* Sterling exchange was again weak and lower. Continental exchange was also lower. Rates are: Long bills, $4.821 @ $4.824; sight drafts, $4.843 @ $4.85, and cable transfers, $4.85 @ $4.85}. Francs are quoted at 5.217 for long and 5.20 for short; reichsmarks, 941 @ 94 for long and 951 @ 95 for short; guilders, 39 @ 391 for long and 40 @ 40 for short. NOTE.-A reichsmark (mark of the empire) is the same as a mark, about 23 cents. The exchange value of 4 marks, or reichsmarks, is given in commercial quotations in the daily newspapers. 39. A person going from New York to England carries with him, instead of money, a draft like the following: Exchange for £820-12-6 sterling. New York, Oct. 1, 1897. At sight pay this First of Exchange, second of same tenor and date unpaid, to Edward Howe, or order, the sum of Eight Hundred Twenty Pounds £820-12-6 sterling. Value received, and charge to the account of To Baring Bros. & Co., London, England. Smith, Jones & Co. EXAMPLE 1.-Find the cost of the foregoing draft in New York when exchange on London is 4.844. SOLUTION.- £820-12-6 = £820 12s. 6d. = £820.625. $4.8475820.625 = $3,977.98. Ans. EXAMPLE 2.-What must be paid for a draft on Paris of 8,000 francs, when $1 is quoted at 5.211? SOLUTION. 1 franc $1 ÷ 5.215; ($1 ÷ 5.215) × 8,000 = $1,534.04. Ans. 40. Rule. To find the cost of a draft upon a foreign country, multiply the quoted value of a foreign monetary unit by the given number of such units. *Sterling exchange is Bills of Exchange payable in English money called Pounds Sterling. Long bills are those payable 30, 60, 90 or more days after being received. Short bills are those payable from sight to 30 days after being received. Sight drafts are payable at sight, that is, as soon as received. EXAMPLES FOR PRACTICE. 41. Solve the following examples: 1. Find the cost of a draft on London, at 60 days' sight, for £987 16s., exchange being $4.823. Ans. $4,768.60. 2. When exchange on Paris is quoted at 5.23, what must be paid for a sight draft for 2,800 francs? Ans. $535.37. 3. I bought a long draft on Berlin for 8,425 reichsmarks when exchange was quoted at 943 per 4 reichsmarks. What did it cost? Ans. $1,995.67. 4. What must be paid for a draft on Amsterdam for 8,000 guilders, exchange being 40? Ans. $3,205. ARBITRATION OF EXCHANGE. 42. Arbitration of exchange is the process of finding the cost of a draft on one place through one or more intermediate places. Thus, the quoted rates between New York and Vienna may be high, while those between New York and London, and between London and Vienna may be low. It may be cheaper for a man in New York to purchase a draft on Vienna through London than to purchase directly on Vienna. In this roundabout or circuitous method, the intermediate brokers charge brokerage for their services, usually %. 43. EXAMPLE 1.-When exchange between New York and Paris is 5.22, between New York and London is $4.83, and between London and Paris 24.84 francs to the pound, which is cheaper-direct or circuitous exchange from New York upon Paris for 10,000 francs, London brokerage being %? SOLUTION. By direct exchange, the cost of a draft for 10,000 francs is 10,000 5.22 = $1,915.71. By circuitous exchange, the cost of the draft in pounds is EXAMPLE 2.-A merchant sends 12,000 reichsmarks from New York to Berlin through London and Amsterdam. Exchange on London is $4.85, between London and Amsterdam 11.86 guilders to the pound, and between Amsterdam and Berlin 1.72 reichsmarks to the guilder. What is the cost of the draft in dollars, if brokerage at each place is %? SOLUTION 1.-First change the reichsmarks to guilders, then the guilders to pounds, and finally the pounds to dollars, adding each time the commission. 12,000 1.00 = 12,015, the number of reichsmarks required to pay the debt and the broker's commission in Berlin. (12,015 ÷ 1.72) × 1.00} = 6,994.197, the number of guilders required in Amsterdam. (6,994.197÷ 11.86) 1.00 = 590.467+, the number of pounds required in London. 590.467 × 4.85 × 1.00 = 2,867.34, the number of dollars required to purchase the bill of exchange in New York. $2,867.34. Ans. SOLUTION 2.-Another solution is the following, in which the vertical line is one of the signs of division, and indicates that the product of the numbers on the left of the line is to be divided by the product of the numbers on the right. To avoid the use of decimals having such an inconveniently large number of figures, it is better to use common fractions. Thus, 1.00} 801 8.01 8 = 800; hence, the last expression above becomes $4.85 (88) 12,000 $4.85 X 801 X 12,000 11.86 X 1.72 = $2,867.34. 11.86 X 800 X 1.72 By using common fractions instead of the decimals, the results will be more accurate and the principle of cancelation can be more readily employed. 44. It will be noticed that in the above arrangement the various monetary units appear once on each side of the vertical line of division. The same method may be employed with other than monetary units. EXAMPLE.-If 4 apples are worth 3 peaches, and 9 peaches are worth 5 oranges, how many apples must be given for 60 oranges? EXPLANATION. The unknown quantity x should always be placed on the right-hand side of the vertical line of division, and the given quantity to which is equivalent on the lefthand side. Then arrange the other quantities so that each quantity of the same kind appears on each side of the line. In the present example, 60 oranges are equivalent to a certain number of apples; hence, we place 60 oranges on the left and x on the right. Now, since 5 oranges are equivalent to 9 peaches, and we already have oranges on the left-hand side, we place the 5 oranges on the right-hand side and the 9 peaches on the left-hand side. For the same reason, we place 4 apples on the left-hand side and 3 peaches on the right-hand side. Canceling, we find that x = 144 apples. EXAMPLES FOR PRACTICE. 45. Solve the following examples: 1. I sent from New York to Christiania, Norway, 4,740 crowns through London and Amsterdam. If 1 crown = .667 guilder, 11.85 guilders = £1, and $4.85 £1, what does the draft cost, brokerage at London on Amsterdam, and at Amsterdam on Christiania, being %? Ans. $1,300.62+. 2. If 5 cords of oak wood are worth 3 cords of hickory, and 4 cords of hickory are worth 10 cords of pine, what should be paid for oak when pine is $1.25 per cord? Ans. $1.871. 3. If 9 bushels of wheat are worth 14 bushels of rye, 12 bushels of rye are worth 17 bushels of corn, and 3 bushels of corn are worth 5 bushels of oats, how many bushels of oats should be given for 324 bushels of wheat? Ans. 1,190 bu. $9 AVERAGE OR EQUATION OF PAYMENTS. 46. Suppose that A owes B any sum, say $100, due in 10 days, a second $100, due in 20 days, and a third $100, due in 30 days, there is evidently a time when he may pay B the entire $300 without loss of interest to either party. Clearly, this time is 20 days after A incurs the debts. The conditions are that A may retain and use the first $100 for 10 days, the second $100 for 20 days, and the third $100 for 30 days. But, so far as the interest is concerned, the use of $100 for 10 days is equivalent to the use of $100 × 10, or $1,000, for 1 day; $100 for 20 days equals $2,000 for 1 day; $100 for 30 days equals $3,000 for 1 day. A's privilege, therefore, equals $1,000+ $2,000+ $3,000, or $6,000 for 1 day. But $6,000 for 1 day is the same as $300 for 20 days. Expressing this argument more briefly, we have $100 for 10 days = $ 1,0 0 0 for 1 day. $300 ) $ 6,000 20 days. 47. Average, or equation, of payments is the process of finding the equitable time when payment of several sums, due at different times, may be made in one payment. 48. The equated, or average, time of payment is the time when several debts with different terms of credit may be equitably made in one payment. 49. EXAMPLE 1.-At a certain time A agrees to pay $1,000 as follows: $300 in 30 days, $200 in 60 days, and $500 in 90 days. Find the equated time of payment; that is, the time at which the entire debt may be paid without interest and still be fair to both parties. SOLUTION. $300 × 30 $9000 $200 X 60 = $12000 $500 × 90 = $45000 $1000 $66000 6 6 days. The whole sum may equitably be paid 66 days after the obligation is incurred. Ans. |