III. PERCENTAGE. PERCENTAGE has already been explained in page 163. Since PER CENT. indicates hundredths, it is properly expressed in the first and second decimal places, taken together. Thus, 6 per cent. is .06; 12 per cent. is .12. A fraction of 1 per cent. is expressed in decimals lower than hundredths. Thus, per cent. is .005; per cent. is .0025; 6 per cent. is .065; 12 per cent. is .1275. Multiplying by a decimal, produces such a part of the multiplicand, as the decimal indicates. Therefore, TO FIND THE PERCENTAGE ON ANY SUM,-Multiply the sum by the decimal which denotes the rate per cent. 1. A merchant having $1426 in the bank, drew out 5 per cent. of it. What sum did he draw? 1426 .05 $71.30 5 100 Since 5 per cent. of any quantity is of that quantity, the question in this example is, What is 5 of 1426 dollars? Or, decimally, What is .05 of 1426 dollars? 100 2. What is 1 per cent. of $100? of $834? 6. What is 24 per cent. of 1852 dollars? When the rate is a fraction of 1 per cent. - First, reduce the rate to a decimal, by multiplying .01 by the fraction. Then multiply by the decimal rate as before. 7. What is 3 per cent. of 234 dollars? .01x=.0075. Then 234x.0075=1.755. 8. What is per cent. of 524 dollars? 9. What is per cent. of 190 dollars? 10. What is 2 11. What is 6 12. What is 10 per cent. [.025] of 50 dollars? per cent. of 75 dollars? per cent. of 200 dollars? 13. Find 7 per cent. of 344 dolls. When there is a fraction in the 344÷100=3.44 quotient by the mixed number that expresses the rate. 14. What is 4 15. What is 6 16. What is 34 17. What is 9 per cent. of 624 dollars? per cent. of 38 dollars? 24.32 .07 $1.7024 18. What is 7 per cent. of 24 dolls. 32 cts. ? Here we have cents [decimals] in the number on which the percentage is to be taken. We however multiply as usual in decimals, and the first two decimal figures in the product express cents, the third mills, the fourth tenths of a mill. 19. What is 14 per cent. of $641.94 ? 20. What is 4 per cent. of $37.26 ? 21. What is 11 per cent. of $150.75 ? To find what per cent. a smaller number is of a larger,Consider the smaller number as a numerator, and the larger as a denominator of a fraction; then reduce this fraction to a decimal. See page 188. 22. If a man, having $94 deposited in bank, draw out $25, what per cent. of his deposit does he draw? 25 is of 94. Then 3.26. Ans. 262 per cent. 23. What per cent. of 240 dollars is 32 dollars? 24. What per cent. of 12 dollars is 7 dollars? 25. What per cent. of $95.21 (9521 cts.), is $4.22 ? To find a percentage of a compound number,-Multiply by the rate per cent., as a whole, or mixed number, and divide the product by 100, or the factors of 100. 26. What is 6 per cent. of £ 22 10s. 9d.? 27. What is 4 per cent. of £41 15s. 6d.? 28. What is 3 per cent. of £8 16s. 8d.? COMMISSION. COMMISSION is the compensation made to factors and brokers for their services in buying or selling. It is reckoned at so much per cent. on the money employed in the transaction. 29. What is the commission on $500, at 2 per cent. ? 30. If I allow my factor a commission of 3 per cent. for disbursing 725 dollars 50 cents, on my account, what does his commission amount to? 31. How much does a broker receive for his services on a sale of stocks amounting to 52648 dollars, allowing his commission to be of 1 per cent.? STOCKS. STOCK is a property, consisting in shares of some estabishment, designed to yield an income. It includes government securities, shares in incorporated banks, insurance offices, factories, canals, rail-roads, &c. The par value of a share, is what it originally cost; and the real value, at any time, is what it can be sold for. When it will sell for more than it originally cost, it is said to be above par, and the excess is stated at so much per cent. advance. When its real value is less than the original cost, it is below par, and is sold at a discount. 32. Sold 10 shares in the Manufacturers' Insurance Company, at 5 per cent. advance, the par value of a share being 100 dollars. How much did I receive? 33. Bought 15 shares in the Boston Bank, at 2 of 1 per cent. advance, the par value being 50 dollars a share. How much did I give for them? 34. Sold 64 shares in the State Rail-road, at 1 per cent. discount, the par value being 100 dollars a share. How much did I receive for them? INSURANCE. INSURANCE is security given, to restore the value of ships, houses, goods, &c., which inay be lost at sea, or R by fire. The security is given in consideration of a premium paid by the owner of the property insured. This premium is a percentage on the value of the property. The written instrument, which is the evidence of the contract of indemnity, is called a policy. 35. What is the amount of premium for insuring 19416 dollars, at 2 per cent., on a ship from Liverpool? 36. I effected an insurance of 3460 dollars on my dwelling-house for one year, at of 1 per cent. What did the premium amount to? at 37. If you obtain an insurance on goods valued at $7325, of 1 per cent., what will the premium amount to? IV. INTEREST. INTEREST has already been defined, and rules for computing it without decimals have been given, in Chap. VI., Sect. 23. The rules are repeated in this article, with such modifications as provide for the use of decimals. To compute interest for one or more YEARS. RULE. Multiply the principal by the decimal that expresses the rate, and the product will be the interest for I year. Multiply the interest for one year by the number of years. years, at 6 per cent. 1. Find the interest of $ 87.41, for 3 years, at 6 per cent. 87.41X.06x3=15.7338. Ans. $15.73+ In the answers, fractions of a cent may be omitted. 2. Find the interest of $ 644, for 4 years, at 6 per cent. 3. Find the interest of 92 cents, for 7 4. Find the interest of $7.50, for 2 years, at 4 5. Find the interest of $ 2.91, for 3 years, at 4 per cent. 6. Find the interest of $9.53, for 4 years, at 53 per cent. 7. What is the interest of $752.25, for 3 years, at 5 per cent.? What is the amount? per cent. 8. What is the interest of £16 8s. 6d., for 1 year, at 6 per cent.? What is the amount? To compute interest when there are MONTHS in the time. RULE. First find the interest for the years, if there be any. Then take of a year's interest for 1 month; or for 2 months; or for 3 months; and so on. 6 3 9. What is the interest of 224 dollars for 7 months, at per cent. per annum? 10. What is the interest of 75 dollars and 50 cents, for 5 months, at 6 per cent.? 11. What is the interest of 145 dollars, for 1 3 months, at 6 per cent.? year and 12. What is the interest of 95 dollars and 25 cents, for 2 years and 8 months, at 5 per cent.? 13. What is the interest of $351.09, for 3 years and 9 months, at 7 per cent.? What is the amount? To compute interest, when there are DAYS in the time. RULE. First find the interest for the years and months, if there be any. Then take of a month's interest for 1 day; or for 2 days; 33 or for 3 days; and so on. 14. What is the interest of $1000 for 1 year, 1 month and 1 day, at 6 per cent.? 15. What is the interest of $356.75 for 8 months and 10 days, at 6 per cent.? 16. What is the interest of $76.81 for 5 years, 2 months and 18 days, at 4 per cent.? 17. What is the interest of $250 for 1 year and 29 days, at 6 per cent. ? What is the amount? 18. What is the amount of $92.86 for 3 years, 7 months and 14 days, at 7 per cent.? 19. What is the interest of $175.63, from May 19, 1842, to January 4, 1844, at 6 per cent.? We find the time between the two dates by subtracting the first from the last, as in compound subtraction; the months being denoted numerically. 1844 1 4 1842 5 19 1 7 15 20. What is the interest of $208.90, from June 2, 1843, to August 4, 1845, at 5 per cent.? 21. What is the interest, at 6 per cent., on a note of $110, dated Sept. 7, 1843, and paid July 9, 1846? What is the amount? |