? What two circumstances determine each one's share of the profits ? Give the rule finding each one's share?

EXAMPLES.

1. A and B enter into partnership: A puts in £840 for
4 months, and B pu in £650 for 6 months: they gain
£300: what is each one's share of the profits ?
A's stock £840 X4=3360
B's stock £650 x 6=3900

£ S d
£7260 :
3360

$ 138 16 10

39001: : £300 : 3161 2. A put in trade £50 for 4 months, and B £60 for 5 months: they gained £24: how is it to be divided between them? Ans. A's share=£9 12s; B's=£14 8s.

3. C and D hold a pasture together, for which they pay £54: C pastures 23 horses for 27 days, and D 21 horses for 39 days: how much of the rent ought each one to

Ans. C, £23 5s 9d; D, £30 14s 3d.

pay?

TARE AND TRET.

§ 169. Tare and Tret are allowances made in selling goods by weight.

Draft is an allowance on the gross weight in favour of the buyer or importer: it is always deducted before the Tare.

Tare is an allowance made to the buyer for the weight of the hogshead, barrel or bag, &c., containing the commodity sold.

Gross Weight is the whole weight of the goods, together 'with that of the hogshead, barrel, bag, &c., which contains them.

Suttle is what remains after a part of the allowances have been deducted from the gross weight.

Net Weight is what remains after all the deductions are made.

Q. What are Tare and Tret? What is Draft? What is Tare ? What is Gross Weight? What is Suttle? What is Net Weight ?

EXAMPLES.

1. What is the net weight of 25 hogsheads of sugar, the gross weight being 66cwt. 3qr. 141b.; tare 11lb. per hogshead?

cut. qr. Ib.

66 3
25 X11=27516. 2 1 23 tare.

Ans. 64 1 19 net.

14 gross.

2. If the tare be 416. per hundred, what will be the tare on 6 T. 2cwt. 3qr. 1416.? Tare for 6 T. or 120cwt.=48076.

2cwt.= 8
3qr.

3
14 16. 01
Tare

. 4911 Ans. 4cwt. lqr. 15418.

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