22. Find the rate per cent at which $22,200 will yield a semi-annual return of $999. Ex. If $5125 is invested in 6% stock, at 102, what income will be obtained? $1 stock costs 1.025 of $1. Hence $5125 will be the cost of $51251.025 = $5000 stock. And 6% of $5000 = $300. $300. Ans. 23. Find the income on $39,000 invested in 4% stock, at 91. 24. Find the income on $7000 invested in 4% stock, at 1031. 25. Find the income on $13,600 invested in 7% stock, at 130. 26. A person invests $14,280 in railroad stock, at 1271. What will he receive if a dividend of 31% be declared? 27. Find the income on $14,000 when invested in 8% stock, at 1034. Ex. If a person buys 5% stock at 120, what rate of interest does he receive on his money invested? $100 stock costs $120. $100 stock pays $5. Hence the $120 invested yields $5. 5 Therefore, the rate of interest is 0.04, or 41%. 120 41%. Ans. 28. If an 8% stock is worth 150, what rate of interest will a purchaser receive on his money? 29. If a 10% stock is worth 175, what rate of interest will a purchaser receive on his money? 30. If a 9% stock is worth 170, what rate of interest will a purchaser receive on his money? 31. If a 4% stock is worth 70, what rate of interest will a purchaser receive on his money? 32. If a 3% stock is worth 65, what rate of interest will a purchaser receive on his money? Ex. Find the sum required for an investment in a 4% stock, at 98, to produce an income of $200 a year. $4 are received from $100 stock. 200 = Hence $200 will be received from x$100 stock $5000 stock. $100 stock costs $98. Therefore $5000 stock will cost 50 x $984 $4925. = $4925. Ans. 33. How much money must be invested in 8% stock, at 92, to produce $400 income? 34. How much money must be invested in a 3% stock, at 871, to produce an income of $250 ? 35. A person bought some bank stock at 107, and received $265 when a 5% dividend was declared by the bank. How much money had he invested? 36. A person buys some 6% railroad stock at 75, and receives $750 income. How much money has he invested? Ex. What must be the price of a 5% stock in order that a buyer may receive 6% on his investment? $100 must be invested to produce $6. Hence of $100 $83 must be invested to produce $5. 831. Ans. 37. What must be the price of a 6% stock in order that a buyer may receive 7% on his investment? 38. What must be the price of an 8% stock in order that a buyer may receive 6% on his investment? 39. A person invested $5710 in bank stock when the stock was at 1423. What per cent dividend is declared, if he receives $300? 40. A person receives 5% interest on his money by investing in some six per cent stock. At what price did he buy it? 41. What must be the price of a 7% stock in order that a buyer may receive 6% on his investment? EXCHANGE. 242. A draft or bill of exchange is a written order directing one person to pay a specified sum of money to another. 243. A time draft is a draft payable at a specified time after sight (or date). When the person on whom a draft is drawn accepts a draft, he writes the word "Accepted," with the date, across the face, and signs his name. The draft is then called an acceptance, and the acceptor is responsible for its payment. An acceptance is of the nature of a promissory note, the acceptor and maker having respectively the same responsibility for payment as the maker and indorser of a promissory note. 244. The system of paying debts due to persons living at a distance by transmitting drafts instead of money is called exchange. When a draft can be bought for its face, it is said to be at par. When the cost is less than the face, it is said to be at a discount; and when the cost is more than the face, it is said to be at a premium. Ex. 154. Ex. Find the cost of a draft on New York for $1000, at of 1% premium. 1% of $1000 = $2.50 (premium). $1000+$2.50 $1002.50 (cost). = $1002.50. Ans. 1. Find the cost of a draft on New York for $1200, at of 1% discount. 2. Find the cost of a draft on St. Louis for $2000, at of 1% premium. 3. Find the cost of a draft on New Orleans for $2400, at 1% premium. 4. Find the cost of a draft on Chicago for $3200, at % discount. Ex. Find the cost of a draft on Cincinnati for $1000, payable in 30 dys. after sight, exchange being % premium, and interest 6%. 5. Find the cost of a draft for $800, payable 30 dys. after sight, when exchange is 1% premium, and interest 6%. 6. Find the cost of a draft for $1900, payable in 30 dys., when exchange is at par, and interest 41%. 7. Find the cost of a draft for $1450, payable in 60 dys., when exchange is 1% discount, and interest 5%. 8. Find the cost of a draft for $1000, payable 60 dys. after sight, when exchange is 1% discount, and interest 7%. CHAPTER XII. PROPORTION. 245. The relative magnitude of two numbers is called their ratio, and is expressed by the fraction which has the first number for numerator, and the second number for denominator. Thus the ratio of 2 to 3, commonly written 2:3, is expressed by the fraction. 246. The first term of a ratio is called the antecedent, and the second term the consequent. 247. If both terms of a ratio be multiplied or divided by the same number, the ratio is not altered. 2 = Thus, if both terms of the ratio 21:33 be multiplied by 6, the resulting ratio is 15: 20, and the two ratios are equal, for Since 15, the simplest expression for 21 : 31 is 3 : 4. 31 248. If the numerator and denominator are interchanged, the fraction is said to be inverted; likewise, if the antecedent and consequent of a ratio are interchanged, the resulting ratio is called the inverse of the given ratio. Thus, if the fraction ‡ is inverted, the resulting fraction is §, and the inverse of the ratio 4:5 is 5: 4. 249. If two quantities are expressed in the same unit, their ratio will be the same as the ratio of the two numbers ly which they are expressed. Thus the quantity $7 is the same fraction of $9 as 7 is of 9. |