§ XX. PERCENTAGE. ART. 190. PERCENTAGE and per cent. are terms derived from Latin words, per centum, which signify by the hundred. Percentage, therefore, is any rate or sum on a hundred, or it is any number of hundredths. Thus, if an article is bought for $100, and sold for $105, the gain is 5 per cent., because $5 are To of $100, or of the original cost. Again, if an article is bought for $25, and sold for $30, the gain is 20 per cent., because $5 are=% of $25, or of the original cost. Since per cent. is any number of hundredths, it is a decimal written in the same manner as hundredths in decimal fractions. Thus, 5 per cent., 25 per cent., &c., are written .05, .25, respectively. (Art. 175.) When the per cent. is more than 100 it is an improper fraction, and if expressed decimally it becomes a mixed number; thus, 103 per cent., equal to 183, is written 1.03. If the per cent. is less than 1, or a part of one hundredth, to be expressed decimally, it must be written at the right of hundredths in the place of thousandths, &c. Thus, of 1 per cent., of 1 per cent., 12 per cent., are written .005, .0075, .122, respectively. 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.; 30.1 per cent.; 40 per cent. ; 50 per cent.; 60 per cent.; 75 per cent.; 100 per cent.; 105 per cent.; 115 per cent.; 6 per cent.; 83 per cent.; 20 per cent.; of 1 per cent.; of 1 per cent.; of 1 per cent.; of 1 per cent.; of 1 per cent. ART. 191. To find the percentage on any sum or quantity. 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. QUESTIONS. Art. 190. From what are the terms percentage and per cent. derived, and what do they signify? How, then, will you define percentage? How will you illustrate it? How is per cent. written when less than 100? How, when more than 100?. If the per cent. is a fraction, or contains a fraction, what is the fraction, and, if expressed decimally, what place must it occupy? RULE. · Multiply the given quantity or number by the rate per cent., considered as a decimal, and point off the product as in multiplication of decimal fractions. (Art. 185.) NOTE.If the per cent. contains a fraction that cannot be expressed decimally, or, if thus expressed, would require several figures, it is more convenient to multiply by it as a mixed number. (Art. 155.) EXAMPLES FOR PRACTICE. 2. What is 2 per cent. of $325? ing? Ans. $6.50. Ans. $39.45. Ans. $51.38,9. Ans. 57.375 tons. 8. What is 41 per cent. of 587 yards of cloth? Ans. 26.415 yards. 9. I lost 10 per cent. of $975; how much have I remainAns. $877.50. 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. per 11. T. Page received a legacy of $8000; he gave 19 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 66 new suit"? Ans. 6yd. 1qr. 1,773,na. 13. A man having $10000, lost 15 per cent. of it in speculation; what sum had he remaining? QUESTIONS. Ans. $8500. Art. 191. Will you explain the operation for finding the percentage on any sum or quantity? Give the reason for the process. What is the rule? § XXI. SIMPLE INTEREST. ART. 192. INTEREST is the compensation which the borrower of money makes to the lender. The rate per cent. is the sum paid for the use of $100, 100 cents, or 100£., for one year. The principal is the sum lent, on which 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, New Jersey, Pennsylvania, Delaware, Maryland, Virginia, North Carolina, Tennessee, Kentucky, Ohio, Indiana, Illinois, Missouri, Arkansas, Mississippi, Florida, District of Columbia, and on debts or judgments in favor of the United States, it is 6 per cent. In New York, Michigan, Wisconsin, Iowa, Georgia, and In Canada, Nova Scotia, and Ireland, it is 6 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 Ohio, Indiana, Michigan, Illinois, Iowa, and Arkansas, interest can be taken as high as 10 per cent. ; in Florida and Louisiana, as high as 8 per cent. ; in Texas and Wisconsin, as high as 12 per cent.; and in California, any per cent. In New Jersey, by a special law, 7 per cent. may be taken in Jersey city and the township of Hoboken. ART. 193. To find the interest of $1 at 6 per cent. for given time. any Since the interest of $1 is 6 cents, or 18 of the principal, for 1 year, or 12 months, for 1 month it will be of 6 cents, or a cent, equal to 5 mills, or do of the principal; and for QUESTIONS. Art. 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? months, twice 5 mills, or 1 cent, or do of the principal. Now, since the interest for 1 month, or 30 days, is 5 mills, the interest for 6 days, or of 30 days, will be one mill, or ro of the principal. And as 1 day, 2 days, &c., are д, &, &c., of 6 days, the interest for 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 ʊ of the principal, for 100 times 2 months, or 200 months, or 16 years 8 mo., it will be 100 cents, or equal the whole principal; and in the same proportion for any other length of time. Hence, the INTEREST OF $1, AT 6 PER CENT., FOR of the prin. o of the prin. of the prin. of the prin. ʊʊ prin. 1 yr., or 12 mo., is 6 cents, or $0.06, equal ALSO, 16 yr. 8 mo., or 200 mo., is 100 cts., or $1.00, equal the whole prin. 4 mo., or 100 mo., is 50 cts., or $0.50, equal of the prin. 5 yr. 6 mo., or 66 mo., is 33 cts., or $0.333, 8 yr. of prin. equal è̟ of prin. 4 yr. 2 mo., or 50 mo., is 25 cts., or $0.25, equal of prin. 3 yr. 4 mo., or 40 mo., is 20 cts., or $0.20, equal of prin. 2 yr. 9 mo., or 33 mo., is 163 cts., or $0.1663, equal of prin. 2 yr. 1 mo., or 25 mo., is 12 cts., or $0.125, equal 1 yr. 8 mo., or 20 mo., is 10 cts., or $0.10, equal of prin. 1 yr. 43 mo., or 163 mo., is 8 cts., or $0.083, equal of prin. of a yr., or 10 mo., is 5 cts., or $0.05, equal z of prin. of a yr., or 63 mo., is 3 cts., or $0.033, equal of a yr., or 5 mo., is 24 cts., or $0.025, equal of a yr., or 4 mo., is 2 cts., or $0.02, equal of prin. of prin. of prin. Ex. 1. What is the interest of $1 for 2yr. 7mo. 20da.? FIRST OPERATION. Interest for 2y. = = .12 7mo. Ans. $0.1581. The interest for 2 years will be. twice as much as for 1 year, equal 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 33 mills. Adding the several sums together, we have $0.158 for the answer. Ans. $ 0.1 5 8 QUESTION.-Art. 193. How do you explain the operation? 20da. Now, since the in $ 0.1 5 8 Int. for 2y. 7mo. 20da. terest 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, the interest for 2y. 1mo. The balance of time, 6mo. 20da., or 63 mo., being of 200 months, we take 3 of the principal, equal 3 cents and 33 mills, as the interest for the 6mo. 20da. We add together the interest for the parts of the whole, 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 ly. 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. $0.2231. 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. $0.1281. Ans. $0.4224. Ans. $0.019. 8. What is the interest of $1 for 4y. 2mo. 5da.? Ans. $0.250§. 9. What is the interest of $1 for 4mo. 3da.? Ans. $0.0201. QUESTIONS.-How do you explain the second operation? What is the first rule? What is the second rule? |