SECOND METHOD.-The person desiring to send the money instructs his creditor to draw for the amount on his agent at an intermediate place, and his agent to draw upon him for the

same amount.

This is called the method by drawing.

THIRD METHOD.—The person desiring to send the money instructs his agent at an intermediate place to draw upon him for the amount, and buy a bill on the place to which the money is to be sent, and forward it to the proper party.

This is called the method by drawing and remitting.

These methods are equally applicable when the exchange is made through two or more intermediate places, and the solution of examples under each is only an application of compound numbers and business. Probs. VIII, IX, X, and XI.

650. 1. Exchange in New York on London is 4.83, and on Paris in London is 244; what is the cost of transmitting 63994 francs to Paris through London?

SOLUTION.-1. We find the cost of a bill of exchange in London for 63994 francs. Since 24 francs £1, 63994 ÷ 24 is equal the number of £ in 63994 francs, which is £2612.

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2. We find the cost of a bill of exchange in New York for £2612. Since £1 $4.83, the bill must cost $4.83 × 2612= $12615.96.

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2. A merchant in New York wishes to pay a debt in Berlin of 7000 marks. He finds he can buy exchange on Berlin at .25, and on Paris at .18, and in Paris on Berlin at 1 mark for 1.15 francs. Will he gain or lose by remitting by indirect exchange, and how much?

3. What will be the cost to remit 4800 guilders from New York to Amsterdam through Paris and London, exchange being quoted as follows: at New York on Paris, .18; at Paris on London, 24 francs to a £; and at London on

Amsterdam, 12 guilders to the £. How much more would it cost by direct exchange at 39 cents for 1 guilder?

4. An American residing in Berlin wishing to obtain $6000 from the United States, directs his agent in Paris to draw on Boston and remit the proceeds by draft to Berlin. Exchange on Boston at Paris being .18, and on Berlin at Paris 1 mark for 1.2 francs, the agent's commission being 1% both for drawing and remitting, how much would he gain by drawing directly on the United States at 24 cents per mark?

EQUATION OF PAYMENTS.

651. An Account is a written statement of the debit and credit transactions between two persons with their dates.

The debit or left-hand side of an account (marked Dr.) shows the sums due to the Creditor, or person keeping the account; the credit or right-hand side (marked Cr.) shows the sums paid by the Debtor, or person against whom the account is made.

652. The Balance of an account is the difference between the sum of the items on the debit and credit sides.

653. Equation of Payments is the process of finding a date at which a debtor may pay a creditor in one payment several sums of money due at different times, without loss of interest to either party.

654. The Equated Time is the date at which several debts may be equitably discharged by one payment.

655. The Maturity of any obligation is the date at which it becomes due or draws interest.

656. The Term of Credit is the interval of time from the date a debt is contracted until its maturity.

657. The Average Term of Credit is the interval of time from the maturity of the first item in an account to the Equated Time.

PREPARATORY PROPOSITIONS.

658. The method of settling accounts by equation of payments depends upon the following propositions; hence they should be carefully studied:

PROP. I.-When, by agreement, no interest is to be paid on a debt from a specified time, if any part of the amount is paid by the debtor, he is entitled to interest until the expiration of the specified time.

Thus, A owes B $100, payable in 12 months without interest, which means that A is entitled by agreement to the use of $100 of B's money for 12 months. Hence, if he pays any part of it before the expiration of the 12 months, he is entitled to interest.

Observe, that when credit is given without charging interest, the profits or advantage of the transaction are such as to give the creditor an equivalent for the loss of the interest of his money.

PROP. II.-After a debt is due, or the time expires for which by agreement no interest is charged, the creditor is entitled to interest on the amount until it is paid.

Thus, A owes B $300, due in 10 days. When the 10 days expire, the $300 should be paid by A to B. If not paid, B loses the use of the money, and is hence entitled to interest until it is paid.

PROP. III. When a TERM of CREDIT is allowed upon any of the items of an account, the date at which such items are due or commence to draw interest is found by adding its term of credit to the date of each item.

Thus, goods purchased March 10 on 40 days' credit would be due or draw interest March 10 + 40 da., or April 19.

659. PROB. I.-To settle equitably an account containing only debit items.

R. Bates bought merchandise of H. P. Emerson as follows: May 17, 1875, on 3 months' credit, $265; July 11, on 25 days, $460; Sept. 15, on 65 days, $650.

Find the equated time and the amount that will equitably settle the account at the date when the last item is due, 7% interest being allowed on each item from maturity.

SOLUTION BY INTEREST METHOD.

1. We find the date of maturity of each item thus: $265 on 3 mo. is due May 17+ 3 mo. =

Aug. 17
Aug. 5.

= Nov. 19.

2. As the items of the debt are due at these dates, it is evident that when they all remain unpaid until the latest maturity, H. P. Emerson is entitled to legal interest

On $460 from Aug. 5 to Nov. 19 = 106 da.

The $650 being due Nov. 19 bears no interest before this date.

3. On Nov. 19, H. P. Emerson is entitled to receive $1375, the sum of the items of the debt and the interest on $265 for 94 da. plus the interest on $460 for 106 da. at 7%, which is $14.12.

Hence the account may be equitably settled on Nov. 19 by R. Bates paying H. P. Emerson $1375 + $14.12 $1389.12.

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4. Since H. P. Emerson is entitled to receive Nov. 19, $1375 + $14.12 interest, it is evident that if he is paid $1375 a sufficient time before Nov. 19 to yield $14.12 interest at this date, the debt will be equitably settled. But $1375, according to (596), will yield $14.12 in 53+ a fraction of a day.

Hence the equated time of settlement is Sept. 26, which is 54 days previous to Nov. 19, the assumed date of settlement.

SOLUTION BY PRODUCT METHOD.

1. We find in the same manner as in the interest method the dates of maturity and the number of days each item bears interest.

2. Assuming Nov. 19, the latest maturity, as the date of settlement, it is evident that H. P. Emerson should be paid at this date $1375, the sum of the items, of the account and the interest on $265 for 94 days plus the interest on $460 for 106 days.

3. Since the interest on $265 for 94 days at any given rate is equal to the interest on $265 × 94, or $24910, for 1 day at the same rate, and the interest on $460 for 106 days is equal to the interest on $460 × 106, or

$48760, for 1 day, the interest due H. P. Emerson Nov. 19 is equal the interest of $24910 + $48760, or $73670, for 1 day.

4. Since the interest on $73670 for 1 day is equal to the interest on $1375 for as many days as $1375 is contained times in $73670, which is 531, it is evident that if H. P. Emerson receive the use of $1375 for 54 days previous to Nov. 19, it will be equal to the interest on $73670 for 1 day paid at that date. Consequently, R. Bates by paying $1375 Sept. 26, which is 54 days before Nov. 19, discharges equitably the indebtedness.

Hence, Sept. 26 is the equated time, and from Aug. 5 to Sept. 26, or 52 days, is the average term of credit.

Observe, that R. Bates may discharge equitably the indebtedness in one of three ways:

(1.) By paying Nov. 19, the latest maturity, $1375, the sum of the items of the account, and the interest of $73670 for 1 day.

In this case the payment is $1375 + $14.12 interest = $1389.12. (2.) By paying $1375, the sum of the items in cash, on Sept. 26, the EQUATED TIME.

(3.) By giving his note for $1375, the sum of the items of the account, bearing interest from Sept. 26, the equated time.

Observe this is equivalent to paying the $1375 in cash Sept. 26.

From these illustrations we obtain the following

660. RULE.-I. Find the date of maturity of each item.

II. Assume as the date of settlement the latest maturity, and find the number of days from this date to the maturity of each item.

In case the indebtedness is discharged at the assumed date of settlement:

III. Find the interest on each item from its maturity to the date of settlement. The sum of the items plus this interest is the amount that must be paid the creditor.

In case the equated time or term of credit is to be found and the indebtedness discharged in one payment, either by cash or note: