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RULE.

As the amount of 1001. or dols. at the rate and time given,
Is to 100l. or dollars;
So is the whole debt,
To the present worth: (See case 5th Simple Interest.)

Subtract the present worth from the whole debt, and the remainder will be the rebate.

PROOF. Find the amount of the present worth for the time and rate proposed, which must equal the given sum. Note. Rebate, or Discount, is not the interest of the sum

due (as some mistake it,) but of the present worth. See example 7.

EXAMPLES. 1 What is the rebate of 7951, ils. 2d. for 11 months, at 6 per cent. per annum

m. £ m. 6. s. As 12 : 6 :: 11 : 5 10

100 0

Amount 105 10

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. $.

L. s. d. $
As 105. 10 : 100 795 11 2; 754 1 8

4. S. d.
795 11 2
754 18 present worth.

41 9 6 Rebate, answer. 2 What is the present worth of 430 dols. 67 cts. for 19 months discount at 5 per cent. ? answer 399,07 cts.

3 Sold goods for 7951. 11s. ad. to be paid 4 months hence; what is the present worth, at 3) per cent?

answer 7861. 7s. 8d. 4. What is the rebate of 1121. 12s. for 20 months, at 7

answer 111. 155. 3d. 5 Sold goods for 832 dols. one half to be paid at 3 months, and the other half at 8 months ; what must be discounted for present payment, at 5 per cent. ? uns. 15,28,5 mills. 6 What is the present worth of 100l. one half payable at 4 months, and the other at 8 months; discount at 5 per cent?

per cent ?

answer :971. 11s. Ad. 7 What difference is there between the interest of 500dola at 5 per cent. per annum, for 12 years, and the discount of the same sum, at the same rate, and for the same time?

answer 112,50.

1

EQUATION.
QUATION is the method of reducing several stated

times, at which money is payable, to one mean, or equated time.

RULE. Multiply each payment by its time, and divide the total of the products by the sum payable at the tiine required; the quotient will be the equaied time.

PROOF. The interest of the sum payable at the equated 'tiine, at any given rate, will equal the interest of the several pay ments for their respective times.

EXAMPLES 1 A owes B 1001. of which 5ol. are to be paid at 2 months, and 501. at 4 inonths, but they agree to reduce them to one payment; when must the whole be paid ?

50 X2=100
50 X4=0

1100)3 00

answer3 M. 2 A merchant has owing to hinx 3001. to be paid as folkows, viz. 501. at 2 months, 1001. at 5 months, and the restat 8 months, but it is agreed to make one payment of the whole; when will that time be? answer at 6 months.

3 F owes H 1000 dols.of which 200 dols. are to be paid present, 400dols. at 4 months, and the rest at 10 months, but they agree to make one payment of the whole, and wish to know the time?

anneer 6 months,

4 C owes D a sum of money, which is to be discharged, viz. 1 at 2 months, 1 at 4 inonths, 4 at 6 months, and at 8 months; but they agreeing to make one payment of the whole, the equated time is required ? answer 5 months.

5 E is indebted to F 240 dols, which by agreement is to be paid 5 months hence, but E is willing to pay him 40 dols. present, provided he will give him longer time to pay the remainder, which is agreed on; the time of payment is therefore required ?

answer 6 months.' 6 P owes Q 4201. which will be due 6 months hence, but P is willing to pay him 601. preserit, provided he can have the remainder foreborne a longer time, to which Q agrees ; the time of payment is required ? answer 7 months,

BARTER.

ARTER is the exchanging of one commodity for arr

RULE.

Work by the Rule of Three direct, or inverse, op by Practice, as the tenor of the question may require.

EXAMPLES.

C. qr:

1 How much sugar at 9d. per lb. should be bartered for s} Cwt. of tobacco, at' 14d. per

16.2 ib. d.

d.
As 1 : 14 :: 6.2 : 10192
d. lb.

d. C. gr. lb.
Then, As-9: 1 :: 10192 : 10 0.127 ansier.

Or, thus;

d per.lb.C.gr. d.per.lb.C.gr.lb. Inverse, If 14 : 6 2

9 10.0 12 9 What quantity of tea, at 10s, per lb. must be given for 1 Crt. of chocolate, at 4s. per lb. ? answer 441b. 12oz. +

3 How much rice, at 28s. per. Cwt. must be bartered for SIC. of raisius, at 5d. per lb. ? answer 50. 388. 9lb.

:

4 A hug linen cloth worth 20cts. an ell, ready money, but in barter he will have 25cts. B has broad cloth worth 2 dols. per yard, ready money; at what price ought the broad cloth to be rated in barter ?

answer 2,50cts. 5 Suppose C has tea at 8s. 6d. per lb. ready money, but in barter he will have 10s. per lb. D has tobacco worth 18d. per lb. ready money; how must he rate his tobacco

per

lb. to equal the tea in value ?

answer 1s. 9d.+ 6 A has nutmegs worth 1 dol. per pound, ready money, but in barter will have 106 cts, per pound, D has tobacco worth 10 cts. per lb. ready money; how must D rate his tobaceo, that his profits may be equivalent with A's ?

answer 106 mills. 7 A had 41 Cwt. of iron, at 30s. per Cwt. for which B gave him 201. in money, and the rest in pork, at 5d. per

lb. how much pork must be given besides the 201.? ans. 1992lb.

8 A has 320 dozen of candles, at 1,20cts. per dozen, for which B

agrees

to
pay

him 160 dols. in cash, and the rest in cotton at 2ucts. per pound, how much cotton must B give A:

answer 1120lb. 9 K has 75 sheep at 14s. 64. each, for which L is to give him 171. 12s. and the rest in Indian corn, at 3s. 6d.

. per bushel ; how much corn müst L give K? ans. 210bu. 4qt.

10 A and B bartered ; A had 5C. of sugar, at 6d. per pound, which he gave to B for a quantity of cinnamon, at 10s. 8d. per pound, how much cinnamon did B give A ?

answer 261b. 402 11 B delivered 3 hogsheads of brandy at 6s. 8d. per gallon, to C, for 126 yards of cloth'; what was the cloth per

answer 10s. 12 C has candles at 12s. per dozen, ready money, but in barter he will have 13. per dozen, D has cotton at 18d. per pound, ready money; what price must the cotton be atin bar. ter, and how

much must be bartered for 100 dozen of candles? answer the cotton at 19d., per pound, and 800lb. must

be given for 100 dozen candles. 13 A has linen at 10d. per ell, ready money, but in barter is. B has 3610lb. of sugar at 7d.jper lb. ready money, and will have of A 35l. in cash, and the rest in linen-; at "what rate is the sugar in barter, and how much linen must A give B? answer the sugar 9d. and 1867} ells.

14 Two

yard

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14 Two merchants barter ; A receives 20Cựt, of cheese,

Cwt. per piece; which of them must receive money, and how much?

answer A 8l. 2s. 15 If 24 yards of cloth be given for 5C. Iqr. of tobacco, at 1l. 18s. per Crt. what is the cloth rated at per yard?

answer 8s. 3d, 16 A barters 40 yards of cloth at 78. 4d. per yard, with B for 281ib. of tea, at 11s. 6d. per pound; which must pay balance, and how much?

answer A ll. 143. 5d. 17 A has 7Cwt. of sugar, at 8d. per pound, for which B gave

him 12 Cwt. of cheese ; what was the cheese rated at per pound?

answer 4d.. 18 What quantity of sugar at 8d. per lb. must be given in barter for 20 Cwt. of tobacco, at st. per hundred weight?

answer 16 Cwt. 8lb. 19 P has coffee which he barters with B at 10d per

lb more than it cost him, against tea, which stands Q in 10s. the lb. but puts it at 12s. 6d. query the prime cast of the coffee?

answer 3s. 4d. 20 A and B barter ; A has 12 Cwt. of hops, at 21. 16s per Cwt. but in barter insists on 3l. B has wine worth 5$ a gallon, which he raises in proportion to A's demand: on the balance, A received but a hhd. of wine ; what had he in ready money ?

ansuer 201. 12s. 6d

L

LOSS AND GAIN.

oss OSS and Gain is a method of computing the profit or loss on the purchase or sale of goods, &c.

RULE. Work by the Rule of Three, or by Practice, as the na ture of the question may require.

EXAMPLES. 1 Bought 18C. of iron, at 28s. per hundred, and retailech it at 3d.) per pound; what is gained by the whole ?

C.

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f 1 : 28 :: 18 : 25 4 Prime costa

18C.=20161b. at 3d.d=291. 88. sold for 291. 88.251. 45=4l. 48. answera

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