ARBITRATED EXCHANGE.

607. Arbitration of Exchange is the process of computing exchange between two places by means of one or more intermediate exchanges.

NOTES.-1. When there is only one intermediate exchange, the process is called Simple Arbitration; when there are two or more intermediate exchanges, the process is called Compound Arbitration.

2. The arbitrated price is generally either greater or less than the price of direct exchanges; and the object of arbitration is to ascertain the best route for making drafts or remittances.

608. There are always three methods of receiving money from a place, or of transmitting money to a place, by means of indirect exchange through one intervening place. Thus,

If A is to receive money from C through B,

1st. A may draw on B, and B draw on C; 2d. A may draw on B, and C remit to B; 3d. B may draw on C, and remit to A.

If A is to transmit money to C through B, 1st. A may remit to B, and B remit to C; 2d. A may remit to B, and C draw on B; 3d. B may draw on A, and remit to C.

1. A man in Albany, N. Y., paid a demand in Paris of 5400 francs, by remitting to Amsterdam at the rate of 21 cents for 10 stivers, and thence to Paris at the rate of 28 stivers for 3 franes; how much Federal money was required?

OPERATION.

$ (?)

3 francs 10 stivers

=

5400 francs.
28 stivers.
$21.

(?)= $1058.40, Ans.

Or,

(?) 15400

ANALYSIS. We are to determine how much Federal money is equal to 5400 francs, and the question may be represented thus: $(?)=5400 francs. Now since 3 francs 28 stivers, and 10 stivers$.21, we know that if the required sum be multiplied successively by 3 francs and 10 stivers, the result will be equal to the product of 5400 francs by 28 stivers and $.21 successively, (Ax. 3). Canceling the units of currency, 1 franc, 1 stiver, and $1, and also the equal numerical factors, we have (?) = $1058.40, the sum required.

328

10.21

() = $1058.40, Ans.

28

Or, since the course of exchange between Amsterdam and Paris gives 1 franc 23 stivers, and the course between Albany and Amsterdam gives 1 stiver cents, we multiply the 5400 francs by 3 and successively, using the vertical line and cancelation, and obtain $1058.40, as before.

NOTE. In the first statement the rates of exchange are so arranged that the same unit of currency shall stand on opposite sides in each two consecutive equations, in order that these factors may all be canceled.

2. A resident of Naples having a bequest of $8720 made him in Boston, orders the remittance to be made to his agent in London, who remits the proceeds to Naples, reserving his commission of 1% on the draft sent. If exchange on London is 9% in Boston, and the rate between London and Naples is £1 for 5 scudi, how much does the man realize from his bequest?

of the draft before the purchase, we place 1.005 on the left as a divisor, (159), and obtain by cancellation 8955 scudi 3 carlini as the proceeds of the exchange.

=

NOTE. Since the par of exchange on England is £9 $40, the course of exchange will always be £9 $40 X 1 plus the rate of exchange.

=

3. A merchant in Chicago directs his agent in Albany to draw upon Baltimore at 1 % discount, for $1200 due from the sales of produce; he then draws upon the Albany agent at 2% premium, for the proceeds, after allowing the agent to reserve % for his commission. What sum does the merchant realize from his produce?

by the initial letter, and make the statement as in the other examples. Then, since the agent is to reserve % commission from the avails of his draft, we place 1-.005.995 on the right as a multiplier, and obtain by cancellation (?) = $1205.70, the answer.

From these principles and illustrations we have the following RULE. I. Represent the required sum by (?), with the proper unit of currency affixed, and place it equal to the given sum on the right.

II. Arrange the given rates of exchange so that in any two consecutive equations the same unit of currency shall stand on opposite sides.

III. When there is commission for drawing, place 1 minus the rate on the left if the cost of exchange is required, and on the right if proceeds are required; and when there is commission for remitting, place 1 plus the rate on the right if cost is required, and on the left if proceeds are required.

IV. Divide the product of the numbers on the right by the product of the numbers on the left, cancelling equal factors; the result will be the answer.

NOTES. -1. Commission for drawing is commission on the sale of a draft; commission for remitting is commission on the purchase price of a draft.

2. The above method is sometimes called the Chain Rule, or Conjoined Proportion.

EXAMPLES FOR PRACTICE.

1. A gentleman in Philadelphia wishes to deposit $5000 in a hank at Stockholm, by remitting to Liverpool and thence to Stockholm; if exchange on Liverpool is at 10 % premium in Philadelphia, and the course between Liverpool and Stockholm is 6 roubles 48 copecks per £1, how much money will the man have in bank at Stockholm, allowing the agent at Liverpool% for remitting? 661-7 Ans 6245 roubles 66 copecks.

2. When exchange at New York on Paris is 5 francs 16 centimes per $1, and at Paris on Hamburg 23 francs per marc banco, what will be the arbitrated price in New York of 7680 mare bancos of Hamburg? Ans. $3162.79.

3. A man in Cleveland wishes to draw on New Orleans for a bank stock dividend of $750, and exchange direct on New Orleans is 1% discount; how much will he save by drawing on

his agent in New York at 14 % premium, allowing his agent to draw on New Orleans at 1 % discount, brokerage at 3 %? 924

4. A gentleman in Boston drew on Wurtemberg for 6000 gilders at $.415 per gilder; how much more would he have received if he had ordered remittance to London, and thence to New York, exchange at Wurtemberg on London being 11 gilders per £1, and at London on New York 91 %, in favor of sterling, brokerage at 1% in London for remitting? Ans. $67.66.

5. If at Philadelphia exchange on Liverpool is at 9 % premium, and at Liverpool on Paris 26 francs 86 centimes per £1; what is the arbitrated course of exchange between Philadelphia and Paris, through Liverpool? Ans. 1 franc = $.181.

6. An American resident of Amsterdam wishing to obtain funds from the U. S. to the amount of $6400, directs his agent in London to draw on the U. S. and remit the proceeds to him in a draft on Amsterdam, exchange on the U. S. being at 8% in favor of London, and the course between London and Amsterdam being 18d. per gilder. If the agent charges commission at % both for drawing and remitting, how much better is this arbitration than to draw directly on the U. S. at 40 cents per gilder?)

7. A speculator in Pittsburgh, having purchased 58 shares of railroad stock in New Orleans, at 95 %, remits to his agent in New York a draft purchased at 2 % premium, with orders for the agent to remit the sum due in N. O. Now, if exchange on N. O. is at% discount in N. Y., and the agent's commission for remitting is %, how much does the stock cost in Pittsburgh?

Ans. $5606.08.

8. A banker in New York remits $3000 to Liverpool, by arbitration, as follows: first to Paris at 5 francs 40 centimes per $1; thence to Hamburg at 185 francs per 100 marcs; thence to Amsterdam at 35 stivers per 2 marcs; thence to Liverpool at 220 stivers per £1 sterling. £1 sterling. How much sterling money will he have in bank at Liverpool, and what will be his gain over direct exchange at 10 % premium?

Ans.

S Proceeds in Liverpool, £696 11s. 2d.
Gain by arbitration, £82 18s. 5d.

EQUATION OF PAYMENTS.

609. Equation of Payments is the process of finding the mean or equitable time of payment of several sums, due at different times without interest.

610. The Term of Credit is the time to elapse before a debt becomes due.

611. The Average Term of Credit is the time to elapse before several debts, due at different times, may all be paid at once, without loss to debtor or creditor.

612. The Equated Time is the date at which the several debts may be canceled by one payment.

613. To Average an Account is to find the mean or equitable time of payment of the balance.

614. A Focal Date is a date to which all the others are compared in averaging an account.

NOTE. Each item of a book account draws interest from the time it is due, which may be either at the date of the transaction, or after a specified term of credit.

In averaging, there are two kinds of equations, Simple and Compound.

615. A Simple Equation is the process of finding the average time when the payments or account contains only one side, which may be either a debit or credit.

616. A Compound Equation is the process of averaging when both debts and credits are to be considered.

SIMPLE EQUATIONS.

CASE I.

617. When all the terms of credit begin at the same date.

1. In settling with a creditor on the first day of April, I find that I owe him $12 due in 5 months, $15 due in 2 months, and $18 due in 10 months; at what time may I pay the whole amount?