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in 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.

:) What is the rebate of 7951. 11s. 20. for 11 months, at 6 per cent. per annum?

m. m. 6. S.
As 12 : 6 :: 11 : 5 10

100 0.
Amount 105 10
As 105 10 : too :: Link s d.

5 11 2 : 754 1 8
{ s. d.
795 11 2
- 754 18 présent worth. n.

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. 20. 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 per cent ?

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 ? ans. 15,28,5 mills.

6 What i

.

t 6 What is the present worth of 100l. one halt payalile at - 4 months, and the other at 8 months; discount at 5 per cent?

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

· answer 112,50.

FQUATION.
UN QUATION is the method of reducing several stated

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

Lis: 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 equated 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 50l. 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 2

50X2-100
50 X450

. . .1100)3 00

i answer '3 M. -,2 A merchant has owing to hinx 3001. to be paid as fola

Eows, 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 payınent of the whole, and wish to know the time ? ;.;

answer 6 months,

:.4C owes D a sum of money, which is to be discharged, viz. ] at 2 months, I at 4 inonths, 4 at 6 months, and 1 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 ? C

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

BARTER.

DARTER is the exchanging of one commodity for ar-
other, by duly proportioning their quantities and values. '

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

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4 A has 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. t : 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 to. baceo, 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. 19921b.

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 20cts. per pound, how much cotton must B give A ?

answer 1120lb. 9 K has 75 sheep at 145. 6d. 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. 49t.

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. 4027 11 B delivered 3 hogsheads of brandy at 6s. 8d. per gal. lon, to C, for 126 yards of cloth ; what was the cloth per yard ?

answer 10s. 12 C has candles at 12s. per dozen, ready money, but in barter he will have 13s. per dozen, D has cotton at 18d. per .pound, ready money; what price must the cotton beatiu 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 bar. ter Is. B has 3610lb. of sugar at 7d.per 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 Od, and 1867 ells.

14 Two merchants barter; A receives 20 Cưt. of cheese, at 218. 6d. per Cwt. B eight pieces of linen, at 31. 14s, per piece; which of them must receive money, and how much?

Sie answer A 8l. 2s. 15 If 24 yards of cloth be given for 5C. Igr. of tobacco, at 11. 18s. per Crt. what is the cloth rated at per yard?

answer: 8s. 3d.. 16 A barters 40 yards of cloth at 7s, 4d. per yard, with B for 28şib. of tea, at 11s. 6d. per pound; which must pay , balance, and how much?

answer A ll. 145. 5d.. 17 A has 7Cwt. of sugar, ati 8d. per pound, for which B gave him 12Cwt. of cheese; what was the cheese rated at per pound ?"

in answer 4d.i. 18 What quantity of sugar at 8d. per lb. must be given in barter for 20 Cwt. of tobacco, at sl. 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 1-2s, 6d. query the prime cost of the coffee?

..answer 3s. 4d. 20 A and B barter ; A has 12_Cwt. of hops, at 21. 1657 per Cwt. but in barter insists on 31. B has wine worth 58. å 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

answer 201. 125. 6d.

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NI

LOSS AND GAIN.
I OSS and Gain is a method of computing the profit or
LA loss on the purchase or sale of goods, &c.

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

EXAMPLES. 1 Bought 1-8C. of iron, at 28s, per hundred, and retailed t at 3da per pound; what is gained by the whole P .

and C. s. C. de Seating intern a

e If 1 : 28 :: 18:25 4Prime costa
de 18C. 5 20161b. at 3d.d=291. 8s. sold for

291. 88.251. 454. 45. answera

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