RULE.

Find the first year's amount by simple interest, which will be the principal for the second year; and the amount of this will be the principal for the third year, &c.

From the last amount, take the given principal, and the remainder will be the compound interest.

EXAMPLES.

What is the compound interest of 450%. for three years, at 5 per cent. per annum ?

answer £.70 18 75

2 What will 40pl. amount to in 4 years, at 6

per annum?

per cent. answer 5041 19s 9d.1 3 How much is the compound interest of 1280dols, for six years, at 5 per cent. per annum ? answer 435,32,2 1 13. 4 What will 500l. amount to in

per annum ?

5. What is the compound interest cent. per annum for 3 years?

4

years, at 44 per cent. answer 5901 11s 5d.4 of 400l 103. at 3 per answer 43 10s 94.4

REBTE, OR DISCOUNT.

RE EBATE, of Discount, is an abatement for the pay.

ment of money before due, by accepting so much, as would amount to the whole debt at the time payable, at a given rate.

RULE.

As the amount of 100%. or dols. at the rate and time given, Is to 10. 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.

PROOK

Find the amount of the present worth for the time and rate proposed, which must equal the given sum.

Note. Rebate, or Difcount, is not the intereft of the futa due (as fome mistake it) but of the prefent worth. See example 7.

EXAMPLES.

I What is the rebate of 7954 112 2d. for 11 months, at cent per annum?

6

per

41 9 6 Rebate, answer.

What is the present worth of 430dols. 6fets. for 19

months, discount at 5 per cent?

3 Sold goods for 795 115 2d. to hence; what is the present worth, at 3

399,07cts.

be paid 4 months per cent ?

answer 7861 75 8d.

4 What is the rebate of 112l 12s for 20 months, at 7

per cent ?

answer il 15s 3d. 5 Sold goods for 832dols. one half to be paid at 3 months, and the other half at 6 months; what must be discounted for answer 15,28,5 mills.

present payment, at 5 per cent ?

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? answer 971 11s 4d.

7 What difference is there between the interest of 500dol. 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

EQUATION.

EQUATION 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 time required : the quotient will be the equated time.

PROOF:

The interest of the sum payable at the equated time, at any given rate, will equal the interest of the several payments for their respective times.

EXAMPLES.

1 A owes B 100l. of which 50l. are to be paid at a months, and 50l. at 4 months, but they agree to reduce them to one payment; when must the whole be paid?

50X2=100
50X4=200.

100) 300

answer 3 M.

2 A merchant has owing to him 300l. to be paid as fol lows, viz. 50%. at 2 months, 100l. at 5 months, and the rest at 8 months, but it is agreed to make one payment of the whole; when will that time be? ans. at 6 months.

3 F owes H 1000dol. of which 200dol. are to be paid present, 400dol. at 5 months, and the rest at 10 months, but they agree to make one payment of the whole, and wish to know the time? ans. 6 months.

4 C owes D a sum of money, which is to be discharged, viz. at 2 months, at 4 months, 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 240dol. which by agreement is to be paid 5 months hence, but E is willing to pay him 4odol. prest sent, provided he will give him longer time to pay the mainder, which is agreed on; the time of payment is there fore required? answer 6 months. 6 Powes Q 420l. which will be due 6 months hence, but is willing to pay him 60l. present, provided he can have the remainder foreborne a longer time, to which Q agrees; tine of payment is required?

the

answer 7 months

B

BARTE R.

ARTER is the exchanging of one commodity for another, by duly proportioning their quantities and values.

RULE.

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

As I

per 1. should be Bartered får per lb.?

b. d. C.gr.

d.

14:6 2

10192

d. lb. d. C.gr. lb.

Then, As 9.1 :: 10192 15 O 12 answer

Or thus,

d per.lb.C.qr. d per.lb.G.gr.lb.

Inverse. If 14

62:9 10 0 12

2 What quantity of tea, at 10s. per lb. must be given for C.wt. of chocolate, at 4s. per 16? 3 How much rice, at 28s. per C.wt. 312. of raisins, at 5d. per lb.

ans. 44lb. 120x%. + must be bartered for ans. 5C, 3gr. glb.+

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 8 d. per 16. ready money, but in barter he will have os. per lb. D has tobacco worth 184. ready money; how must he rate his tobacco per lb. al the tea in value? answer is gd.4has 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 bacco, that his profits may be equivalent with A's?

answer 106 mills, 7 A had 41Ć. wt, of iron, at 30s. per C.. for which B gave him 20l. in money, and the rest in pork, at 5d. per lb. how much pork must be given besides the 201.? answer ib.

8 A has 320 dozens of candles, at 1,20 cts. per dozen, for which B agrees to pay him 16odols. in cash, and the rest in cotton at zocts, per pound, how much cotton must B give A? dnswer 1120lb.

9 K has 75 sheep at 14s 6d, each, for which L is to. give him 17 125. and the rest in Indian corn, at 38 6d. per bushel; how much corn must L give Kans. 210bu. 4gt.

10 A and B bartered; A had 5. 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 25lb. 462. 11 B delivered 3 hogsheads of brandy at 6 8d. per gallon, to C, for 126 yards of cloth; what was the cloth per yard?

answer 103.

12 C has candles at 125. per dozen, ready money, but in barter he will have 135. per dozen. D has cotton at 18d. per pound, ready money; what price must the cotton be at in barter, and how much must be bartered for 100 dozen of candles! answer the cotton at 19d. per pound, and 8e0fb. must be given for ico dozen candles. 13 A has kinen at 10d. the ell, ready money, but in barter is. B has 3610lb. of sugar a 7d. per lb. ready money, and will have of A 351. 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 18671 ells.