Solution. The sum to be expended is 188 of itself, and the commission is of the same sum; hence the sum sent to the agent is 185 or 3 of the sum expended. $42 is of $40; therefore, etc. 32. A man sends his agent in Oregon $515, from which he is to take a commission and invest the balance in land; the commission being 3 per cent. on the purchase, what sum was invested in land? 33. If 12 per cent. is gained by selling hay at $18 per ton, what did it cost? 34. If 163 per cent. is lost by selling a watch for $40, what did it cost?? 35. An agent retained a commission of 12 per cent. for collecting money, and paid $56 over to his employer; what sum did he collect? Solution. Since 12 per cent. or of the sum collected was retained by the agent, the $56 paid ́over was of the sum collected. $56 is of $64; therefore, etc. 36. A farmer engaged a laborer to thresh his wheat, agreeing to give him 10 per cent. of all he threshed; how many bushels must he thresh that the farmer may keep 54 bushels? 37. If it requires $125 in paper currency to buy $100 in gold, how much gold may be bought for $100 in paper currency? NOTE. When it takes more than $100 in bank bills, government bonds, or other paper currency, to buy $100 in gold, gold is said to be at a premium if the paper currency is taken as the standard of value, and the paper currency is said to be at a discount if gold is taken as the standard. 38. If it takes $150 in paper currency to buy $100 in gold, what is the per cent. of discount on the paper? Solution. The paper is worth +88= as much as gold; therefore the discount on the paper is 33 per cent. of its nominal value. = 39. If it takes $1663 of paper to buy $100 in gold, at what per cent. of premium is gold, paper being taken as the standard? At what per cent. of discount is paper, gold being taken as the standard? LESSON II. REMARKS. 1. INTEREST is money paid for the use of borrowed money. The money borrowed is called the Principal. The sum of the principal and interest is called the Amount. 2. In many of the United States interest is computed at 6 per cent., and this will be the per cent. understood in this book if no other is mentioned. 3. In computing interest, thirty days are usually considered a month, and 12 months a year. Ex. 1. The interest of $1 for a year being 6 cents, what is the interest of $1 for 2 years? For 3 years? 4 years? 5 years? 8 years? 10 years? 15 years? 2. What is the interest of a dollar for 1 month? Solution. Since the interest of $1 for 12 months is 6 cents, the interest of $1 for 1 month is of 6 cents, which is or of a cent= 5 mills. 3. What is the interest of $1 for 2 months? For 3 months? 4 months? 6 months? 9 months? 5 months? 8 months? 11 months? 10 months? 7 months? 4. What is the interest of $1 for 1yr. 2m.? For lyr. 6m.? 1yr. 3m.? 1yr. 8m.? 5. What is the interest of $1 for 2yr. 6m.? 2yr. 3m.? 2yr. 10m.? 3yr. 4m.? 5yr. 7m.? 6. What is the interest of $1 for 6 days? Solution. Since the interest of $1 for 30 days is 5 mills, the interest of $1 for 6 days is 3% or 1 of 5 mills, which is 1 mill. 7. What is the interest of $1 for 12 days? For 18 days? 24 days? 1m. 6d.? 1m. 24d.? 2m. 18d.? 4m. 12d.? 7m. 18d.? 8m. 24d.? 8. What is the interest of $1 for 1 day? Solution. Since the interest of $1 for 6 days is 1 mill, the interest of $1 for 1 day is of a mill. 9. What is the interest of $1 for 2 days? days? 4 days? 5 days? 7 days? 8 days? 15 days? 20 days? 28 days? 19 days? 10. What is the interest of $1 for 1m. 15d.? 2m. 3d.? 3m. 9d.? 8m. 4d.? 7m. 27d.? 1yr. 6m. 15d.? 11. What is the interest of $2 for a year? Solution. Since the interest of $1 for a year is 6 cents, the interest of $2 is 2 times 6 cents, which are 12 cents. For 3 9 days? 12. What is the interest of $3 for a year? Of $4? Of $5? $10? $12? $20? $30? 13. What is the interest of $2 for 1yr. 6m.? For lyr. 6m. 24d.? 2yr. 3m. 6d. ? 3yr. 5m. 15d.? 14. What is the interest of $3 for 2yr. 6m. 12d.? Of $5 for 2yr. 3m. 15d.? Of $10 for 1yr. 7m. 14d.? 15. What is the interest of $100 for lyr.? For 2 yr.? 1yr. 6m.? lyr. 10m.? 2yr. 3m.? 16. What is the interest of $200 for lyr.? For 2yr.? 1yr. 4m.? 2yr. 6m.? 3yr. 2m.? 4yr. 8m.? 17. What is the interest of $50 for lyr.? For 2yr.? 5yr.? 6m.? 8m.? 1yr. 4m.? 18. What is the interest of $25 for lyr.? 3yr.? lyr. 6m.? 2yr. 8m.? 19. What is the interest of $100 for 60 days? Solution. The interest of $1 for 60 days is 1 cent; therefore the interest of $100 is 100 cents, or $1. 20. What is the interest of $30 for 60 days? For 30 days? 20 days? 40 days? 21. What is the interest of $40 for 60 days? For 30 days? 15 days? 45 days? 75 days? 22. What is the interest of $20 for 33 days Suggestion. 33 days 30 days of 30 days, 23. What is the interest of $40 for 33 days? For 66 days? 90 days? 93 days? 24. The interest of any sum of money for 1 year, at 5 per cent., is what part of the principal? Solution. 5 per cent. is T=2; therefore, the interest of any sum for 1 year at 5 per cent. is of the principal. 25. What is the interest of $40 for 1 year at 5 per cent.? 26. At 4 per cent., the interest of any sum for 1 year equals what part of the principal? 27. At 10 per cent., the interest equals what pat of the principal? At 12 per cent.? At 20 per cent. ? At 163 per cent.? 28. What is the interest of $24 for 1 year at 163 per cent.? At 12 per cent.? At 25 per cent.? 29. What is the interest of $75 for 1 year at 4 per cent.? At 8 per cent. ? At 33 per cent.? 30. What is the interest of $60 for 1 year and 6 months at 5 per cent.? 31. What is the interest of $32 for 1 year and 6 months at 12 per cent.? 32. At 64 per cent., what is the interest of $32 for 1 year? For 2 years? 1 year and 6 months? 33. At 8 per cent., what is the interest of $72 for 2 years? For 1 year and 6 months? LESSON III. 1. WHAT is the amount of $50 for 1 year? Solution. The interest of $50 for 1 year therefore, the amount is $50+$3=$53. 2. What is the interest of $200 for 2 years and 6 months? What the amount? 3. What is the amount of $60 for 60 days? 6. What is the amount of $50, at 4 per cent., for 2 is $3 7. What is the amount of $60, at 8 per cent., for years and 3 months? 3 8. What is the amount of $64, at 12 per cent., for 2 years and 9 months? 9. What is the amount of $36, at 163 per cent., for 2 years and 3 months? 10. What is the amount of $84, at 25 per cent., for 2 years and 6 months? 11. At what rate per cent. will $6 gain 45 cents interest in 1 years? Solution. The interest of $6 for 1 year, at 1 per cent., is 6 cents, and for 14 years it is 11⁄2 times 6 cents, or 9 cents. If $6, at 1 per cent., gains 9 cents, then to gain 45 cents will require as many per cent. as 9 cents is contained times in 45 cents: 9 cents in 45 cents, 5 times; therefore, $6, at 5 per cent., will gain 45 cents in 1 years. Or, thus: Since the interest for 11 years or years is 45 cents, for year it is of 45 cents, or 15 cents, and for years or a whole year it is 2 times 15 cents, or 30 cents; 30 cents is=15ʊ of $6; rõʊ is 5 per cent.; therefore, $6, at 5 per cent., gains 45 cents in 1 years. 12. At what rate per cent. will $8 gain 96 cents in 1 year and 6 months; that is, in 1 years? 13. At what per cent. will $100 gain $10 in 11 years? 14. At what per cent. will $50 gain $10 in 2 years? 15. At what per cent. will $12 gain 80 cents in 1 year and 4 months? 16. At what per cent. will a given principal double itself in 20 years? Solution. Any principal will double itself in 1 year, at 100 per cent.; and, therefore, in 20 years, at of 100 per cent., viz., 5 per cent. 17. At what per cent. will any principal double itself in 25 years? In 10 years? 12 years? 50 years? 16 years? 33 years? 5 years? 4 years? |