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SECTION XII.

PERCENTAGE.

ART. 386. The terms Percentage and Per Cent. signify a certain allowance on a hundred; that is, a certain part of a hundred, or simply hundredths. Thus, the expression 6 per cent. signities 6 hundredths, (18,) 7 per cent., 7 hundredths, (TZT,) &c., of the number, or sum of money under consideration.

Note. The terms Percentage and Per Cent. are derived from the Latin per and centum, signifying by the hundred.

387. We have seen that hundredths are decimal expressions, occupying the first two places of figures on the right of the decimal point. (Arts. 311, 314.) Now, since percentage and per cent. signify hundredths, it is manifest that they can be expressed by decimals, as in the following

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OBS. 1. It will be seen from the preceding Table, that when the given per cent. is less than 10, a cipher must be prefixed to the gure expressing it in the same manner as when the number of cents is less than 10. (Art. 369. Obs. 1.)

QUEST.-386. What do the terms percentage and per cent. signify? What is meant by 6 per cent., 7 per cent., &c., of any number, or sum

When the given per cent. is more than 100, it must plainly require a mixed number to express it. (Art. 315. Obs. 2.)

2. Parts of 1 per cent. may be expressed either by a common fraction, or by decimals. Thus, the expression 17 per cent., is equivalent to .17625 percent. 3. The first two decimal figures properly denote the per cent., for they are hundredths; the other decimals being parts of hundredths, express parts of 1 per cent.

EXAMPLES.

1. Write 1 per cent., 2 per cent., 4 per cent., 6 per cent., 7 per cent., 8 per cent., in decimals.

2. Write 11 per cent.; 12; 14; 15; 16; 23; 65; 93.

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3. Write per ct.; ; ; ; ; ; ; ; ; ; ; ; ; 号;吾;言;舌 7 3.

4. Write 4 per ct.; 61; 71; 91; 12; 161; 115; 4004.

5. An agent collected $700 for a merchant, and received 5 per cent. for his services: how much did he receive?

Analysis. Since 5 per cent. is the same as 5, the agent must have received 15 of $700. Now of $700 is $788, which is equal to $7; and 5 hundredths is 5 times $7, or $35.

Operation. $700

.05

Since .05, we multiply the given number of dollars by .05, and it gives the answer in cents, which we reduce to dollars by pointing Hence,

$35.00 Ans. off 2 decimals. (Art. 372.)

388. To calculate percentage on any number, or sum of

money.

Multiply the given number or sum by the given per cent. expressed decimally; and point off the product as in multiplication of decimal fractions. (Art. 324.)

OBS. 1. It is important for the learner to observe, that the amount of money collected, is made the basis upon which the percentage is computed. That is, the agent is entitled to 3 dollars, as often as he collects 100 dollars, and not as often as he pays over 100 dollars, as is frequently supposed. For in the latter case he would receive only, instead of of the sum in question. This distinction is important, especially in calculating percentage on large sums.

QUEST.-387. How may per centage or per cent. be expressed? Obs. When the given per cent. is less than 10, how is it written? When more than 100, how? 388. How is percentage calculated? Obs. In collecting money, upon what basis is the per cent. calculated? If the per cent. contains a common fraction which cannot be expressed deci mally, how proceed?

2. Hence, if the per cent. contains a common fraction which cannot pressed decimally, first multiply by the decimal, then by the common 1 of the given per cent., and point off the sum of their products as above

6. What is 4 per cent. of $300?

Solution.-Expressed decimally, 4 per cent.=.042; (Art Obs. 2;) and $300.042=$12.60. Ans.

7. What is 3 per cent. of $256.25 ? 8. What is 2 per cent. of $437.63 ? 9. What is 24 per cent. of $138.432 ? 10. What is 6 per cent. of $145.13?

11. What is 7 per cent. of $1630.10?

12. A man borrowed $150, and paid 7 per cent. for the it: how much did he pay y?

13. A merchant bought goods amounting to $1825, an them so that he gained 12 per cent.: how much did he gai 14. A constable collected $862.56, and charged 5 per ce his services: how much did he receive; and how much d pay over?

15. What is 10 per cent. of $4020.50 ?

16. What is 8 per cent. of $1675?

17. What is 4 per cent. of $725 ?

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21. What is 83 per cent. of $100.25 ?

22. A farmer having 1500 sheep, lost 25 per cent. of t how many did he lose?

23. A merchant having $1960 on deposit, drew out 20 per of it how much had he left in the bank?

24. A merchant imported 1500 boxes of oranges, and 12 cent. of them decayed: how many boxes did he lose; and many had he left?

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32. A merchant bought a stock of goods amounting to $4565, and paid 3 per cent. for freight: what was the whole cost of his goods?

33. A man's salary is $2000 a year, and he lays up 371 per cent. of it: how much does he spend?

34. A youth who inherited $20000, spent 40 per cent. of it in dissipation: how much had he left ?

35. Two merchants embarked in business with $18250 capital apiece; one gained 20 per cent. and the other lost 20 per cent. the first year what was then the amount of each man's property?

36. Two men invested $10000 apiece in stocks; one lost 8 per cent., the other 6 per cent.: what was the difference of their loss? 37. What is the difference between 6 per cent. of $1040, and per cent. of $905?

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APPLICATIONS OF PERCENTAGE.

389. PERCENTAGE, or the method of reckoning by hundredths, is applied to various calculations in the practical concerns of life. Among the most important of these are Commission, Brokerage, the Rise and Fall of Stocks, Interest, Discount, Insurance, Profit and Loss, Duties, and Taxes. Its principles, therefore, should be thoroughly understood by every scholar.

COMMISSION, BROKERAGE, AND STOCKS.

390. Commission is the per cent. or sum charged by agents for their services in buying and selling goods, or transacting other business.

OBS. An Agent who buys and sells goods for another, is called a Commission Merchant, a Factor, or Correspondent.

391. Brokerage is the per cent. or sum charged by money dealers, called Brokers, for negotiating Bills of Exchange, and other monetary operations, and is of the same nature as Commission.

QUEST.-390. What is commission ? Obs. What is an agent who buys and sells goads for another usually called?

392. By the term Stocks, is meant the Capital of m institutions, as incorporated Banks, Manufactories, Railroa Insurance Companies; also, Government and State Bonds,

OBS. 1. Stocks are usually divided into portions of $100 each, called and the owners of these shares are called Stockholders.

2. The association or company thus formed, is called a corporation; strument specifying the powers, rights, and privileges invested in the tion, is called a charter.

393. The original cost or valuation of a share is cal nominal, or par value; the sum for which it can be sold real value.

OBS. 1. The rise or fall of Stocks is reckoned at a certain per cen par value. The term par is a Latin word, which signifies equal, or a equality.

2. When Stocks sell for their original cost or valuation, they are sa at par; when they sell for more than cost, they are said to be above p premium, or an advance; when they do not sell at cost, they are sa below par, or at a discount.

3. Persons who deal in Stocks are usually called Stock Brokers, o Jobbers.

394. The commission or allowance made to factors and b also the rise and fall of stocks, are usually reckoned at a vercentage on the amount of money employed in the trans or on the par value of the given shares. Hence,

395. To compute commission, brokerage, and the prem discount on stocks.

Multiply the given sum by the given per cent. expressed i mals, and point off the product as in Percentage. (Art. 388

OBS. The commission for the collection of bills, taxes, &c., also for or purchase of goods, varies from 24 to 12 or 15 per cent., and should be reckoned on the amount of money collected, or paid out, or employe

transaction.

The brokerage for the sale or purchase of stocks, varies from t cent., reckoned on the par value of the stock.

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QUEST.-391. What is brokerage? 392. What is meant by the term stocks? are stocks usually divided? 393. What is the par value of stocks? What the rea Obs. What is the meaning of the term par? When are stocks at par? When ab When below? 305. How do you compute commission, brokerage, &d. I

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