And D-558625-D.512-5-D.46 12c. 5m. =discount. Or, As D.1 09 amount of D.1 for the given time): D.1 :: D.50.27625 (= interest of the debt for the given time): D.46 125-discount, as above. And, D.558-625-D 46·125 D 512-5-present worth, as above. 3. Required the present worth and discount of D.4125 50c. at 6 per cent. per annum, due 18 months hence? D. c. m.

Ans. S present worth 3746 19 74 379 30 2/

discount

4. What ready money will discharge a debt of 13541. 8s due 3 years, 3 months, and 12 days hence, at 571. per cent. per annum? Ans. 1135 75. 9d.

BARTER

IS the exchanging of one commodity for another, and teaches traders to proportion their quantities without loss.

CASE I.

When the quantity of one commodity is given, with its value, or that of its integer, that is, of 1lb. Icwt. lyd. c. as also the value of the integer of some other commodity, to be given for it, to find the quantity of this; or, having the quantity thereof given, to find the rate of selling it.

RULE. Find the value of the given quantity by the concisest method, then find what quantity of the other, at the rate proposed, you may have for the same money: Or, if the quantity be given, find from thence the rate of selling it. Or, As the quantity of one article is to its price, so, inversely, is the quantity of the other to its price. Or, as the price of one article is to its quantity; so, inversely, is the price of the other to its quantity.

EXAMPLES.

1. How much tea at 9s. 6d per lb. must be given in barter for 156 gallons of wine, at 12s. 3 d. per gallon?

Galls.

2. How much cloth, at 15s. 8d. per yard, must be given for 5cwt. 3qrs. 19ibs. of steel, at 5 guineas per cwt.? Ans. 52yds. 3qrs. 2n. 3. Suppose A has 350 yards of linen, at 25c. per yard, which he would truck with B for sugar, at D.5 per cwt. How much sugar will the linen come to ? Ans. 17cwt. 2qrs.

4. A has broadcloths at D.44 per piece, and B. has mace, at D.1 42c. per lb.: How many pounds of mace must B give A for 35 pieces of cloth? Ans. 1084 lbs.

5. A has 7 cwt. of sugar at 12 cents per lb. for which B gaye him 12 cwt. of flour: What was the flour rated at per lb. ? Ans. 7c. 2m.

CASE II.

If the quantities of two commodities be given, and the rate of selling them, to find, in case of inequality, how much of some other commodity must be given. RULE. Find the separate values of the two given commodities; subtract the less from the greater, and the difference will be the amount of the third commodity, whose quality and rate may be easily found.

EXAMPLES.

1. Two merchants barter; A has 30cwt. of cheese, at 23s. 6d. per cwt. and B has 9 pieces of broadcloth, at 31. 15s. per piece: Which must receive money, and how much?

Ans. B. must pay A. £1 10s.

2. A and B would barter; A has 150 bushels of wheat, at D.1 25c. per bushel, for which B gives 65 bushels of barley, worth 62 c. per bushel, and the balance in oats at 37 c. per bushel: What quantity of oats must A receive from B? Ans. 391 bushels.

CASE III.

Sometimes, in bartering, one commodity is rated above the ready money price; then, to find the bartering price of the other, say,

As the ready money price of the one, is to its bartering price; so is that of the other, to its bartering price: Next, find the quantity required, according to either the bartering or ready money price.

EXAMPLES.

1. A has ribbands at 2s. per yard ready money; but in barter he will have 2s. 3d. B has broadcloth at 32s. 6d. per yard ready money; at what rate must B value his cloth per yard, to be equivalent to A's bartering price, and how many yards of ribband, at 2s. 3d. per yard, must then be given by A for 488 yards of B's broadcloth?

Ans. B's broadcloth, at .1 16s 6d. per yd. 7930 yds. ribband. 2. A and B barter; A has 150 gallons of brandy, at D 1 37 c. per gallon ready money, but in barter he will have D.1 50c.; B has linen at 44c. per yard ready money; how must B sell his linen per yard in proportion to A's bartering price, and how many yards are equal to A's brandy?

Ans. barter price is 48c. and he must give A 468 yds. 3qrs.

3. P and Q barter; P has Irish linen, at 60c. per yard, but in barter he will have 6c Q delivers him broadcloth at D.6 per yard, worth only D5 50c per yard: Pray which has the advantage in barter, and how much linen does P give Q for 148 yards of broadcloth?

As 60 645 50 5 86; therefore, Q by selling at D.6 has the advantage. Then,

4. A has 200 yards of linen, at 1s. 6d. ready money per yard, which he barters with B, at Is. 9d. per yard, taking buttons at 74d. per gross, which are worth but 6d. : How many gross of buttons will pay for the linen, who gets the best bargain, and by how much, both in the whole, and per cent. ?

Yd. d. Yds. d.

d. Gross d. Gross. Yd. d. Yds. £. As 1 21: 200: 4200. As 74: 1 :: 4200 : 560. As 1: 18 :: 200: 15 gr. d.

gr. £.

As 1: 6: 560: 14 value of B's goods.

£. As 14

[value of A's linen. So that B gains 11. of A. £. s. d.

£. £.

1: 100 7 2 10 per cent.

5. A has linen cloth, at 30c. per yard, ready money, in barter 36c. B has 3610 yards of ribband. at 22c. per yard ready money, and would have of A D 200 in ready money, and the rest in linen cloth; what rate does the ribband bear in barter per yard, and how much linen must A give B ?

Ans. The rate of ribband is 26c. 4m. per yard, and B must receive 1980 yards of linen, and D.200 in cash.

LOSS AND GAIN

IS an excellent rule, by which merchants and traders discover their profit, or loss per cent. or by the gross: It also instructs them to raise or fall the price of their goods, so as to gain or lose so much per cent. &c.

First see what the gain or loss is, by subtraction; then, as the price it cost, is to the gain or loss: so is 1001. to the gain or loss per cent.

Or, in federal money, annex two cyphers to the gain or loss, and divide by the cost for the gain or loss per cent.

EXAMPLES.

1. If I buy serge at 90c. per yard, and sell it again at D.1 2c. per yard: What do I gain per cent. or in laying out D.100 ?

Sold

⚫90

Sold for D.1.02 As 90: 12: 100: 13 per cent. gain, Ans.

Cost

Gain

Or, 1·02-9012-gain per yard; and

13 per cent. gain,

N. B. The first questions in the several cases, serve to elucidate each other.

2. If I buy serge at D.1 2c. per yard, and sell it again at 90c. per yard: What do I lose per cent. or in laying out D.100?

Cost

D. c.

D. c C. D. D. c. m.

1.02 As 1 02:12:: 100 11 76 5 per cent. loss, Ans. Sold for 90

12.00

Or,

Loss .12

--=11.765 per cent. loss, Ans. as before.

1.02

3. If I buy a cwt. of tobacco for 91. 6s. 8d. and sell it again at 1s. 10d. per lb. do I gain or lose, and what per cent.?

| 2d. | | 11 4 value at 2s. per lb. 0 18 8 gained in the gross,

As 9 6 8 18 8: 100: 10 Ans. 10 per cent. gain. 4. A draper bought 60 yards of cloth at D.4 50c. per yard, and 38 yards of cloth at D.2 50c. per yard, and sold them, one with another, at D 4 25c per yard: Did he gain or lose, and what per

which subtract from 98 yds. at D.4 25c.=416.50

5. Bought sugar at 64d per lb. and sold it at 21. 3s. 9d. per cwt. What was the gain or loss, per cent. ?

6. At 4s. 6d. in the pound profit: How much per cent.?

7. If I buy candles at Is 6d. per lb, and sell them again at 2s. per lb. and allow 3 months for payment: What do I gain per cent.? d. d. £ £. s. d. Mo. Mo..s

As 18: 24: 100: 133 6 8; then by discount, As 12:6:: 3:1 10 £. s. d. £. s. d.

£. s.

1 10 ::

£. s. Then, as 101 10 1331. 6s. 8d. leaves 1311. 7s.

133 6 8 1 19 4, which taken from 34d therefore, Ans. £.31 7s. 31d.

8. If I buy cloth at 13s per yard, on 8 months credit, and sell it again at 12s. ready money, do I gain, or lose, and what per cent.? Mo. £. Mo. £. f. S. £. s. d.

As 12 6: 8:4 As 104: 13 :: 100: 126: So that 13s. on 8 months credit at 61..per cent. is equal to 12s. 6d. ready money;

then,

s. d.

Prime cost 12 6 ready money,

Sold at

Lost

d. £.£. 6 :: 100:4

s d. As 12 6

12 0 ready money,

6 in the yard.

9. If I buy gloves at D.1 25c. per pair: How long credit must I have, to gain D.13 per cent. when I sell them at D.1 36c. per pair?

1.96 As 1:25:11: 100: 880 gain per cent. rdy. mo.

Sold at
Prime cost 1.25

D. D.c. D.c.

Then, 13-8.80=4.20 Now,
D. Mo. D c. Mo days.
As 6 12 :: 4·20: 8 12 Ans.

In casting up the amount of goods bought, imported or exported; to the prime cost of such goods we must add all the charges upon them, in order to fix the price they stand us in.

10. Suppose I import from France, 12 bales of cloth, containing 10 pieces each, which, with the charges there, amounted to D 360: I pay duty here 92c. per piece, for freight D 12 and portage D.1 25c.; What does it stand me in per piece, and how must I sell it per piece to gain D.10 per cent.

[per piece.

D.4.43 3 the price at which it must be sold

CASE