to $100, which makes it perfectly evident, that it is entirely wrong to suppose, that the interest and discount of any given sum, for any given rate and time, are the same.

3. What is the discount of $300, due 2 years hence, at 6 per cent.? Ans. $32,14,2m.

4. What is the discount of $595, due 2 years hence, at 7 per cent.? Ans. $73,07c.

5. What is the discount on $2000, due 4 years hence, at 7 per cent.? Ans. $437,50c.

6. What is the present worth of $600, due 4 years hence, at per cent.? Ans. $500.

7. What is the present worth of $500, due 2yr. and 8mo. hence, at 7 per cent.? Ans. $421,35c.

8. What is the present worth of a note, for $345,50c., due 10mo. hence, at 7 per cent.? Ans. $326,45,7m.

9. A merchant bought goods, amounting to $615,75c., at 6 months' credit, how much ready money must he pay, if a discount of 4 per cent. be allowed? Ans. $602,20c.

10. What is the difference between the interest of $1204, at 5 per cent., for 8 years, and the discount of the same sum, for the same time and rate per cent.? Ans. $137,60c.

NOTE. When sundry sums are to be paid at different times, you must find the present worth of each payment separately, and then add them into one sum.

1. What is the present worth of $2000, of which $500 are due in 6mo., $800 in lyr., and the balance, $700, in 3yr., at 6 per cent.? Ans. $1833,37,4m.

12. What is the present worth of $1600, one half due in lyr., and the other half in 2yr., at 7 per cent.? Ans. $1449,41,6m. 13. What is the present worth of $2000, one half due in 9 months, and the other half in 2 years, at 6 per cent.? Ans. $1849,79,6m,

NOTE: But when discount for the present payment of notes, obligations, &c., for money is made, without regard to time, it is then found precisely as the interest of the given sum for one year.

14. What is the discount of $476, at 6 per cent.? Ans. $28,56c.

15. What is the discount of $853, at 4 per cent.? Ans. $34,12c.

16. A merchant bought goods on credit, amounting to $1656, but by paying ready money he has a discount of 5 per cent. allowed, how much ready money must he pay? Ans. $1573,20a

LOSS AND GAIN

Q. What is Loss and Gain?

A. Loss and Gain teaches merchants and traders the knowledge of what is gained or lost in buying or selling goods, produce, &c.; and it also teaches them to raise or fall on the price of their goods, &c., so as to gain or lose so much per cent., &c.

EXPLANATIONS.

Loss and Gain is merely a particular application of the Rule of Three Direct, as was stated on page 168; and I wish you continually to bear in mind, that in the operation of all these rules, there is no new principle involved, but that the particular application of the fundamental rules, gives each rule its peculiar name.

RULE.

Q. How do you state and work the terms to find what is gained or lost per cent.?

A. You must first find what the gain or loss is by Substraction; that is, if the gain be required, substract the price it cost from the price for which it was sold, and the remainder, or difference, will show the gain on the sum first expended; and, if the loss be required, substract the price for which it was sold from the price which was paid for it, and the remainder

or difference will show the loss on the sum first expended. Then, as the price it cost is to the gain or loss, so is $100, or £100, to the gain or loss per

cent.

EXAMPLES.

1. A merchant bought coffee at 22c. a pound, and sold it for 33c. a pound, what did he gain per cent., or what did he gain in buying to the amount of $100, at that rate? Ans. $50, or 50 per cent.

11c., so is $100 to the given per cent. You will readily perceive, that the merchant, on the sale of one pound, gained half what it cost him, because 11c., the gain, is half of 22c., the cost; and, therefore, he must have gained $50 in buying to the amount of $100, as $50 is half of $100; and the gain on $100 must be in the same proportion as the gain on 22c.

2. A merchant bought a piece of velvet, at $2 a yard, and sold it for $1,50c., what did he lose per cent.? Ans. 25 per cent.

In this example, you first substract $1,50., the price for which one yard of velvet was sold, from $2, the price it cost; and then say, as $2 is to 50c., so is $100 to the loss per cent.

EXPLANATIONS.

$c.
2,00 bought
1,50 sold.

50

$ c. C. $ c.
2,00,50 :: 100,00

It is perfectly evident, that he lost 25 per cent., because 50c. is one fourth of $2, and $25 is one fourth of $100.

3. If a grocer buys butter, at 12c. a pound, and sells it at 16c., how much does he gain per cent.? Ans. 331 per cent.

4. A merchant bought 4 pieces of cloth, each piece containing 30 yards, at $1,25c. a yard, but on examining it he found one piece so badly damaged that he could not sell it, how much per yard must he sell the remainder to gain $10 on the whole? Ans. $1,77,7m.

RULE.

Q. How do you state and work the terms to find how a commodity must be sold, to gain or lose so much per cent.?

A. As $100, or £100, is to the price it cost, so is $100, or £100, with the profit added, or the loss substracted, to the gaining or selling price.

EXAMPLES.

1. If a merchant buys calico at 24c. a yard, how must he sell it a yard to gain 25 per cent.? Ans. 30c.

EXPLANATIONS.

To gain 25 per cent., is, as you will readily perceive, adding one fourth the given sum or cost to itself; and, therefore, as the third term is increased by the per cent. above the first term, so the fourth term, or answer, must increase above the second.

2. If a merchant buys wheat at 50c. a bushel, how must he sell it to gain 10 per cent.? Ans. 55c.

3. A merchant bought a piece of cloth, at $2 a yard, which proved to be not as good as he expected, and he is willing to lose 124 per cent., how must he sell it a yard? Ans. $1,75c.

4. A merchant bought a hogshead of molasses, at 50c. a gallon, which he found to be of an inferiour quality, so that he must lose 10 per cent., what will it then be a gallon? Ans. 45c

RULE.

Q. How do you state and work the terms to find what the commodity cost, when there is gain or loss per cent.?

A. As $100, or £100, with the gain per cent. added, or the loss per cent. substracted, is to the price, so is $100, or £100 to the first cost.

EXAMPLES.

1. If a merchant, by selling tea at 87c. 5m. a pound, loses $12,50c. per cent., what did it cost a pound? Ans. $1.

EXPLANATIONS.

In this example, you first substract $12,50c., the loss per cent., from $100; and then say, as $87,50c. is to 87c. 5m., the price for which it is sold, so is $100 to the price it cost.

$ c. c.m. $ c.
87,50,87,5 100,00
10000

87,5|0)875000 | 0(1,00,0 875

000

2. If a merchant, by selling cloth at $3 a yard, gains 20 per cent., what did the cloth cost a yard? Ans. $2,50c.

3. If a merchant, by selling broadcloth at $3,25c. a yard, loses 20 per cent., what did the cloth cost a yard? Ans. $4,06,24m. 4. A merchant sold 80lb. of chocolate at 25c. a pound, and gained 9 per cent., what did the whole cost him? Ans. $18,34,8m.

RULE.

Q. How do you state and work the terms, when, if commodities be sold at a given rate there is so much gained or lost per cent., to find what would be gained or lost per cent., if sold at another rate?

A. As the first price is to $100, or £100, with the profit per cent. added, or the loss per cent. substracted, so is the other price, to the gain or loss per cent., at the other rate or price.