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 × $100 stock = $5000 stock.

$100 stock costs $98.

Therefore $5000 stock will cost 50 x $98 $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.
Therefore the price of the 5% stock must be 83.

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 142. 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 commercial draft is a draft payable at a specified time after sight (or date).

When the person on whom a commercial 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 money to persons at a distance by transmitting bank drafts or bills of exchange 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 facə, 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.

4% 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%.

0.0055 of $1000 =

0.005 of $1000

=

$1000.00

$5.50 discount for 33 dys. $994.50 cost of draft at par.

5.00 premium.

$999.50 cost of draft.

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, when 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.

21

Thus, if both terms of the ratio 21:31 be multiplied by 6, the resulting ratio is 15: 20, and the two ratios are equal, for Since, the simplest expression for 21: 33 is 3: 4.

31

=

15.

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 by which they are expressed.

Thus the quantity $7 is the same fraction of $9 as 7 is of 9.

250. Since ratio is simply relative magnitude, two quantities different in kind cannot form the terms of a ratio; and two quantities of the same kind must be expressed in a common unit before they can form the terms of a ratio.

Thus no ratio exists between $5 and 20 dys.; and the ratio of 3 t. to 5000 lbs. can be expressed only when both quantities are written as tons or pounds.

251. When two ratios are equal, the four terms are said to be in proportion, and are called proportionals.

Thus 6, 3, 18, 9 are proportionals; for § = 18.

252. A proportion is written by putting the sign = or a double colon between the ratios.

Thus 6:318: 9, or 6: 3 :: 18: 9, means, and is read, the ratio of 6 to 3 is equal to the ratio of 18 to 9.

253. The first and last terms of a proportion are called the extremes, and the two middle terms are called the means.

254. Test of a proportion. When four numbers are proportionals, the product of the extremes is equal to the product of the means.

This is seen to be true by expressing the ratios in the form of fractions, and multiplying both by the product of the denominators.

Thus the proportion 5 : 3 :: 15 : 9 may be written § = 5; and, îî both be multiplied by 3 × 9, the result will be 5 × 9= 3 × 15.

255. Either extreme, therefore, will be equal to the product of the means divided by the other extreme; and either mean will be equal to the product of the extremes divided by the other mean. Hence, if three terms of a proportion are given, the fourth may be found.