170. My store is insured for $8000 at 11% premium, and my stock for $15000 at 3%. If both are entirely consumed, what is the underwriters' loss? 171. The difference between 24% and 55% of a number is 60.45. What is the number? 172. Bought a range of wood 20 ft. long, 12 ft. high, and 4 ft. wide, at $5 per cord, and sold the whole for $50. Required the per cent of gain. 173. Paid $30 for my winter's wood, which was to have been 4 feet in length. It averaged, however, but 44 inches. Out of how much money was I cheated? 174. In a school of 400 scholars there were 120 absences in 4 weeks; the school has 2 sessions 5 days in a week. What was the per cent of attendance ? 175. How must I mark cloth which cost $2.50 so as to gain 20% and still fall 25% from my marked price? 176. A cubic foot of water weighs 623 pounds and a cubic foot of ice 57 pounds. Ice is what per cent lighter than an equal bulk of water? 177. The population of Chicago in 1880 was 503620, an increase of 69% in ten years; what was the city's population in 1870 ? QUESTIONS. 233. What does per cent mean? 235. Of what does percentage treat? 236. What is the rate per cent? 237. The base? 238. The percentage of a number? 239. How may the rate per cent be expressed? 240. What is the amount? 241. The difference? 242. The base and rate being given, how is the percentage found? 243. The base and percentage being given, how is the rate found? 244. The rate and percentage being given, how is the base found? 245. Define profit and loss. 246. What is the base of computation? 247. What is commission, or brokerage? 248. What is the base? The percentage? 249. What is insurance? 250. The premium? 251. The policy! INTEREST. 253. 1. When money is loaned for a year at 7%, what part of the money is the per cent? 2. How much must be paid for the use of $15 for 1 year at 5%? At 6% ? 3. How much must be paid for the use of $20 at 7% for 1 year? For 2 years? 4. When $200 is borrowed for 2 years at 7% a year, what amount should the borrower pay at the end of that time? 254. Interest is the money paid for the use of money. 255. The Principal is the money for whose use interest is paid. 256. The Amount is the sum of the principal and the interest. 257. The Rate of interest is the number of hundredths of the principal taken as the interest for one year or other specified time. NOTE 1. — The rate for one year and at 6% is to be understood in this book when no other time or rate is specified. NOTE 2. — The rate of interest is regulated by law. The legal rates in the different States may be found in a table in the Appendix. SIMPLE INTEREST. 258 Simple Interest is interest on the principal alone. Interest is an application of percentage, the principal being the base, the annual rate multiplied by the time in years being the rate per cent, and the interest the percentage. 259. In the computation of interest it is customary to consider a year as consisting of 12 months of 30 days each. General Method ORAL EXERCISES. 5. What is the interest of $50 for 1 year at 4%? Solution.-At 4% 1 year's interest is .04 of the principal, and. 04 of $50 is $ 2. 6. What is the interest of $ 60 for 1 year at 5% ? 7. What is the interest of $200 for 1 year at 6%? For 3 years? For 5 years? 8. What is the interest of $200 for 2 years 6 months at 7%? Solution. As at 7% the interest of $200 for 1 year is $ 14, for 2 years 6 months, or 2 years, it must be 2 times $ 14, or $35. 9. What is the interest of $100 for 2 years 3 months at 8%? For 3 years 1 month? 10. What is the amount of $400 for 2 years 9 months at 6%? For 3 years 4 months? WRITTEN EXERCISES. 11. What is the interest and what is the amount of $26.25 for 2 years 4 months at 7%? $26.25 Principal = .07 = Rate $1.8375 = 1 year's interest $4.2875 = Interest $30.54 = Amount Solution. One year's in terest is .07 of $26.25, or $1.8375; 2 years' interest is 2X $1.8375, or, to the nearest cent, $4.29. Adding the principal to the interest, we have the amount, $30.54. 12. What is the interest and what is the amount of $1728 for 3 years 9 months at 6%? 13. What is the interest of $144 for 1 year 8 months at 5%? 14. What is the interest of $556 for 3 years 5 months 7 days at 8%? 15. What is the interest of $ 720 at 5% for 1 y. 7 mo. 18 d.? $720 12) $36.00 $3.00 19.6 $58.80 Solution. One year's interest is .05 of $720, or $36; the interest for 1 y. 7 mo. 18 d., or 19.6 mo., or 19 years, is 196 $36, or $58.80. In this example, 1 year's interest being a multiple of 12, we divide by the denominator of the multiplier before multiplying by the numerator. 16. Find the amount of $1500 for 2 y. 6 mo. 15 d. at 6%. 260. General Rule for Interest. Multiply the principal by the rate, and this product by the time in years. To find the amount, add the principal and the interest. Let p represent the principal, r the rate per cent, i the interest, t the time, and a the amount, and we have the FORMULAS. i=pxrxt. a = p + i. NOTE. In interest partial results may be carried to four places of decimals. The answers, in business transactions, are deemed sufficiently exact if the mills are omitted, and when they are five or more, the cents are increased by 1. 17. What is the interest of $2464 for 2 y. 9 mo. 15 d. at 5%? 18. What is the interest of $2503.75 for 3 y. 10 mo. 21 d. at 6%? y. 10 d. at 7 % ? 19. What is the interest of $ 560.50 for 4 20. What is the interest of $ 97.16 for 1 y. 5 mo. at 6% 21. What is the interest of $156.80 for 3 y. 1 mo. 3 d. at 4%? 22. What is the interest of $865 for 1 y. 9 mo. 24 d. at 8%? 23. What is the interest of $ 890 for 5 y. 7 mo. 8 d. at 6%? 24. What is the amount of $5000 for 3 y. 11 mo. 10 d. at 7%? Six per cent Method. 261. The Interest of any sum, at 6 per cent a year, For 12 months, or 1 year, is .06 of the principal. For 2 months, or year, is .01 of the principal. For 1 month, or 30 days, is .001 of the principal. month, or 6 days, is .001 of the principal. month, or 1 day, is .0001 of the principal. For For 262. Hence, as a convenient method of reckoning interest at 6 per cent, Or, Or, Multiply of .01 of the principal by the time in months. Multiply .001 of the principal by of the time in days. Of the principal take 6 times as many hundredths as years, as many hundredths as months, and as many thousandths as days. |