RULE. Multiply the percentage by 100, and divide the product by the base. NOTE. This rule is the converse of that in Art. 226; thus, 25 per cent. $1; and, conversely, $1.00 $4.25, i. e. 25 per cent. of $4 is $4 X .25 = = 2. What per cent. of $150 is $18? 1800 15012 per cent., Ans. Ans. 63 per cent. Ans. 12 per cent. 3. What per cent. of $300 is $19? 4. What per cent. of $350 is $43.75? 5. What per cent. of $340 is $34? 6. What per cent. of $64 is $16? 7. What per cent. of $1000 is $5? per cent. 8. B inherited $3500, and in 6 months spent $875; what per cent. of his inheritance did he spend? What per cent. had he remaining? Ans. Spent 25 per cent., and had 75 per cent. Ans. of 1 9. Out of a cask of wine containing 96 gallons, 32 gallons were drawn ; what per cent. of the whole remained in the cask? 10. A merchant having $1000, deposited $650 in a bank; what per cent. of his money did he deposit? 11. A teacher having a salary of $2400, spends $2000 annually; what per cent. of his salary does he save? PROBLEM 3. 228. To find the base when the percentage and the rate are given. Ex. 1. $6 is 3 per cent. of what sum? If $6 is 3 per cent., then 1 per cent. is of $6, which is $2, and if $2 is 1 per cent., then 100 per cent. is 100 times $2, which is $200; .. $6 is 3 per cent. of $200, Ans. The same result is obtained by first multiplying $6 by 100, and then dividing the product by 3; thus, $600 ÷ 3 = $200, Ans. Hence, RULE. Multiply the percentage by 100, and divide the product by the rate. 227. Rule for finding the rate when the base and percentage are known? What of this rule, and that in Art. 226? 228. Rule for finding the base when the percentage and rate are known? 2. $9 is 4 per cent. of what sum? Ans. $225. Ans. $1250. Ans. $171.429. Ans. 400. 9. A farmer bought a farm for $2756, which was 25 per cent. of his property; what was his property? Ans. $11024. 10. A man sold 56 geese, which was 28 per cent. of his flock; how many geese had he? 11. A merchant having a quantity of flour, bought 600 barrels more, when he found that the quantity bought was 75 per cent. of all he then had; how many barrels had he before he bought the last lot? Ans. 200. 12. A teacher saves $400 annually, which is 163 per cent. of his salary; what is his salary? 13. The population of a town was 769 greater in 1800 than in 1850, and this was an increase of 20 per cent, on the population of 1850; what was the population in 1850 ? 229. INTEREST. INTEREST is money paid for the use of money. 230. An example in interest is only a question in percentage. The principal is the base of percentage (Art. 224), the interest is the percentage (Art. 223), and the interest on $1 for a year is the rate written decimally (Art. 222). 231. The rate is usually fixed by law, and a higher rate than the law allows is usury. In New England and most of the United States the legal or 229. What is Interest? What the Principal? what relation to percentage? What is the base? 231. How is the rate fixed?, What is usury ? of the States. Amount ? 230. Interest, The percentage? The rate? Name the legal rate in some lawful rate is 6 per cent. ; in New York, 7 per cent.; in Illinois and most of the Western States, as high as 10 per cent. by agreement; in Texas, as high as 12 per cent.; in California, any rate by agreement, etc. In France and England, 5 per cent. NOTE. In this treatise, 6 per cent. is understood when no per cent. is mentioned. 232. When the rate is 6 per cent., the interest of $1 for a year is 6c.; for 2 years, 12c., etc.; for 1 month, or c.; for 2 months, 1c.; 3 months, 14c.; months, 4c., etc.; for 1 day, 3 of 5 mills m.; 3 days, m.; 4 days, m.; 5 days, 7 days, 14m.; 9 days, 14m.; 12 days, 2m.; of 6c. = 5 mills 6 months, 3c.; 9 mill; for 2 days, m.; 6 days, 1m.; 24 days, 4m.; etc., To find the interest of $1 at 6 per cent. for any time, RULE. Take 6c. (= $.06) for each year, 1c. for each 2 months in the part of a year, 5 mills (= $.005) for the odd month, if there be one, and 1 mill for each 6 days in the part of a month. Ex. 1. What is the interest of $1 for 3yr. 9m. 18d.? 2. What is the interest of $1 for 2yr. 5m. 20d.? 231. What will be understood when no rate is mentioned ? 232. Rule for finding the interest of $1 at 6 per cent. for any given time? 186 NOTE. With very little practice the pupil will, without making a figure, mentally determine the interest of $1 for any length of time. This habit is very desirable, as it will greatly facilitate the computation of interest. 3. What is the interest of $1 for 3yr. 1m. 15d.? Ans. $.187. 4. What is the interest of $1 for 1yr. 3m. 29d. ? 5. What is the interest of $1 for 4yr. 2m. 4d.? Ans $.0795. Ans. $.250%. 6. What is the interest of $1 for 4yr. 3m. 17d.? 7. What is the interest of $1 for 4yr. 9m. 12d.? 8. What is the interest of $1 for 10yr. 11m. 7d.? 9. What is the interest of $1 for 2yr. 11m. 5d.? 10. What is the interest of $1 for 1yr. 8m. 3d.? 233. To find the interest of any sum at 6 for any given time. per cent. The interest of $2 is evidently twice as much as the interest of $1; so the interest of $3, $4, or $7, is 3, 4, or 7 times the interest of $1; and the interest of $2.25 is 2.25 (i. e. 2 and 25 hundredths) times the interest of $1; .. to find the interest of any number of dollars we have only to find the interest of $1, and then repeat that as many times as there are dollars in the principal. 11. What is the interest of $2 for 1yr. 5m. 9d.? $.0861 2* interest of $1 for 1yr. 5m. 9d. $.17 3 interest of $2 for 1yr. 5m. 9d., Ans. 12. What is the interest of $6.50 for 3yr. 8m. 18d.? interest of $1 for 3yr. 8m. 18d. $.223 11150 $ 1.4 49 50 interest of $6.50 for 3yr. 8m. 18d., Ans. 232. What is the Note? 233. Rule for finding the interest of any sum at 6 per cent., for any time? Reason? 13. What is the interest of $300 for 2yr. 7m. 24d.? $.1 59 300 $47.700 interest of $300 for 2yr. 7m. 24d., Ans. 14. What is the interest of $700 for 1yr. 9m. 12d.? Ans. $74.90. 15. What is the interest of $400 for 2yr. 6m. 15d.? 16. What is the interest of $350 for 3yr. 8m. 24d.? 234. The mode of casting interest given in Art. 233 is perfectly simple, but the product is not changed when the multiplicand and multiplier change places (Art. 59, Note). Hence, To cast interest at 6 per cent. per annum, on any sum, for any time, RULE. Multiply the principal by the decimal which represents the interest of $1 for the given time. 17. What is the interest of $468 for 2yr. 6m. 11d.? 234. Second rule? Reason? Easiest way of multiplying by five sixths? Why correct? Easiest way for two thirds? |