Ch. IV. Fluctuations in the price of foreign bills.

Abgesehn von den lezt genannten cases the purchase and sale of Foreign bills originally represent a simple transfer of debts. (43)

The primary difference of value  Zusatz von Marx.
(der Foreign bills)
clearly arises either from the aggregate amount of claims of any country upon others exceeding the sum of its liabilities to them, or vice versa, falling short of that sum. In the first case, those who have bills to draw (call them the exporters, though the class embraces all those who have claims of any kind on foreign countries) will not find sufficient purchasers to take all their bills; for only those will buy who have debts abroad to settle. Daher competition for the sale of bills. They will take less money for them than their par value; i.e. sell them at a discount. In the other case competition of importers, i.e. the purchasers of foreign bills; the they pay a premium to secure them. (44) Wenn bills nicht sufficient, jeder Importer will avoid the necessity of sending bullion falling to his individual share; hastens to offer a slight premium to those who draw, to secure himself against the greater loss in freight, insurance, and interest, which is always involved in a bullion remittance. The premium may rise to within a fraction of this expense or loss; nay, may even reach that actual point; because though the premium paid for the bill and the cost of the specie remittance were absolutely equal, it would still be more convenient to send the bill. Beyond this point the balance of trade cannot cause the premium to rise. (45)

On the other hand, it cannot cause the discount at which bills are sold ever to exceed the sacrifices which exporters would incur, if they found themselves obliged to instruct their foreign debtors to send them bullion, in consequence of bills upon them being no longer saleable. The time, however, when they would receive payment would, in this case, be an important consideration. As long |94 as the exporters can find purchasers for their bills, they get payment at once; but when they cannot dispose of their bills any more, they are not reimbursed for the value of their exports till the equivalent for them is returned in gold. Accordingly, competition of the sellers of Foreign bills; discount derselben; aber der discount will not be greater than the estimate which the seller makes of the sacrifices pointed out. (45, 46) Z.B. New Orleans und New York, vor der secession, when their exchanges not disturbed by independent issues of inconvertible paper money. If at any time the amount of bills on New York offered for sale in New Orleans = the amount of remittances required for the payment of debts due to New York, i.e. if equilibrium of debts between the two cities, a bill for 100$ payable at sight in New York, would be exactly 100$. If greater sum due to New York, vielleicht 1001/2$ paid, to be not be obliged to send gold, which might cost them 11/2$ for each 100$ in freight and insurance. The more the supply of bills diminished, the more the premium would rise, till the sellers might realise almost 11/2$ profit. At this point the premium clearly so high, that it would be indifferent to remitters whether they bought bills or sent gold, and some would despatch gold and others buy the bills, the surplus excess required to be remitted being in the mean time gradually lessened by this despatch of gold. The exporters being less pressed for their bills, soon had the opportunity of feeling the change in the situation, and might content themselves with a smaller premium in order to secure some profit before the demand was entirely satisfied. Hence a fall in the price of bills, till the exchange once more at par, or below it. ([46,] 47, 48)

Conversely, when more bills than purchasers for them, the drawers feeling that their export business might have to bear the charge of 11/2 P.Ct. for bullion shipped to them from New York  Zusatz von Marx.
as returns, were ready to sell at a discount long before that point was reached; a discount which would, however, not exceed 11/2$ P.Ct., the charges on bullion shipment.  Kommentar von Marx.
(Abgeschmackte Illustration! Wenn die importers von New Orleans und nicht die Exporters von New York have to pay, in case of gold remittance, the 11/2 P.Ct. on the bullion shipment, then, vice versa, the importers of New York, and not the exporters of New Orleans have to defray these charges. Other considerations must sway them to sell at a discount on their bills on New York.)
Wenn also bills at sight und in the same currency, the limits within which the exchanges may vary are, at the one extreme, the par value, plus the cost of the transmission of bullion; at the other extreme, the par value, minus the identical sum. Practically the exchanges rarely touch either extreme, but fluctuate between them, owing to the various measures and influences brought to bear upon the situation before the extreme case arrives, which cause a reaction in the opposite direction. (48)

There are occasions, however, when the exchanges sink and rise much above or below the specie point. (48[, 49])

Z.B. in the first months of 1861, under the growing apprehension of the civil war in the U. St., fluctuations in the American rates of exchange much below the specie point. The balance of trade was much in favour of America. Very considerable exports of grain and flour, coupled with a reduction of imports, in consequence of political apprehensions. Hence natural that exchanges should fall to specie point. But they fell much below it. Reason: the peculiarly urgent necessity der exporters, of selling their bills immediately, at any sacrifice. It was a question of time. Three or 4 P.Ct. were sacrificed to secure the proceeds of the bills on England at once, instead of waiting for the arrival of gold. The exporter either might sell his bills at what they would fetch, or send them himself to Europe, with instructions to his correspondent to encash them, and remit the amount in bullion. The latter course was cheaper, but as he required funds immediately (or, under the influence of panic, believed that he would so require them) he adopted the former. ([49,] 50)

In ordinary times, capitalists would have competed with each other in buying up the drafts of urgent sellers. They would then have remitted |95 them to Europe on their own account, so as to secure the profit between the low price paid for the bills and their specie value. They would have bought at a heavy discount, in order subsequently to realise at least the specie value. But, at a time of commercial panic, such capitalists are seldom willing to launch out into a speculation which deprives them, during the weeks which must elapse before the gold arrives, of the command over their funds. Interest may rise during the interval – they may anticipate. (50) Z.B. They expected to gain 11/2 P.Ct. net on the exchange. In their calculation the interest taken into account they would lose from the time when they paid the drawer for his bill up to the moment when the returns in gold arrive. The interval sei a month, interest calculated on it at 6% p.a., or 1/2 P.Ct. for the month. If it rise suddenly to 24 P.Ct. p.a., they would have to borrow money at the rate of 2% for the month, in order to replace that portion of their capital which is travelling to Europe and back; also 11/2% more than they calculated. Thus they would gain nothing on their exchange operation. Also stringent moneymarket acts materially upon the exchanges, inducing sellers to force sales, and creating a reluctance on the part of purchasers to buy unless absolutely compelled to remit. This cause will not come forcibly into operation, when the international transactions are in a state of equilibrium; for there will be then as many purchasers on compulsion as there are sellers, and the dearness of money may only operate so far as to induce purchasers to defer their remittances to the last moment, whereas sellers would wish that they should be hastened. Its full force will be felt at a time when the country where money is supposed to be dear, or where panic exists, has exported more than it has imported, and when it is consequently certain that gold will finally have to be ordered, while no individual is himself willing to wait for its arrival. This peculiar contingency will seldom occur; as, generally, the money market in such a country as has taken less from other countries than it has given to them, is particularly well supplied with surplus capital. (51, 52)

Aber ferner: Practically, an immense majority of bills are drawn payable at various periods after the date of their issue or first presentation to the acceptors – so many days after date, or so many days after sight. (52) Also 1) deduction to be made from the price  Zusatz von Marx.
(der bill)
which is bought for ready money not being itself payable till after a certain time; 2) as to the security, which the purchaser of the bill can feel that the drawer and acceptor of the bill will continue solvent till it becomes due. Thus, the state of credit in both countries, and the rate of interest in that country whither the bill is remitted, likewise become determining elements in the rate of exchange. (53)

The state of the moneymarket where the bill is drawn, affects the exchanges, since it makes the seller more eager and the purchaser more reluctant; and, as one or the other must bear the loss of interest which must ensue till the proceeds of the bill reach their hands, this loss of interest will be at the rate established in their own money market at home. But when bills not payable at once, form the subject of bargain, the buyer must further consider what is the rate of interest in the country on which the bills are drawn. If he owes money abroad, he will be paying interest to his foreign creditor at the foreign rate, and this interest will not cease till his remittances become due. Difference to him of 2 months’ interest at the foreign rate, whether the bill he purchases is payable at once or 60 days after its arrival. As the foreign interest rises, he will insist on paying less for the 60 day bill, whereas, if it falls, he can afford to pay more. Im ersten case heavier deduction als im zweiten.

Or, in the case of the capitalists who buy up bills at a time of pressure in order to send them abroad and have them converted into gold, their foreign correspondents will have to discount the long bills for them, and the amount of discount affects their profits. |96 If they fear the rate of interest in the country on which the bills are drawn will be high, they pay so much less for the bills; if they anticipate cheap rates, they pay so much the more. The New York capitalists, who suffered the price of bills upon England to sink 3 or 4 P.Ct. below the specie point, felt anxious as to the rate to be paid in England for the discount of their 60 day remittances. ([53,] 54)

In den Bills nicht at sight, no element of value so constant and so effective as the rate of interest in the country on which the bill is drawn. The fluctuations in long bills daher, verglichen mit short ones, illimited. (55)

Extent to which solvency and credit of the drawer as well as of the acceptor, of a bill, affects the value of that bill: Firms of first rate standing „make the best exchanges“. Price paid to a merchant of undoubted position for his 60 days’ sight bill on a foreign country, higher than that granted for a second-rate bill on the same place. Concession in price must be made to purchaser, to take an article of inferior security. They must be indemnified for greater risk. … Amongst those engaged in international trade, the price at which exporting houses can sell their foreign bills, is looked upon as an unerring test of the credit which they enjoy among their neighbours. Thus credit causes a difference in the value even of such foreign bills as are drawn on the same day, rendering it difficult to give any exact or definite quotation of the price of long-dated paper. Ausserdem, Credit operates on exchanges generally in times of commercial panic or excitement, and causes the prices of all bills to fall. ([55,] 56)

In the case of America (1861) purchasers made a large discount for the risks which they thought they ran. Either the bills might not be accepted at all, in consequence of an enormous fall in the value of the goods against which they were drawn, and the drawers whom the purchaser would then have to call upon to refund the amount, might have failed in the interim. Or, the bills might have been accepted, but not be paid at maturity, owing to the difficulties in which it was expected that all connected with America would be involved. (57)

Depreciated Currency: The basis of a settlement through a bill of exchange, consists in the payment of a certain amount in sterling money to a merchant trading with France, against his giving an assignment for the same value on a French merchant. (58) Schwierigkeit d’abord, wenn doppelte currency, Gold in einem Land, Silber in dem andern. What is value of £100 in Vienna? (59)

Suppose a country in which there is a depreciated currency, but in which a premium on gold is regularly established, and is not restricted by artificial means. Add the premium commanded by gold in the depreciated currency to the expenses incurred by the creditors of such a country, who have to recover their claim by sending for the gold instead of selling bills, or, in the opposite case of the debtors, make a corresponding deduction. (61) If these debtors, instead of paying an extradordinary price for the bills which they wish to purchase and remit, incur the expense of sending bullion, the premium which they will obtain on such bullion will naturally go in reduction of the expenses incurred. This will accordingly give them a great advantage over the sellers; in other words, over the creditors of the country in question. (62) The depreciation of the paper circulation und the premium on bullion is almost  Zusatz von Marx.
the same thing. (63)

Wo large and inconvertible paper currency »the precious metals … no longer constitute the standard, but themselves become subject to another standard[«]. Den  Zusatz von Marx.
(nominellen, notabene!)
Preisfluctuationen der andern Waaren entspricht der des Goldes. Steigen sie, so auch price of gold, as measured by paper money. (63) So wenn östreichisch Papiergeld fällt, Gold steigt in Oestreich und English £ worth so many more Austrian paper florins. … An English traveller in Austria obtains at such a time f.i. 15 florins instead of 10 for £1. Thus those who pay sovereigns for florins on the London Exchange, require the same favourable terms. Alle andren Ursachen, die influence die Fluctuations of Foreign Exchanges produciren selten combined a variation of 10%. Anders mit den effects of variations produced etc durch die currency. (64)

diese fluctuations, in a certain sense, apparent, die 15 depreciirten florins nicht mehr werth als vorher die 10fl. (65) The purchasing power of the nominally larger sum |97 is not greater than that of the smaller. (66) Ebenso, after the new standard of exchange is established, seller has no loss. Z.B. seller, drawing for export of sugar to Vienna, sold his sugar for 10,000 florins, 10fl. = 1£, also = £1000 for his sugar. A fluctuation of 10% now occurs, owing to an over issue of paper in Austria. Prices generally rise 10%, and the exchange rises also. He sells now his sugar for 11,000 florins, and sells his florins at the rate of 11fl. = 1£, thus realising £1000, precisely as before. (66, 67)

Der rise der Prices ist nicht sofort general. In Austria the manufacturers insisted that they made considerable profits by the depreciation of the currency, as the cost of labour had not risen in the same proportion as the manufactured goods. The raw material being imported from abroad had risen to the full extent at once; and this enabled the manufacturers to increase the price paid for their products in the same ratio, though one element of production, labour, remained comparatively stationary. (67)

The apparent fluctuation in the exchanges extends no further than the apparent increase of value which has resulted from the same cause. (68) A parcel of manufactured goods commands more florins, and an English sovereign commands more florins also. (l.c.)

Anders verhält es sich, when the fluctuation (in the value of currency) occurs between the beginning and end of the same (mercantile) operation. Z.B. der shipper of sugar shipped his sugar before the depreciation, sold it at 10,000fl., 10fl. = 1£. Defers his drafts against these florins for some time. In the interval, the rate of exchange changes to 11fl. = 1£. He gets now only 909£ instead of 1000£, which the former exchange would have given him. In fact, a fluctuation in the exchange, produced by a depreciation of the currency, makes the existing claims on a country in such a situation worth so much less, whereas all debts due to it can be so much more advantageously discharged; the creditor of the country loses and its debtor gains. Wären its imports und exports in equilibrium, there would, on the aggregate of transactions, be neither loss nor gain. Der individual creditor of the country would lose, the individual debtor gain. (68, 69)

The bills on a given country fluctuate in value to the extent worin die prices of all purchaseable articles – bullion included – are affected by the depreciation of currency; in other words, in proportion to the discount of the paper money, or the premium on gold. Beyond this proportion, the fact of the depreciation of the currency cannot cause them to depreciate. Sonst the creditor of any sum payable in the inferior money would request his debtor to send him gold for the amount of his debt, notwithstanding the premium upon it; for, under the hypothesis, such a premium would be less than the loss entailed in settling the transaction by the sale of a bill. (70)

Aber if the Export of bullion, from the country, where the depreciated currency exists, is prohibited? or if it is impossible to buy up gold, either because it is illegal to pay a premium, or because all bullion has actually disappeared? (70) How is the holder of a claim on such a country to encash that which is due to him? (70)

Z.B. A merchant has supplied Russia with cotton when the export of bullion from Russia was practically prohibited. How was he to exact payment? He is entitled so many roubles in St. Petersburg. How could he convert those roubles into English sovereigns? Oder: A Russian spinner has imported cotton from Liverpool. How shall he pay? He must either buy a bill on England from others who happen to have sent produce thither, and thus have claim on an English house, which he can buy and transfer to his Liverpool creditor; or he must send the produce, which will sell for sovereigns, himself. Aber in Russia pause in exportation during a large portion of the winter season. He would be unable to send any remittances at all, unless he could find bankers or others who might draw on England, or on some other foreign banking centre, in anticipation of future exports, and would sell him the bills. But as to price, he is entirely in their hands. ([70,] 71) Muß er das Geld an |98 bestimmtem Tag in England zahlen, dann no limit to the price exacted from him – in other words no limit to the fluctuations in the exchange. If the exports of such a country do not equal the imports (by far the most general case) the balance which the country has to pay can only be settled by an enormous sacrifice, – in fact, cannot be settled at all except by a cessation or diminution of imports, or by a foreign loan, the latter being only an expedient to gain time and an adjournment of the payment of the balance due. (72) Wären die imports dieser country > exports, bullion would be flowing to it, and no grounds for the prohibition of its export would have existed. (73) The consequence of the depreciation of currency in any country is to offer inducement for further importation, by creating an appearance of high prices. (74) Für den debtor to Foreign Country in such case  Zusatz von Marx.
(wo kein bullion, or its export prohibited)
, if the demand for bills exceeds the supply, there is theoretically no limit whatever to the price of bills. (75)

In case of equilibrium of exports and imports the natural value would be, not the nominal par of exchange, not the value of the rouble when it was convertible and was in reality a silver coin, but this value minus the depreciation which the rouble has suffered in Russia itself. (75) Practically, owing to the system of credit and deferred payments, there is never an equality between exports and imports; and an increasing balance of debts lowers more and more, at least in reference to the Foreign Exchanges, the value of what, in this case, we have called the rouble. (76)

Case of different standard of value (gold and silver), as between Hamburg and London: Either gold or silver will be at a premium. Except France, with its double standard, gold is simply merchandise in countries of silver currency, and silver merchandise is in countries which have a gold standard. According to the price of the merchandise at a given moment, the exchanges fluctuate. When a bill on Hamburg is to be sold in London, the value of silver in England will enter largely into consideration, or, in the opposite case, the value of gold in Hamburg. When great demand for silver in England, as in case when large shipments are to be made to the East, there will be a great demand of bills upon Hamburg; for one means of procuring silver … buying up bills on Hamburg, send this these bills for encashment, send instructions that the silver thus encashed is to be actually shipped to England. If silver at premium in Hamburg England, the sellers of bills on Hamburg exact premium from the purchaser by raising the price of their bills; the buyer will have to pay more £ for marks banko, or, what comes to the same, will receive less marks for 1£ St. (78 76, 77) When silver not a premium 1£ = 131/4 marks; wenn silver rises, vielleicht nur 131/8 marks. The exchange on Hamburg being expressed by the number of marks banco, which are to be had for 1£, the exchange on Hamburg will be said to have fallen. But in fact bills on Hamburg have then risen in price, a less amount of marks commanding the same amount of gold. Umgekehrt. Hamburg merchant wants gold, z.B. to buy cotton with it in America. Bills on London serve the purpose. Competition for such bills. Premium on them, they rise in price. More bancos demanded for every £ which is placed in London at the disposal of the purchaser of the bills. Hamburg exchange will rise; z.B. 131/2 marks given for 1£. Limit of this fluctuation will be the extent of premium of premium obtainable. Silver may be sent to London, and sold there for gold; oder im umgekehrten Fall Gold may be sent to Hamburg, sold there at the discount at which gold will stand in Hamburg, under the circumstances, the proceeds invested in silver and shipped over to England. The assumption necessary for the argument is, that a sale of gold is always possible in Hamburg, and a sale of silver possible in England. (78, 79) The sale is generally possible, and thus defines the limits of the fluctuations in the rates of exchange. ([79,] 80)

Wenn es sich nicht, wie unterstellt um merchants handelt, die want to possess themselves of gold or silver, sondern um creditors und debtors, the case is the same. An English merchant owes a certain amount of Hamburg money. He is bound to pay in silver. When debt becomes due, silver be dearer than usually in England. Er muß buy silver at the enhanced price in the English market and ship it to Hamburg, oder buy bill on Hamburg, payable in marks, at an unfavourable exchange. The price of silver having risen, the price of bills payable in silver rises also, and the purchaser will receive fewer marks for his £. Aber limit the premium he has to pay for silver itself in the open market. (80, 81)|


Mit France, wo double standard, no difficulty at all. (81) A bill in Paris will be paid in that coin which is least in demand, which is at a discount as compared with the other. The purchaser of such a bill will not allow the price to be enhanced by the existence of a premium on one portion of the currency. (82)

 Feller/Odermann, S. 162.

100 als Maaßstab für arithmetische Verhältnisse. Es handelt sich um die Procentrechnung: 1) Aufsuchung der von einem gegebnen Werth nach Maaßstab eines bestimmten Procentsatzes zu nehmenden Procente, ohne Rücksicht darauf, wie sie sich auf den Werth, auf den sie sich beziehn, etwa einwirken. 2) Aufsuchung eines nach einem gewissen Procentfuß veränderten Werths, bestehe die Veränderung in Vermehrung od. Verminderung des gegebnen Werths. 3) Aufsuchung des Werths, von welchem gewisse Procente berechnet worden sind. 4) Aufsuchung des Procentfusses.

Der Werth, oder das Kapital, von welchem Procente gerechnet werden sollen, entspricht jedoch nicht immer vollkommen der Normalzahl 100.

Z.B. Jemand sagt: Eine Waare kostet mit Inbegriff von 10% Unkosten 51/2 Th. So entsprechen diese 51/2 Th. nicht dem Maaßstab 100, weil die 10% ursprünglich auf kleinren Werth als 51/2 Th. berechnet, auf einen Geldwerth, ehe man diese 10% Unkosten hinzurechnete. Solche Werthe wie diese 51/2 Th. können ein um die Procente vermehrtes Kapital heissen.

Ein andrer sagt: Ich habe diese Waare, nach Abzug von 2% für baare Zahlung, mit 4f. 30xr bezahlt. Diese 4f. xr entsprechen dem Maaßstab 100 nicht. Die 2% sind auf einen Werth berechnet, der vorhanden war, bevor die 2% abgezogen wurden. Daher können die 4f. 30xr ein um die Procente vermindertes Kapital heissen.

Es fragt sich also stets, ob der gegebne oder zu suchende Werth rein, vermehrt, oder vermindert ist.

Dieser dreifachen Beschaffenheit des gegebnen od. zu suchenden Werths entsprechen 3 Procentsätze, vom Hundert, auf Hundert, im Hundert.

Procente vom 100: 100 = 3. Procente auf 100: 103 = 3. Procente im Hundert: 97 = 3.

I)  Feller/Odermann, S. 164.
Aufsuchung der Procente allein.

a) Der reine Werth ist gegeben. (Procente vom 100.)

Wieviel betragen 4% von 1975 Th. u. 6% von 1812f.?

100 : 1975 = 4 : x 100 : 1812 = 6 : x
x = 79 Th. x = 108,72f.

b) Der vermehrte Werth ist gegeben. (Procente auf 100)

Wenn 1545 Th. eine Vermehrung von 3%, u. 1920f. 72 cts. eine Vermehrung eine von 6% einschliessen, wieviel beträgt diese Vermehrung, od. die Procente auf 100 von diesen Kapitalien?

103 : 1545 = 3 : x 106 : 1920,72 = 6 : x
x = 45 Th.  Anmerkung von Marx.
Es stecken in den 1545 Th. 45 Th. Pr. Cent.
x = 108,72 fcs.

Alle Procentsätze vom hundert, die einen bequemen Theil von 100 geben, bilden auch einen Theil auf 100 + dem Procentsatz, wenn sie als Procente auf 100 benuzt werden. Man findet diesen Theil, wenn man zu dem Nenner des Bruchtheils, den der Procentsatz vom 100 bildet, den Zähler desselben Bruchs addirt.

Z.B. 61/4% vom 100 = 1/16; ist auf 100 = 1/16+11/17. 371/2 vom 100 = 3/8; auf Hundert = 3/8+33/11.

c) Der verminderte Werth ist gegeben. (Procente im 100.)

Wenn ein Werth durch Abrechnung von 3% auf 582 Th., u. ein andrer durch Abrechnung von 31/2% auf 239 Fcs. 32 cts. vermindert worden, wie viel diese Verminderung? od. wieviel von diesen Werthen die Procente im 100?

97 : 582 = 3 : x 961/2: 239,32 = 31/2: x
x = 18 Th. x = 8,68 Fcs.

Alle Procentsätze, die vom u. auf 100 einen bequemen Theil aus dem Capital bilden, können auf dieselbe Weise als Procente im 100 benutzt werden. Man findet diesen Theil, wenn man von dem Nenner des Bruchs, den sie vom 100 bilden, den Zähler desselben Bruchs abzieht.

Z.B. 81/3% vom 100 = 1/12. Dann 81/3% im 100 = 1/12–11/11.

II)  Feller/Odermann, S. 169.
Aufsuchung eines nach einem gewissen Procentsatz veränderten Werths.

Ist der zur Veränderung gegebne Werth rein, dann wird er nach dem gegebnen Procentsatz vom 100 vermehrt od. vermindert.

Schließt der Werth die Vermehrung nach dem gegebnen Procentsatz bereits ein, so soll er auf seinen ursprünglichen Werth reducirt, also nach dem gegebnen Procentsatz (auf 100) vermindert werden.

Ist der gegebne Werth nach dem gegebnen Procentsatz vermindert, so soll er auf seinen ursprünglichen Werth reducirt, also nach demselben Procentsatz (im 100) vermehrt werden.

a) Der reine Werth ist gegeben.

Wieviel betragen 978 Th., um 3% vermehrt od. vermindert?

978 978
+29,34 = 3% = 1007,34 Th. (10 Sgr.) –29,34 = 3% = 948,66 Th. (20 Sgr.)

b) Der vermehrte Werth ist gegeben.

Wie groß waren 1) 2054 Th. und 2) 1925£ 11s., ehe sie resp. um 3% u. 371/2% vermindert wurden?

103 : 2054 = 100 : x
x = 1994 Th. 5 Sgr.

 Selbständige Anwendung einer bei Feller/Odermann, S. 171, erwähnten Regel durch Marx.
In dem 2t Beispiel unnütz die Regel de Tri anzuwenden, weil 371/2% = 3/11 des Werths. Also:

1925£ 11s.
525. 3 = – 3/11 aus 1925£ 11s.
1400£. 8

c) Der verminderte Werth ist gegeben.

Wie groß waren 1) 582 Th., bevor sie um 3% 2) u. 16011/4 Th., bevor sie um 61/4% vermindert wurden?

1) 97 : 582 = 100 : x 2) 16011/4 Th.
x = 600 Th. 1063/4 Th. = +  Feller/Odermann, S. 172: 1/15
(16011/4),  Zusatz von Marx, der hier fälschlicherweise Feller/Odermann korrigieren will.
da 61/41/16
1708 Th.

III) Aufsuchung des Werths von welchem gewisse gegebne Procente gerechnet worden sind.

Neben den Procenten muß hier auch der Procentsatz gegeben sein, wonach die Berechnung der Procente erfolgt ist. Dann ist die Frage:

Wenn der Procentsatz das ihm entsprechende Grundkapital (100, 100 + %, 100 – %) erfordert, welchen Werth erfordern die gegebnen Procente?

Von welchen Beträgen ist gerechnet worden 75 Th. à 6% vom 100? 1)
78f. à 3% auf 100? 2)
(à 31/2%–) 8f. 68 cts. im Hundert? 3)
ad 1.) 6 : 75 = 100 : x ad 2) 3 : 78 = 103 : x ad 3) 31/2: 8,68 = 961/2: x
x = 1250 Th. x = 2678f. x = 239,32 fcs.

IV) Aufsuchung des Procentsatzes.

Obgleich auch hier ein reines, vermehrtes od. vermindertes Kapital gegeben sein kann, so ist hier doch nur der Procentsatz vom 100 aufzusuchen. Denn Procentsatz vom 100 wird nur dadurch Procentsatz auf od. im 100, daß er sich auf einen nach demselben Procentsatz vermehrten od. verminderten Werth bezieht. Also bleibt der Procentsatz überall derselbe, u. nur die Beschaffenheit des Kapitals ist es, die den Unterschied bewirkt.|


a) Wenn man an 175 Th. einen Gewinn od. Verlust von 7 Th. hat, wie viel Procent beträgt dieß? Das reine Kapital ist gegeben, also PCte vom 100.

175 : 100 = 7 : x
x = 4%.

b) Wenn von 126 M.B. 12β abgezogen werden 24 M.B. 9β, wie viel PCt auf 100 beträgt dieß? Das vermehrte Kapital ist gegeben.

Man fragt also: wieviel geben 100, wenn 102 M.B. 3β ⦗126 M.B. 12β ÷ 24.9⦘ geben 24 M.B. 9β?

1023/16: 100 = 249/16: x
x = 24%.

Oder wenn in 182 Rth ein Gewinn von 7 Th. steckt, wie viel Procent beträgt dieß: (182 ÷ 7) : 100 = 7 : x. und x = 4%.

c) Wenn ein Kapital durch einen Verlust von 7 Th. auf 168 Th. reducirt ist, wie viel % beträgt der Verlust? Vermindertes Kapital gegeben. Procente im 100.

(168 + 7) : 100 = 7 : x
x = 4%.

Oft sind die Procente nicht geradezu gegeben, sondern müssen erst aus den gegebnen Werthen gefunden werden.

Wenn statt 950 Thl. bezahlt werden 988 od. 912: wie viel Procent mehr od. weniger bezahlt?

950 : 100 = 38 ⦗= 988 – 950. (950 – 912)⦘ : x. x = 4%.

Wenn man statt 3463 M.B. 1β nur 3186 M.B. 14β bezahlt, wie viel % auf 100 beträgt der Verlust? Abzug = 3463 M.B. 1 – 3186.14 = 276 M.B. 3β.

Also: 31867/8: 100 = 2763/16: x. x = 82/3%.

Wieviel % im 100 beträgt es, wenn statt 1875f. berechnet werden 2000f? Die Verrechnung im 100 = 2000–1875 = 125f. Also:

2000 : 100 = 125 : x.
x = 61/4%.

Manchmal wird statt von 100 von 1000 gerechnet ‰, besonders in der Wechselcourtage oder Sensarie.

Verwandlung eines Procentsatzes in den andern.

Wie viel % vom 100 betragen 12% auf 100? 112 : 100 = 12 : x. x = 105/7%.

Wieviel % auf 100 betragen 5% vom 100? 95 : 100 = 5 : x. | x = 55/19%.

Wieviel % vom 100 betragen 4% im 100? 96 : 100 = 4 : x. | x = 41/6%.

Wie viel Pct im 100 betragen 4% vom 100? 104 : 100 = 4 : x | x = 311/13%.

Anwendung der Procentrechnung.

 Feller/Odermann, S. 180. Marx lässt das bei Feller/Odermann eigentliche a) Berechnung von Provision, Courtage, Assecuranzprämie usw. aus.
a) Gewinn- u. Verlustrechnung

α) Wie viel gewinnt od. verliert man an Waare, zu 15 Th. eingekauft, mit 6% Gewinn od. 6% Verlust verkauft? | 15 Th. reines Kapital. Procente vom 100. | 1% = 0,15  Anmerkung von Marx.
(100ste Theil von 15)
6% = 0,9 Thl.

β) Wieviel beträgt der im Verkaufspreis von 15,9 Th. enthaltne Gewinn, à 6%? 15,9 = Vermehrtes Kapital. Procente auf 100. Also: 106 : 15,9 = 6 : x. x = 0,9 Thaler.

γ) Wieviel der durch den Verkaufspreis von 14,1 Rth hervorgebrachte Verlust à 6%? 14,1 Th. = vermindertes Kapital, also Procente im 100. ∴ 94 : 14,1 = 6 : x | x = 0,9 Thl.


1) Wie ist Waare mit 15 Th. gekauft mit 6% Gewinn od. Verlust zu verkaufen?

15 Th = Reines Kapital. Also Vermehrung od. Verminderung auf % vom 100.
100 : 15 = 106 : x. x = 15,9. Oder: 6 : 0,9 = 106 : x = 15,9 Th.
100 : 15 = 94 : x x = 14,1 Th. 6 : 0,9 = 94 : x. x = 14,1 Th.

2) α) Wenn der an einem Verkauf gemachte Gewinn oder Verlust à 6% = 0,9 Th., wieviel beträgt der Einkauf?

Das Einkaufskapital ist reines Kapital. Also Procente vom 100. Der Ansatz ist in beiden Fällen derselbe.
6 : 0,9 = 100 : x. x = 15 Th.

2) β) Der Verkaufspreis ist 15,9 Th. u. enthält 6% Gewinn. Wie viel kostet die Waare im Einkauf?

15,9 Th. vermehrtes Kapital, also % auf 100.
106 : 15,9 = 100 : x. x = 15 Th.

2) γ) Verkaufspreis, ca 6% Verlust, = 14,1 Th. Wie viel kostet die Waare im Einkauf?

14,1 Th. vermindertes Kapital, also % im 100.
94 : 14,1 = 100 : x. x = 15 Th.

3) α) Einkaufspreis = 15 Th. Darauf Gewinn od. Verlust 0,9 Th. Wie viel Procent beträgt dieß?

Kapital in beiden Fällen 15 Th. reines Kapital, Procente von 100.
15 : 100 = 0,9 : x. x = 6%.

β) Verkaufspreis von 15,9 Th. enthält Gewinn von 0,9. Wie viel % enthält derselbe?

15,9 vermehrtes Kapital, also % auf 100.
15,9 – 0,9 oder 15 : 100 = 0,9 : x. x = 6%.

γ) Verkaufspreis von 14,1 Th. enthält Verlust von 0,9 Th. Wie viel % beträgt derselbe?

14,1 Th. vermindertes Kapital, also % im 100.
14,1 + 0,9  Zwischenschritt von Marx.
= 15. 15
: 100 = 0,9 : x . x = 6%.

Man hätte auch für β) u. γ) sagen können.

β) 15 : 100 = 15,9 : x. x = 106 Th.

γ) 15 : 100 = 14,1 : x. x = 94 Th.

Hier die % im  Feller/Odermann, S. 181: Grundcapitale
versteckt. So viel mehr > 100% Gewinn etc.

Um obige Fragen durch einfache Regel de Trisätze lösen zu können, müssen Einkaufs- u. Verkaufspreis in derselben Valuta (Geldwährung) bestimmt sein u. sich auf dieselbe Quantität beziehn. Wo nicht dieß der Fall, vorherige Reductionen nöthig. Oder Kettensatz anzuwenden.


1 Ctr (à 100lb) kostet im Einkauf 30f. Man verkauft 1lb mit 24xr. |  Zusatz von Marx.
1fl. = 60xr.
 | Wie viel % beträgt Gewinn od. Verlust?

Erste Rechnungsart.

Kostet 1 Ctr = 30f., so 1lb = 18xr. Man gewinnt also 6xr mit 24xr 18xr. Wie viel mit 100?

18 : 100 = 6 : x. x = 331/3%.

Zweite Rechnungsart.

Verkauft man 1lb mit 24xr, so ein Ctr mit 40f. Man gewinnt also 10f. mit 30fc. Wie viel mit 100?

30 : 100 = 10 : x. x = 331/3%.

Dritte Rechenart durch Kettensatz.

x f. Verkauf = 100f. Einkauf.
30 = 100lb.
1 = 24xr Verkauf
60 = 1f.
Also x =  10000×24 600×3 100×24 6×3 400 3 = 1331/3 Verkauf. Die %331/3 hier im Gesammtwerth versteckt.

Unter obigen Voraussetzungen wird der Einkaufspreis eines Centners gesucht?

x f. Einkauf = 1 Ctr
1 Ctr = 100lb.
1 = 24xr
60 = 1f.
1331/3 = 100f. Einkauf. x = 30f.

Ein andrer Fall ist, wenn aus einem Verkaufspreis, wobei gewisse Procente Verlust od. Gewinn, ein Verkaufspreis mit gewissen Procenten Gewinn od. Verlust gesucht werden soll, oder aus einem, Gewinn od. Verlust schon einschliessenden Verkaufspreis ein solcher zu finden ist, welcher erhöhte Procente in sich faßt.

Hier kann man entweder, wie früher gezeigt, zuerst den Einkaufspreis u. dann den Verkaufspreis nach Maßgabe der zu gewinnenden oder zu verliernden % suchen,

Oder jeden dieser Fälle in einem Regel de Tri Satz berechnen,  Zusatz von Marx.
wie folgende Beispiele zeigen. (Verte)



1) Waare verkauft zu 15 Th. mit Verlust von 10%. Wie zu verkaufen, um 5% zu gewinnen? 90 : 15 = 105 : x. x = 171/2 Th.

2) Waare verkauft zu 171/2 Th., wobei 5% Gewinn. Wie ist sie mit 10% Gewinn zu verkaufen? 105 : 171/2 = 90 : x. x = 15 Th.

3) Waare verkauft zu 171/2 Th mit 5% Gewinn. Wie zu 8% Gewinn zu verkaufen? 105 : 171/2 = 108 : x. x = 18 Th.

4) Waare verkauft zu 15 Th. mit 10% Verlust. Wie zu verkaufen, wenn man 20% verlieren muß? 90 : 15 = 80 : x. x = 131/3 Th.

Um jedoch reinen Gewinn oder Verlust auf ein Geschäft berechnen zu können, Zinsen zu berechnen auf die Zeit, worin das Anlagekapital nicht benutzt werden kann.

b)  Feller/Odermann, S. 186.
(Rabbattere ital.)

Bedeutet eigentlich. Rabatt – einen Wiederabzug des vorher zu einem gewissen Betrag hinzugefügten. Im Allgemeinen aber Rabatt = jeden, meist procentweis berechneten Abzug, entweder als Vergütung für frühere Zahlung (Discont) od. als einen besondern oft nur scheinbaren Vortheil, der gewährt wird, oder Abzug den Käufer für Mangelhaftigkeit der Waare macht (Decort).

Das Kapital, von welchem der Rabatt genommen werden soll, heißt das rabattirende; das von welchem er bereits genommen ist, das rabattirte Kapital.

Beispiele. aufgesuch(?)

Wie viel der Rabatt von 1207 Th. à 3% u. 61/4 vom u. auf 100?

Aufsuchung der Procente. Aufsuchung der Procente.

[a)] 12,07 × 3 = 36,21 Th. [b)] 103 : 1207 = 3 : x. x = 3516/103 Th.
[c)] 1207 div. durch 16 = 757/16 Th. [d)] 1207 div. durch 17 = 71 Th.

Wie viel betragen 1207 Th. nach Abzug obiger Rabattprocente? Aufsuchung des rabattirten Kapitals?

[a)] 1207 – 36,21 (= 3%) = 1170,79 Th. [b)] 1207 – 757/16 (= 1/16 aus 1207) = 1131 9/16 Th.
[c)] 103 : 1207 = 100 : x. x = 117187/103 Th. [d)] 1207 – 71 (= 1/17 aus 1207) = 1136 Th.

Von welchem Kapital rechnete man: 36,21 Th. à 3% und 757/16 Th. à 61/4% vom 100; 3516/103 à 3% u. 71 Th. a 61/4% auf 100?

Aufsuchung des zu rabattirenden Kapitals?

[a)] 3 : 36,21 = 100 : x. x = 1207 Th. 757/16 × 16 = 1207 Th.
[b)] 3 : 3516/103 = 103 : x. x = 1207 Th. 71 × 17 = 1207 Th.

Die Usanz Rabatten sind  Feller/Odermann, S. 188: scheinbarer Vortheil
reine Charlatanerie
. Ob sie vom od. auf 100 berechnet, sie sind dem Verkaufspreis schon hinzugefügt.

Z.B. Stück Waare mit dem gewöhnlichen Profit inclusive kostet 20 Th. Wie stellt Verkäufer den Preis, je nachdem er 5% Rabatt auf 100 od. vom 100 gewährt?

Wenn auf 100: 100 : 105 = 20 : x; Wenn von 100: 95 : 100 = 20 : x
x = 21 Th. x = 211/19 Th.

Im zweiten Fall erhält er statt des Verkaufspreises von 100 nur 95; statt 95 muß er 100 fordern. Im ersten Fall erhält er statt 105 nur 100; statt 100 muß er also 105 fordern.

 Kommentar von Marx.
Wenn das Vieh nun ohne den Rabatt trick für 20 Th. 20 Th. forderte, wäre all the same.

10 Stück à 20 Th. ohne Rabatt = 200 Th.
10 St. à 21 Th. mit 5% Rabatt auf 100 = 210.
Ab 5% = 1/21 des Betrags = 10 = 200 Th.
10 St. à 211/19 Th. mit 5% Rabatt vom 100 = 210 Th. 10/19
ab 5% = 1/20 des Betrags = 10 Th. 10/19 = 200 Th.

Für den Verkäufer völlig gleich, ob er Waare ohne Rabatt, mit 5% auf 100, od. mit 5% vom 100 verkauft, wenn er nur den Preis danach stellt.  Kommentierende Zusammenfassung von Marx.
Usanzmässige Rabatte Humbug
, wenn nicht Vergütungen für baare Zahlung. Hätte man hier vom Preis von 21 Th. p. Stück nach 5% vom 100 verkauft = 1/20 des Kapitals = 11/20 Th., so erhielte man für das Stück nur 1919/20 Th., also 1/20 Verlust. Dieser Verlust bildet genau den Rabatt à 5% vom 100 auf den eigentlich zu bewilligenden Rabatt von 1 Th. (100 : 1 = 5 : x = 1/20 Th.)

In der Praxis nicht immer so genau unterschieden, u. mancher Irrthum bei der Feststellung von Preisen mit Rabatt begangen.

Der Rabatt, welchen die Verlagsbuchhändler dem Sortimentsbuchhändler auf den Laden- od. ordinären Preis geben, wird stets vom 100 gerechnet, u. ist die einzige Vergütung, die der Sortimentsbuchhändler für Unkosten, Zeit u. Mühe hat. Dieser Rabatt wird von 10–331/3% berechnet. Der Preis eines Buches nach Abzug des Rabatts ist sein Nettopreis.

Wie viel beträgt eine Buchhändlerrechnung von 432f. 48xr nach Abzug von 61/4% Rabatt?

432f. 48xr.
÷ 27. 3 = 1/16 aus dem Betrag
405f. 45xr


  • Inhaltsverzeichnis von Friedrich Engels
  • 1869 I Heft
  • Money Market. 1868.
  • Money Market Review. Jahrgang 1868.
  • The Economist. Jahrgang 1868. Nachträge
    • The Economist. Jahrgang 1868.
    • Inhaltsregister für 1868 Jahrgang. („Money Market Review“ und „Economist“.)
    • Kommentar zu George Joachim Goschen
      • George J. Goschen: The Theory of the Foreign Exchange. 7th edit. London 1866.
      • Friedrich Ernst Feller, Carl Gustav Odermann: Das Ganze der kaufmännischen Arithmetik
      • Inhalt.