OF REBATE OR DISCOUNT.

Q. WHAT is Rebate or Discount?,

A. Rebate or Discount is when a sum of Money due at any time to cònre, is satisfied by paying so much present money as being put out to interest, would amount to the given sum in the same space of time.

Q. How is the operation performed?

A. 1. As 12 Months:

Are to the Rate per Cent,

So is the Time proposed:
To a fourth Number.

2. Add that fourth Number to 100%.

3. As that sum :

Is to the fourth number:

So is the given Sum:

To the Rebate.

4. Subtract the Rebate from the given Sum, and the Remainder is the present worth. Or thus,

-3. As that Sum:

Is to 1007:

So is the given Sum:

To the present Payment.

4. Subtract the present payment from the given Sum, and the remainder is the Rebate.

Q. How do you prove questions in Rebate?

A. Find the amount of the present Payment at the Time and Rate per cent given, and that will be equal to the given Sum.

EXAMPLES.

1. What is the Rebate of 7951 11s 2d for 11 months, at 6 per cent? Ans. 417 9s 5d 3qrs 1333.

1572

2. What is the present worth of 1617 10s for 19 months, at 5 per cent? Ans. 1491 13s cd 2.

3 Sold goods for 7957 11s 2d to be paid 4 months hence, what is the present worth, at 3 per cent? Ans. 7861 7s 8d!.

4 What is the present worth of 4000 months at 4 per cent? Ans. 38621 8s Odž.

payable in 9

5 How much ready money for a note of 187 due 15 months hence, at 5 per cent? Ans. 167 18s 1ed.

6. Suppose 810l were to be paid 3 months hence, allowing 5 per cent discount, what must be paid in hand? Ans. 800!.

If a Legacy of 1000 is left me July 24, 1776, to be paid on the Christmas-day following; what must I receive when I allow 6 per cent for present payment? Ans. 9751 3s ld.

8. Being obliged by a bond bearing date August 29, 1776, to pay next midsummer (which is leap year) 3261 what must I pay down, if they allow me discount after the rate of 8 per cent? Ans. 3051 16s 6d 4.

9. Sold goods for 310l to be paid at two three months (that is, half at three months, and the other half at three months after that) what must be discounted for the present payment at 5 per cent ? Ans 5l. 14s 7d.

10. Sold goods for 300l to be paid at three two months (that is, one third at 2 months, one third at 4 months, and one third at 6 months) what must be discounted for present payment at 4 per cent? Ans. 37 18s. 9d.

11. What is the present worth of 100l at 5 per cent payable at two four months? Ans. 977. lis 4d

12. I would know the present worth of 150l payable at three four months, at 5 per cent discount ? Ans. 1451 3s 9d4.

13. What is the present worth of 2001 at 4 per cent payable as follows, viz. 100l at two months; 50 at 3 months; and 50l at 5 months ? Ans. 1987 Os 6d.

Q.

OF EQUATION OF PAYMENTS.

THE COMMON WAY.

WHAT is Equation of payments?

A. When several sums of money, to be paid at different times, are reduced to one mean time for the payment of the whole, without loss to debtor or creditor, this is called Equation of payments.

Q. Wherein may the debtor or creditor be said to suffer loss; when the debt is paid?

A. 1. When one mean time is assigned for the payment of the whole debt, and the money is not paid till some time afterwards; then the debtor suffers loss by laying not only out of the principal, or sem due, but also the interest of that sum for the time of forbearance, at 3, or 4, or more per cent as they shall agree. Likewise, if the money be paid before it is due. then the creditor suffers loss by allowing so much per cent. by agreement, for the time of prompt pay

ment.

2. The loss to either party may be in redueing the screral times of payment to one, which is not the true equated time; and then if the payment be made after the true time, the creditor suffers loss, because he receives no ing terest for it; if the time agreed on be before the true time, then the debtor suffers loss, because he receives no interest for his early payment.

Q. How is the operation wrought?

A. Multiply each payment by its time, and divide the sum of all the products by the whole debt, the quotient is the equated time.

EXAMPLES.

1. A owes B 100l whereof 50l is to be paid at 2 months, and 501 at 4 months; but they agreed to reduce them to one payment, when must the whole be paid? Answer, three months.

2. A merchant hath owing to him 300l to be paid as follows; 501 at 2 months, 1007 at 5 months, and the rest at 8 months; and it is agreed to make one payment of the whole; I demand when that time must be? Ans. 6 months.

3. F owes H 1000l whereof 2001 is to be paid present, 400 at 5 months, and the rest at 10 months, but they agree to make one payment of the whole; I demand the equated time? Answer, 6 months.

4. K is indebted to L a certain sum which is to be discharged at 4 several payments, that is, at 2 months, at 4 months, at 6 months, and at 8 months; but they agreeing to make up one payment of the whole, the equated time is therefore demanded? Answer, 5 months.

5. H bought of X a quantity of goods upon trust, for which H was to pay of the debt every three months, till the whole should be discharged; but they afterwards agreed to pay the whole at one equated time; the time is demanded? Answer, 3 months.

6. W owes Z a sum of money, which is to be paid present, at 4 months, and the rest at 8 months. What is the equated time for the whole? Answer, 3 months.

7. P owes Q 420 which will be due 6 months hence; but P is willing to pay him 60 now, provided he can have the rest forborne a longer time; it is agreed on; the time of forbearance therefore is required ? An. 7 months. Note This question is in Reverse Proportion. See more of this

Rule in Decimals.

Q.

OF BARTER.

WHAT is Barter?

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A. Barter is the exchanging of one commodity for anether, and informs Merchants so to proportion their quantities, as that neither may sustain loss.

Q. How do you prove questions in Barter?

A. By changing the order of them.

EXAMPLES.

1 How much Sugar at 9d per lb. must be given in Barter for 6C of Tobacco, at 14d per lb.? Ans. 10C oqr 12lb.4.

2 What quantity of Tea, at 10s per lb. must be given in Barter for C. of Chocolate at 4s per lb. Ans. 44lb 12 oz. 1 8

3 How much Rice at 28s per Cwt. must be bartered for 8C of Raisins, at 5d per Ib? Answer 5C 3qrs. 91b112.

336

4 A and B bartered; A had 5C of Sugar at 6d per lb which he gave to B for a quantity of Cinnamon. at Os 8 per lb. I demand how much Cinnamon B gave A ? Answer 261b 4 oz.

5. B delivered 3 hhds. of Brandy. at 68 8d per gallon, to C for 126 yards of Cloth: What was the Cloth per yard? Ans. 10s.

6. A and B bartered: A had 12 C. of Sugar worth 4d per lb. for which B gave him 1C. of Cinnamon; I demand how B rated his Cinnamon per lb? Ans. 27d i qr. 138.

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7. A hath Linnen Cloth worth 20d an ell ready money; but in barter he will have 2s. B hath Broad Cloth worth 14s 6d per yard ready money, at what price ought the Broad Cloth to be rated in Barter? Ans. 17s 4d 3qrs. per yard.

8 A and B bartered: A had 41 Cwt. of Hops, at 30s per C. for which B gave him 207 in money, and the rest in Prunes, at 5d per lb. I demand how many Prunes B gave A, besides the 201? Ans. 17 C. 3 qrs. 4 lb.

9. C hath Candles, at 6s per dozen ready money; but in Barter he will have 6s 6d per dozen; D hath Cotton at 9d per lb ready money; I demand what price the Cotton must be at in Barter: also how much Cotton must be bartered for 100 dozen of Candles ? Ans. the Cotton is 9d 3qrs. per lb. in Barter, and 7C 0qr 161b of Cotton mast he given for 190 dozen of Candles.

OF LOSS AND GAIN.

Q. WHAT is Loss and Gain?

A. Loss and Gain is a rule which teaches merchants what they shall gain or lose in the sale of their goods, having the price that they bought them for, and the price for which they are to be sold both known. Q. How are the following questions proved?

A. Let them be varied.

EXAMPLES.

1 Bought 18C of Cheese, at 28s per C. which I sell out again at 3d per lb. what is the profit of the whole ? Ans. 4l 4s.

2 If I buy deals at 20d a-piece, and sell them again at 17d what shall I lose by 120 dozen? Ans. 187.

3 Hats bought at 4s a-piece, and sold again at 4s 9d what is the profit in laying out 1007? Ans. 187 15s.

4 Bought 19 Fother of Lead, at 14s per C. what is gained by the whole, sold at 4d per lb ? Âns. 4321 5s.

5 Bought 60 reams of Paper, at 15s per ream, what is the loss in the whole quantity, at 4 per cent? Ans. 17 16s.

6 Bought 7 tons of Wine, at 177 per hhd. which I sell again at is per pint: I demand the whole gain, and the gain per cent? Aus. 2291 12s whole gain; and 487 4s 8d 1qr 428 the gain per cent.

7. If I sell 500 Deals at 15d a-piece, & 91 per cent loss, what do I lose in the whole quantity? Ans. 21 16s 3d.

8 Bought 3 oxen for 247 10s which I sell again for 2s per stone; what ought the 3 oxen to weigh together, the hides and offal being the only clear gain? Ans. 245 Stone.

he

9 A Draper bought 100 yards of Broad Cloth, for which gave 56. I desire to know how he must sell it per yard to gain 197 in the whole? Ans. 15s per yard.

1 A Draper bought 100 yards of Broad Cloth for 561 I demand how he must sell it per yard, to gain 157 in laying out 100/? Ans. 12s 10d 2qrs

OF FELLOWSHIP.

Q. How many sorts of Fellowship are there?
A. Two: Single and Compound.

OF SINGLE FELLOWSHIP.

Q. What is Single Fellowship:

A. Single Fellowship is when the Stocks of each Partder continue for an equal term of time.