DISCOUNT.

Art. 151. DISCOUNT is an allowance made for the payment of any sum of money or debt, which is not on interest, before it is due; or it is the difference between any given sum or debt payable at some future time, and its present worth.

The present worth of any given sum or debt, payable at a future time without interest, is such a sum of money as would amount to the given sum or debt, if put on interest, at the time it becomes payable.

The interest of $1.00 for one year at 6 per cent. is .06 cents, and the amount is $1.06; hence, $1.00 is the present worth of $1.06 payable in one year without interest, and .06 cents is the discount.

Therefore, the present worth of any sum or debt, payable in one year and not on interest, is 188 of the sum or debt, and the discount is 18 of the sum. From the above illustrations we obtain the following rules.

RULE I. Make $1.00 the numerator of a fraction, and the amount of $1.00 at the given rate and time the denominator; multiply the given sum or debt by this fraction, the product will be the present worth.

RULE II. Make the interest of $1.00 at the given rate and time the numerator of a fraction, and the amount of $1.00 at the same rate and time the denominator; multiply the given sum or debt by this fraction, the product will be the discount.

1. When money is worth 6 per cent. a year, what part of any sum or debt, payable in 1 year, and not on interest, is the present worth? What part of the sum is the discount?

3. When money is worth 6 per cent. a year, what part of any sum or debt, due at the end of 9 months, and not on interest, is its present worth? What part of the sum is the discount?

5. When money is worth 7 per cent. a year, what part of any sum or debt, payable in 1 year, and not on interest, is the present worth? What part of the sum is the discount?

2. When money is worth 6 per cent. a year, what part of any sum or debt, payable in 6 months, and not on interest, is the present worth? What part of the sum is the discount?

4. When money is worth 6 per cent. a year, what part of any sum or debt, due at the end of 3 months, and not on interest, is its present worth? What part of the sum is the discount?

6. When money is worth 7 per cent. a year, what part of any given sum or debt, payable in 6 months, and not on interest, is its present worth? What part of

the sun is the discount?

7. Purchased goods to the amount of $1224, on a credit of 4 months; what discount must be allowed for present payment, when money is worth 6 per cent. a year?

Ans. 24 dollars. 8. A merchant purchased a quantity of goods for $250, cash, and sold them for $300, payable in 9 months, without interest; what did he gain, supposing the use of money to be worth 6 per cent. a year? Ans. $37.081+.

9. What is the present worth of three notes, one for $960, payable in three months; one of $640, payable in six months; and the other for $375, payable in nine months; supposing money to be worth 6 per cent. a year?

Ans. $1926.023+.

10. Purchased goods of a merchant in New York, to the amount of $1275, and gave him my note for the amount, payable in six months, without interest; what discount could the merchant in New York make for present payment, where money is worth 7 per cent. a year? Ans. $43.115+.

11. A merchant in Boston holds a note against a trader in Worcester, for $575.25, dated January 16th, 1847, payable in six months, without interest; what was the present worth of this note at the time it was dated?

12. Sold goods to the amount of $750; one half of the amount to be paid in three months, and the other half to be paid in six months; what discount can I make for present payment, when money is worth 6 per cent. a year?

13. What is the difference between the interest of $775 for 18 months, at 6 per cent. a year, and the discount of the same sum for the same time?

14. A mechanic, having a carriage for sale, offered it for $750, cash, or $775, payable in 4 months, without interest; the purchaser chose the latter. Did the purchaser gain or lose by his choice, and how much?

15. A owes B $575, to be paid September 1st, 1848, without interest; but B wishes A to pay him April 1st, 1848, to which A agrees. What sum must A pay B, supposing the use of money to be worth 6 per cent. a year?

16. A manufacturer sold 10 bales of sheeting for $1260, on a credit of 6 months; what discount can he afford to make for present payment when the use of money is worth 6 per cent. a year?

The only correct principle of calculating discount is by the preceding rule; yet banks and merchants, in discounting notes, deduct the interest for the time, including 3 days of grace, for the discount.

BANK DISCOUNT.

Art. 152. THE bank discount of a note is the interest of the sum of money for which the note is given, from the time it is dated to the time when it will become due, including 3 days of grace.

It is customary in banks to compute the interest on every note for 3 days more than the time specified in the note. These 3 days are called days of grace, and it is not necessary that the note should be paid until the last day of grace, except when the last day happens to be a Sunday, or a holiday, as the 4th of July; then the note must be paid on the second day of grace.

The sum named in the note is called the face of the note. The avails, or present value, of a note discounted at a bank, is the sum of money received from the bank for the note; or it is the difference between the face of the note and the bank discount.

There are two kinds of notes discounted at banks. 1st. Notes given by one individual to another for property actu ally purchased; notes of this kind are called business notes, or business paper. 2d. Notes made for the purpose of hiring money of the bank. Notes of this kind are called accommodation notes, or accommodation paper.

Business notes are not usually on interest. The legal rate of discount is the legal rate of interest in the state in which the note is discounted.

1. What is the bank discount on a note of $600, for 30 days and grace, at 6 per cent. a year? Ans. $3.30.

2. What is the bank discount on a note of $750, for 60 days and grace, at 6 per cent. a year? Ans. $7.875.

3. A merchant of Boston purchased goods of a merchant in New York to the amount of $1275, and gave him his note, payable in ninety days and grace, for the amount; the New York merchant had the note discounted at a bank in New York, where the legal rate of interest is 7 per cent. What was the avails of the note, or what sum of money did he receive from the bank for the note? Ans. $1251.943+.

4. A merchant of Philadelphia sold a cargo of coal, containing 325 tons, for $1950, for which he received a note payable in six months, without interest; he immediately went to a bank and had this note discounted. What was the bank discount, and how much ready money did he receive for the cargo of coal?

5. A trader from the country purchased goods to the amount of $489.75 of a merchant in Boston, at his lowest cash prices. After purchasing the goods, the trader proposed to the merchant to give him his note for the amount, payable in 4 months, without interest. Yes, says the merchant, provided you will write the note for such an amount that the avails of the note shall amount to just $489.75, after I shall get it discounted at a bank. For what amount must this note be written ?

=

It is plain that the note must be given for such a sum as will leave $489.75 after the bank discount of it for 4 months and 3 days has been deducted from that sum. The interest of $1 for 4 months and 3 days, at 6 per cent. a year, is $.0205, and $1-$.0205 $.9795; and $489.75÷ $.9795 $500, the required amount of the note. Hence, to find the amount for which a note must be given, payable at any future time, which shall leave any required sum after deducting the bank discount for the time specified, we have the following

RULE. Find the bank discount of $1 for the specified time, including 3 days of grace; deduct this bank discount from $1; the remainder will be the present value of $1 payable at the future specified time.

Then divide the sum of money which you wish to obtain from the bank, by this present value of $1; the quotient will be the amount of the required note.

6. Suppose I wish to obtain from a bank $994.50 for 30 days and grace, when the rate of discount is 6 per cent. a year; for what amount must I give my note? Ans. $1000.

7. Suppose I want a loan from a bank in the city of New York, where the rate of discount is 7 per cent. a year, of $578.65 for 6 months; for what amount must a note be given to obtain this sum of money? Ans. $600.

8. A merchant sold 500 barrels of flour, and received a' note at 60 days and grace in payment; he went immediately to a bank and had the note discounted, and received $2968.50. What was the amount of the note?

9. A merchant sold a cargo of coal, and received a note at 90 days and grace in payment; he had this note discounted at a bank, and received $2953.50.

amount of the note?

What was the

PROFIT AND LOSS.

Art. 153. PROFIT and loss are mercantile terms used to express what is gained or lost by business transactions.

The profit or loss on mercantile transactions is usually estimated by the per centage of the first cost of the articles which is gained or lost in trade.

ILLUSTRATION.

1. Samuel purchased a sled for which he paid $1.50, and sold it at a profit of 10 per cent. ; how much did he get for his sled?

In order to make a profit of 10 per cent., he must sell it for the first cost, plus 10 per cent. of the first cost. 10 per cent. of $1.50 is .15 cents, and $1.50 +.15 is $1.65, the sum for which he sold the sled.

2. Purchased a sleigh for $20, and was under the necessity of selling it at a loss of 5 per cent. ; how much did I get for the sleigh?

It is plain that I must have sold it for the first cost, minus 5 per cent. of the first cost. 5 per cent. of $20 is $1, and $20-$1, is $19, the sum for which I sold the sleigh.

3. A farmer purchased a sheep for $4, and sold it at 124 per cent. profit; what did he get for the sheep?

5. A boy purchased a pair of skates for $1.25, and sold them to another boy at 10 per cent. profit; what did he get for his skates?

7. A man bought a lot of land for $500; he afterwards sold it at a profit of 15 per cent.; how many dollars did he gain?

9. A man purchased a house for $5000, and sold it at a profit of 5 per cent.; what number of dollars did he gain?

4. A trader paid $50 for a gold watch, and sold it at a loss of 4 per cent.; what did he get for the watch?

6. William purchased a knife for 50 cents, and sold it at a loss of 20 per cent.; how much did he get for his knife?

8. A man purchased a horse for $125, and sold him at a loss of 8 per cent.; how many dollars did he lose?

10. A broker purchased 10 shares in the Fitchburg Railroad for $1000, and sold them at 8 per cent. advance; what was his gain?

11. Bought a piece of cloth containing 36 yards, at $2.50 a yard, and sold it at $3.25 a yard; what was the whole gain? Ans. $27.

12. A merchant purchased 750 barrels of flour, at $5.75 a barrel, and the next day sold the same at $6.50 a barrel; how much did he gain? Ans. $562.50. 13. A man purchased a farm containing 175 acres, for $3500; he afterwards sold the same farm at $25 an acre ; what number of dollars did he gain? Ans. $875.