PERCENTAGE.

190. PERCENTAGE and Per Cent. are terms derived from per centum, meaning by the hundred.

Percentage is an allowance, at a certain rate, by the hundred.

The Rate per cent. is the rate of allowance by the hundred; as 1 per cent., or 1 hundredth.

The Basis of percentage is the number on which the percentage is reckoned.

Rates per cent. being hundredths may be expressed in the same manner as hundredths in decimal fractions. Thus, 5 per cent is written .05; 25 per cent., .25, &c.

When the rate per cent. is more than 100 per cent. it is expressed decimally as a mixed number. Thus, 103 per cent., equal to 188, is written 1.03.

When the rate per cent. is less than 1 per cent., or less than one hundredth, it may be often conveniently expressed as a complex decimal (Art. 180, Note). Thus, of 1 per cent. may be written .005, or .001; 12 per cent., .122, or .12, &c.

NOTE. The sign % is often used, in business, instead of the words per cent.

EXAMPLES.

Write decimally 2 per cent.; 3 per cent.; 5 per cent.; 6 per cent.; 7 per cent.; 8 per cent.; 10 per cent.; 12 per cent.; 15 per cent.; 25 per cent.; 30 per cent.; 40 per cent.; 50 per cent.; 60 per cent.; 75 per cent.; 100 per cent.; 105 per cent.; per cent.; 6 per cent.; 82 per cent.; 20 per cent.; 1 per cent.? of 1 per cent.; of 1 per cent.; cent.; of 1 per cent.

115

191. To find the percentage of any quantity.

of

of 1 per

Ex. 1. Bought a house for $625, and sold it at 6 per cent. advance; what did I gain by the sale? Ans. $37.50.

190. From what are the terms percentage and per cent. derived, and what the meaning? Define percentage. How is the rate written when more than 100? How when less than 1? If the per cent. is a fraction, or contains a fraction, what is the fraction, if expressed decimally?

Sum,

OPERATION.

Rate per cent.,

Per cent., or gain,

RULE.

$625

.06 $37.50

Since the rate is 6 per cent. or 18.06, we multiply the $625 by the decimal expression .06, and point off as in multiplication of decimal fractions.

· Multiply the given quantity or number by the rate per cent., expressed as a decimal, and point off the product as in multiplication of decimal fractions. (Art. 185.)

185

183-18

NOTE. If the per cent. contains a fraction that cannot be expressed in an exact decimal, or, if thus expressed, would require several figures, it is more convenient to multiply by it as a complex decimal.

10. Sent to Liverpool 5000 bushels of wheat, which cost me $1.25 per bushel; but 25 per cent. of the wheat was thrown overboard in a storm, and the remainder was sold at $2 per bushel; what was gained on the wheat? Ans. $1250.

11. T. Page received a legacy of $8000; he gave 19 per cent. of it to his wife, 37 per cent. of the remainder to his sons, and $2000 to his daughters; what sum had he remaining?

Ans. $2082.40.

12. My tailor informs me it will take 10 square yards of

cloth to make me a full suit of clothes. The cloth I am about to purchase is 12 yards wide, and on sponging it will shrink 5 per cent. in width and 5 per cent. in length. How many yards of the above cloth must I purchase for my "new suit"?

Ans. 6yd. 1qr. 1774na.

2527

13. A man having $10000, lost 15 per cent. of it in speculation; what sum had he remaining?

Ans. $8500.

191. Explain the operation for finding the percentage of any quantity. The reason for the process? The rule?

SIMPLE INTEREST.

192. Interest is an allowance made for the use of money, or for value received.

The Rate per cent. is the sum paid for the use of $100, 100 cents, 100 £, &c., for any given time, but usually for one year. The Principal is the sum on which the interest is computed. The Amount is the interest and principal added together. Legal Interest is the rate per cent. established by law. Usury is a higher rate per cent. than is allowed by law. The legal rate per cent. varies in the different States and in different countries.

In Maine, New Hampshire, Vermont, Massachusetts, Rhode Island, Connecticut, Pennsylvania, Delaware, Maryland, Virginia, West Virginia, North Carolina, Tennessee, Kentucky, Ohio, Indiana, Illinois, Iowa, Missouri, Arkansas, Mississippi, Florida, New Mexico, District of Columbia, and on debts or judgments in favor of the United States, it is 6 per cent.

In New York, New Jersey, Michigan, Wisconsin, Minnesota, Georgia, and South Carolina, it is 7 per

cent.

In Alabama and Texas, it is 8 per cent.

In California, Oregon, Nevada, and Colorado, it is 10 per cent. In Louisiana, except bank interest, it is 5 per cent.

In Canada, Nova Scotia, and Ireland, it is 6 per cent.

In England and France, it is 5 per cent.

NOTE. The legal rate, as above, in some of the States, is only that which the law allows, when no particular rate is mentioned. By special agreement between parties in Indiana, Michigan, Illinois, Iowa, Arkansas, Mississippi, and Missouri, interest can be taken as high as 10 per cent. ; in Ohio, Florida, and Louisiana, as high as 8 per cent.; in Minnesota, Texas, and Wisconsin, as high as 12 per cent.; and in California, Colorado, Massachusetts, Nevada, and Rhode Island, any per cent.

193. To find the interest of $1 at 6 per cent. for any given time.

Since the interest of $1 is 6 cents, or of the principal, for 1 year, or 12 months, for 1 month it will be of 6 cents, or

192. What is interest? What is rate per cent.? What is the principal? What is the amount? What is legal interest? What is usury? What is the legal rate per cent. in the different States? In Canada, Nova Scotia, and Ireland? In England and France ?

cent, equal to 5 mills, or

twice 5 mills, or 1 cent, or

ʊ of the principal; and for 2 months, do of the principal.

Since the interest for 1 month, or 30 days, is 5 mills, the interest for 6 days, or of 30 days, will be 1 mill, or Toʊ of the principal.

for

Since 1 day, 2 days, &c., are †, &, &c., of 6 days, the interest any number of days less than 6 will be as many sixths of a mill, or six thousandths of the principal, as there are days. Also, since the interest for 2 months is 1 cent, or of the principal, for 100 times 2 months, or 200 months, or 16 years 8 mo., it will be 100 cents, or equal to the whole principal. Hence, the

Ex. 1. What is the interest of $1 for 2yr. 7mo. 20da.?

Ans. $0.1584.

The interest for 2 years will be twice as much as for 1 year, or 12 cents; and since the interest for 2 months is 1 cent, for 7 months it will be 3 cents. And as the interest for 6 days is 1 mill, for 20 days it will be 3 mills. Adding for the answer.

193. Explain the operation.

The time, 2y. 7mo. 20da., is equal to 2y. 1mo. + 6mo. 20da. Now, since the interest on any sum, at 6 per cent., in 200 months equals the principal, for 2y. 1mo., or of 200 months, it will equal of the principal. We, therefore, take of the principal, $ 1.00, equal 12 cents and 5 mills, as the interest for 2y. 1mo. The balance of time, 6mo. 20da., or 6 mo., being of 200 months, we take of the principal, equal 3 cents and 33 mills as the interest for 6mo. 20da. We add the interest for the parts of the whole time, and obtain, as by first operation, $ 0.158, as the whole interest.

RULE 1.- Reckon 6 cents for every YEAR, 1 cent for every TWO MONTHS, 5 mills for the odd month, 1 mill for every 6 days; and for any number of days less than six, as many sixths of a mill as there are days. Or,

Reduce the years and months to months, and call half the number of months cents, and one sixth the number of days mills. Or,

RULE 2. Take such fractional part or parts of the principal as the number expressing the time is of 200 months.

EXAMPLES FOR PRACTICE.

2. What is the interest of $1 for 1y. 4mo. 6da.?

Ans. $0.081.

3. What is the interest of $1 for 1y. 9mo. 12da.?

Ans. $0.107.

4. What is the interest of $1 for 3y. 8mo. 19da.?

Ans. $0.223.

5. What is the interest of $1 for 2y. 1mo 20da.?

6. What is the interest of $1 for 7y. 15da.?

7. What is the interest of $1 for 3mo. 28d. ?

Ans. $0.128.

Ans. $0.4224.

Ans. $ 0.0193.

8. What is the interest of $1 for 4y. 2mo. 5da.?

Ans. $0.250g.

9. What is the interest of $1 for 4mo. 3da.? Ans. $0.020.

193. Explain the second operation. The first rule? The second rule?