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TO DISCOUNT BILLS.

To discount a bill means to procure cash for it before it becomes due.

RULE. Find how long the bill has to run, reckoning from the day it is discounted to the day it is payable, adding three days of grace, the interest calculated for this time will give the discount, which, deducted from the bill, will leave the proceeds.

1. Find the proceeds of a bill for £1158, dated 24th May, at 3 months, discounted 6th June, at £5 per cent.? Ans £1144, 19s. 10ąd. zz.

2. Find the proceeds of a bill for £478, 14s., dated 3d January, at 6 months, discounted 20th May, at £4 per cent.? Ans. £475, 188.6 d. §.

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To find the true discount and present value in cash of any sum.

RULE 1.-As the amount of £100 for the given rate and time is to the interest of £100 for that time :: so is the given sum: to the discount.

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2. As the amount of £100 for the given rate and time : is to £100 :: so is the sum : to the present worth.

1. Find the discount of £62, 15s., payable 10 months hence, at £41 per cent. per annum. Ans. £2, 5s. 4 d..

2. Find the discount of £1000, due 70 days hence, at £5 per cent. per annum. Ans. £9, 9s. 10d. 406

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3. Find the present worth of £700, due 18 months hence, at £2 per cent. per annum. Ans. £674, 13s. 11d.79.

4. Find the present worth of £842, 5s., due 350 days hence, at £5 per cent. per annum. Ans. £803, 14s. 5d..

PROFIT AND LOSS.

By profit and loss merchants are directed to rate their goods so as to gain or lose so much per

cent.

I. To find the profit or loss per cent.

RULE. As the prime cost is to the profit or loss on it so is 100: to the profit or loss per cent.

1. Bought cloth at 12s. per yd., and sold it for 13s. 6d., what did I gain per cent.? Ans. £12, 10s. 2. Bought linen at 2s. 10d. per yd., and sold it for 3s. 4d., what did I gain per cent.? Ans. £17, 12s. 111d..

3. Bought tea at 13s. 6d. per lb., and sold it for 9s. 6 d., what was my loss per cent.? Ans. £29, 38. 4d.

4. How much per cent. is 3d. per shilling? Ans. £29, 3s. 4d.

II. To find the selling price at a given rate per cent. profit or loss.

RULE. AS 100 is to 100 with the rate per cent. added in case of gain, or subtracted in case of loss :: so is the prime cost to the selling price.

1. Bought cloth at 12s. per yd., how must I sell it to gain £12 per cent.? Ans. 13s. 6d.

2. Bought cloth at £1 per yd., how must I sell it to gain £17, 10s. per cent. Ans. £1, 3s. 6d.

3. Bought tea at 13s. 6d., at what rate must I sell it to lose £29, 3s. 4d. per cent.? Ans. 9s. 6åd.

4. Bought a firkin of butter at 1s. per lb., at what rate must I sell it to gain £29,3s. 4d. per cent.? Ans. 1s. 3§d.

III. To find the prime cost, at a given rate per cent., profit or loss.

RULE. AS 100 with the rate per cent. added or subtracted is to 100 :: so is the selling price : to the prime cost.

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1. If I gain £12 per cent. by selling cloth at 138. 6d. per yd., what was the prime cost? Ans. 12s. 2. If I gained £17, 10s. per cent. by selling cloth at £1, 3s. 6d. per yd., what was the prime cost? Ans. £1.

3. Lost £29, 3s. 4d. per cent. on tea, which I sold at 9s. 6d. per lb., what was the prime cost? Ans. 13s. 6d.

4. Gained £29, 3s. 4d. per cent. by selling butter at 1s. 3 d. per lb., what was the prime cost? Ans. 1s.

IV. To find the rate per cent. of one selling price, when another selling price and its rate per cent. is given.

RULE. As the price whose rate per cent. is given: is to 100 with the given rate added or subtracted : : so is the other selling price: to a fourth number, which is greater or less than 100 by the profit or loss.

1. By selling cheese at 5s. 9d. per stone, I gained £15 per cent., what did I gain per cent. by selling it at 6s.? Ans. £20.

2. By selling cloth at 12s. 9d. per yd., I gained £6, 5s. per cent., what did I gain per cent. by selling it at 13s. 6d.? Ans. £12, 10s.

3. By selling muslin at 5s. 10d. per yd., I lost £16 per cent., how much will I gain or lose per cent. by selling it at 6s. 3d.? Ans. £10 loss.

4. By selling tea at 10s. 6d. per lb., I gain £15 per cent., what shall I gain or lose by selling it at 9s.? Ans. £1, 8s. 6d. loss.

BARTER.

Barter teaches merchants to regulate the quantities of goods to be exchanged.

RULE. Find the value of the given commodity, and then find what quantity of the other that value will pur

chase.

NOTE. When the quantities of the goods to be exchanged are of unequal values, the balance is generally paid with money.

1. How much cloth at £1, 3s. 4d. per yd. should be given in barter for 9 cwt. 3 qr. 8 lb. of sugar at 10 d. per lb.? Ans. 41 yd. 1 qr.

2. How much cloth at 18s. per yd. should be given for 33 pipes of wine at £28, 10s. per pipe? Ans. 1045 yd.

3. How much cloth at 14s. 10d. per yd. must be given for 51 lb. of candles at 83d. per lb. ? Ans. 2 yd. 2 qr.

4. How much tobacco at £1, 18s. per cwt. must be given for 24 yd. of cloth at 8s. 3 d. per yard? Ans. 5 cwt. 1 qr.

5. How much cheese at 51d. per lb. must be given for a piece of silver plate weighing 3 lb. 6 oz., at 8s. 8d. per oz.? Ans. 832 lb.

6. How much tea at 7s. 7d. per lb. must be given for 100 galls. of rum at 13s. 34d. per gall. ? Ans. 175 lb.

7. A has 41 yd. of cloth at 7s. 4d. per yd., which he barters with B for 28 lb. of tea at 11s. 6d. per lb.; what balance is due? Ans. £1, 1s. 4d. due by A.

8. Å has 120 yd. of cloth at 14s. 74d. per yd., for which B would give him 52 yd. at 12s. 3d. and the balance in money; how much money I will A receive? Ans. £55, 18s.

9. A has 174 lb. of fine soap at 73d. per lb., for which B would give him 90 lb. of double loafsugar at 1s. 3d. per lb.; what balance is due? Ans. 1d. due to B.

INVOLUTION.

Involution is the method of finding the powers of numbers.

RULE.-Multiply the given number by itself continually till the number of multiplications be 1 less than the index of the power to be found; the last product will be the power sought.

Evolution is the method of finding the roots of numbers.

TO EXTRACT THE SQUARE ROOT.

RULE.-Divide the given number into periods of two figures each, counting from the right in integers, and from the left in decimals; find the greatest square number contained in the left hand period, and place its root in the quotient; subtract this square from the said period,