Ch. VI. Socalled Correctives of the Foreign Exchanges.

At all events, it must be borne in mind that that which is really to be corrected is not the actual position of the exchanges, but that state of things which has brought it about. (125)

Unfavourable exchanges – und daher export of bullion – the result either of the settlement of indebtedness, or of differences in the value of money, or of differences in currency. (126)  Kommentar von Marx.
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(Die leztre Ursache illusorisch, currency principle. Es könnte nur dann der Fall sein, abgesehn von indebtedness, or rate of interest, wenn aus Panic Geld in Sicherheit oder zu Zins (statt hoarding) abroad angelegt wird; aus Ursachen, die nicht direkt die depreciation der currency sind. Im Gegentheil, wenn, wie zur Zeit der Depreciation der Banknotes in England, das Land der depreciated currency gute Handelsbilanz hat, sezt die depreciated currency Gold als Exportartikel etc frei. Daher konnten die Engländer es in Kriegssubsidien und Kriegs-Ausgaben vermöbeln.)

The mutual indebtedness of two countries, und the relative value of money, or rate of interest, in each, – these 2 influences will be generally found to be operating simultaneously in opposite directions. Money will be dear and scarce in the country which owes much to foreign creditors, and plentiful in that which has exported much; and, high interest will be attracting money to that quarter whence specie is flowing out in payment of foreign debts. (127)

The adverse balance of trade will, as far as its power extends, render the bills on the country which is most in debt difficult to sale, and tend to compel it to export specie; whereas the high rate of interest, which is generally cotemporaneous with a drain, or the prospect of a drain, of specie, will revive a demand for bills on this same country; and enhance their value in other quarters; for there will be a general desire to procure the means of remitting capital to that market where it commands the highest value. (127)

In 1861, when the excessive indebtedness of England to America, for corn and cotton, lowered the price of English bills in New York, and rendered specie remittances to the States inevitable, the high rate of interest in England which this situation had brought about, was so attractive to continental bankers, that they drove up the price of bills upon this country to specie point, and were finally induced even to resort to bullion remittances. [(127, 128)]|

105

When the payments for imports continue for any length of time in excess of the receipts for exports, the redress of the balance can clearly only take place by ceasing to incur liabilities … If however, the derangement is but temporary, and while it consumes more in the first 6 months of the year, it exports more than it imports in the second 6 months, it can, like an individual with a prospective income, raise money to carry it over the interval. By offering a high rate of interest, it will be either able to procure a prolongation of credit from its creditors, till … the balance is paid off, or, it may induce third parties to make it a loan. Even … where a country is actually spending beyond its means, and where, by borrowing, it can only increase the evil …, a very high value of money is … most desirable  Zusatz von Marx.
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(für Göschen)
; as, by the action of the value of money on prices generally, a diminution of imports, and, consequently, of indebtedness is likely to ensue. (128, 129)

Aber hier to examine: the operation of a high rate of interest in those more usual cases where we have to deal with temporary fluctuations and sudden emergencies, such as may be caused by the loss of a harvest, or by a period of general national extravagance, ending in a critical inflation of prices, or by excessive warlike expenditure. (129)  Kommentar von Marx.
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(Er wiederholt jezt d. Bank Parlour, relating Tooke’s „screwing“ theory p. 130 sq.)

In such times influx of capital is only to be procured by offering it the advantages of a high rate of interest – a rate, higher than it can make at home, and sufficient to indemnify the capitalist for the expenses of transmission of his capital from one country to another. (131)

The Foreign Exchanges zeigen sofort, ob the inducement is powerful enough. So, wenn die Engländer shipped weekly (1861) gold for America, the Continental exchanges took a favourable turn; i.e. the Continent sought with greater eagerness for English bills, – a symptom that they were preparing remittances for the purpose of sending over funds to England, and that capital was passing from the Continent to us. The more the price of bills advances, the nearer is the specie limit approached, till finally the remittances are made, not in bills, but in gold. Practically, the effect of the purchase of bills for the purpose of placing funds in England, is identical in its effect with a shipment of gold; for every English bill held by continental capitalists gives to its possessor the power of drawing gold from us. (131, 132)

Where a considerable efflux of specie is taking place, the rate of interest will rise in the natural course of things. The abstraction caused by the bullion shipments will of itself tend to rise that rate;  Kommentar von Marx.
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(aber why, Mr. Gedschen?)
and banking establishments will in their own interest (which will be identical  Zusatz von Marx.
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(!)
with the interest of the public) accelerate this result as far as lies in their power. … A country which is paying off its debts, is sending away a portion of its capital when it exports specie;  Kommentar von Marx. Marx kritisierte die in der politischen Ökonomie fehlende Unterscheidung von Kapital und Geld, die sich etwa in Geldkrisen deutlich zeigt, zum Beispiel im ersten Band des „Kapital“: „Eben noch erklärte der Bürger in prosperitätstrunknem Aufklärungsdünkel das Geld für leeren Wahn. Nur die Waare ist Geld. Nur das Geld ist Waare! gellt’s jetzt über den Weltmarkt. Wie der Hirsch schreit nach frischem Wasser, so schreit seine Seele nach Geld, dem einzigen Reichthum.“ (MEGA² II/5. S. 94.)
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(aber, Theuerster, is iron or wheat or yarn or cloth, or any other commodity exported not also capital, hence, in your argument, a partial abstraction of capital? Der Esel hilft sich durch das Wort Capital statt Gold und folgerecht mußte in Zeiten starken Exports der Zins erhöht werden to stop that export of capital!);
and the foreign bankers who send over gold in order to buy up English bills, are supplying us with capital  Kommentar von Marx.
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(and do foreign importers not so in sending sugar etc, while you want, through the rise in the rate of interest, to stop that supply of capital, caused by import of commodities? Der Oekonom wagt nicht dem special character des Geldcapital in den Rachen zu sehen)
[.] At the same time, the actual export of bullion is a loss to the money  Kommentar von Marx.
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(he means currency)
of the country,  Kommentar von Marx.
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(i.e. durch den Act of 1844, which is not an effect of the nature of things. Quite the contrary.)
and the import of gold from abroad replaces that which has thus been lost. (132, 133)|

106

The real importance of a variation in the minimum rate of the Bank does consist in the indications afforded to the money market. The fixity of the minimum rate has this effect, that practically it becomes a maximum rate to the public.  Kommentar von Marx.
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(Unter public sind hier Göschen und Seinesgleichen zu verstehn)
Persons in good credit are always almost able to procure money a fraction under the Bank rate, and consequently the Bank o. England is generally the last to feel the pressure of a rising demand. Thus, an advance in the Bankrate generally means, that a previous pressure has been put on all other sources where discount is obtainable, and that the demand has reached the last reserve. (133, 134)

The fact has been that almost every advance in the Bankrate of discount is followed by a turn of the exchange in favour of England; and, vice versa, as soon as the rate of interest is lowered, the exchanges become less favourable. (134.  Kommentar von Marx. – Eine Kritik an Goschens Auffassung, dass beinahe jede Erhöhung der Diskontrate der Bank of England zu einem für England günstigen Wechselkurs und eine niedrige Diskontrate zu einem für England ungünstigen Wechselkurs führe, findet sich bereits bei Ernest Seyd: Bullion and Foreign Exchanges. London 1868. S. 568. Marx rezipierte Seyds Kritik in: The Money Market Review, 30. Mai 1868. S. 586. Er las anschließend Seyds Buch und zitierte daraus in Manuskript II zum zweiten Buch des „Kapital“ (MEGA² II/11. S. 33).
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This fact is only true – and still with great exceptions – for very acute panic times.
) In the first instance there are few buyers here for bills on foreign capitals, because foreign creditors give their English debtors a respite, and prefer to wait longer for remittances, gaining interest meanwhile at the profitable English rate. (135)

Bills which have some time to run seldom remain in the hands of the drawers, but are partly used as immediate remittances to the country where the bills are payable, and partly are bought by bankers or capitalists who desire them as an investment of money, yielding a certain interest during the interval between the date of their issue and the date when they fall due. This interest lies in the cheaper price of the bills. A bill payable 3 months after date is bought by a banker at a price which is equal to a bill payable on demand less 3 months’ interest, and this interest will not be that of the country where the bill is drawn, but that of the place where the bill is payable: for the purchaser will have to discount the bill in the foreign country at the rate there ruling, before he can make it equally available with a draft on demand; and the drawer can suffer this deduction from the price of the bill at the same rate without loss, as, giving the foreign acceptor 3 months’ grace before payment, he will receive from him the same amount of interest until the debt is discharged by the actual payment of the bill, as he loses in the price of the bill itself. Accordingly, when foreign bills are bought as an investment, it is with the view of earning the higher rate of a foreign country, in the place of the lower rate ruling at home. … this tendency always in operation when the rate of interest is peculiarly high in any country, the creditor of which is unimpeached. ([135,] 136, 137) As a matter of fact, the interest which can be secured by the speculative purchasers of bills, generally lies between the rate of the country where the bill is purchased, and the rate of that on which it is drawn, as competition enables the seller to secure a portion of this species of profit. If the rate in Germany is 3 P.Ct., and in England 5%, those who have 3 months’ bills on England will not be obliged to submit to a discount of 5% … Many will be found, who, in order themselves to make 1% more than the highest rate which they can secure at home, will not claim to deduct more than 4% from the price which they would pay for a bill on demand, instead of 5%. … These greater or less lesser deductions are generally expressed not in the rate of interest, which is to be deducted, but in the price of the bill – the bill is so much cheaper or dearer. (137)

At any moment there is in the hands of bankers and exchange dealers a large amount of bills on various countries, held partly for speculating on a rise or fall in the price of bills, but, to a very large extent, solely for the sake of the interest which is to be made on them. Bills on England, owing to the high rate of interest which they often bear, as compared with continental rates, are a favourite investment abroad. In Paris, Berlin, Frankfurt, Hamburg etc, the bills on England held by the bankers and joint stock Cos. often amount to many millions £. St.; and a very large sum remains in their hands for several months – in fact, from the time when the bills are drawn to the time when they are due … If at any time the rate of interest here falls below that which rules on the Continent, it is inevitable that the whole mass of those bills will be at once sent to London, |107 and be discounted there at the cheaper rate, so that the proceeds may be remitted in gold to the Continent to be invested there in local securities at the supposed higher rate. On the other hand, so long as the discount in London is higher than abroad, so long the foreign bankers will be induced to hold their bills till they become due. The debt, embodied in the bills in question, must bee be paid sooner or later; but the time when it must be liquidated will, within certain limits, depend upon the rate of interest. If it be high, the bills will be allowed to run off abroad, and the gold will not be exported till the last moment; umgekehrt im andren Fall. (138, 139)

Accordingly, if, f.i., specie is exported from England to America, an advance in the rate of discount, is an inducement to foreign capitalists to hold back their bills upon England to the last moment, as well as to make remittances hither to invest the proceeds at the high rate: both circumstances cause a demand for these bills abroad, and their price must rise. At the same time, a proportionate fall in the price of foreign bills will occur. For, a convenient mode of placing funds in England being to instruct English firms to draw on foreign bankers, these bills are likely to be pressed on the market; whereas, owing to the assumed desire rather to leave capital in England than to call it in, there will be few purchasers for them, and their price must decline. The rise of bills on England abroad is always identical with the fall of the prices of foreign bills in England; for there are 2 ways of settling every international transaction: either the creditor draws a bill on the debtor, or the debtor remits a bill to the creditor; and, accordingly, the same circumstances which make it difficult to the creditor to sell his bill to advantage, will make it difficult for the debtor to purchase the necessary remittances to advantage. When bills on England decrease in value abroad, bills on the continent increase in value on the London exchange; and when, as in the case where a high rate of interest is setting the current of capital towards England, there is a great demand, at high prices, for bills upon London, there is a corresponding absence of demand and low prices in England for bills on foreign cities. (139, 140)

Woher aber, in spite of the rapid flow of capital from one country to another to fill up any gaps, that may have been left, such a difference in the rate of interest between two countries as has occasionally been witnessed for some time in the case of England and the Continent? (140, 141)

Z.B. 6% rate in London, and 2 or 3% in Hamburg, or other continental cities? (141)

In the case of Hamburg there exists a difference of currency. The Hamburg capitalists possess this money in silver. He must ship his silver to England, sell it there, and with the proceeds discount bills at the high rate current in England. When these bills, however, mature, and the Hamburg banker wishes to repossess himself of the money, he must rechange sovereigns into silver, perhaps paying a premium for it; and this silver, he will have to reship to Hamburg. Die difference between interest in England und Hamburg sei = 6% – 2% = 4%. If his money invested in 3 months’ bills, his apparent profit for 1/4 year, = 4/4 = 1%. Nun aber Kost of shipment of specie remittance to and fro. He may lose by difference on price at which he sold his silver in England, and that at which he bought it back for home remittance. The costs of transport and the loss on the silver may far exceed the profit of 1%,  Zusatz von Marx.
Schließen
(derived von der difference of interest)
. Unter gewisser combination of circumstances die difference of 4% in rate of interest kann daher existiren ohne the Hamburg surplus capital finding its way to our money market. Dieß verschwindet wenn die difference noch grösser, particularly if the high rate can be secured for 6 months instead of 3. During most periods of high discount in England, there have been large orders here to take 6 months bills for foreign bankers. The preference is given to the longer paper, because the high rate secured for a so much longer time, while the probable cost of bullion remittance and risk of loss upon silver remain the same. (141–143) Hamburg shows the difficulties attending the transmission of capital from one country to another. (143)|

108

When the currency is identical, still possibility for differences in the rate of interest to exist in a greater or less degree. Z.B. cost of transmission of gold to and fro, between Paris and London, reduced to a minimum. The difference can never be very great.  Kommentar von Marx.
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(Was it not in 1866?)
Aber: interest calculated by a percentage per annum. The probable profit, when operation in 3 months bill contemplated, to be divided by 4, whereas the percentage of expense has to be wholly borne by one transmission. So a very slight expense becomes a great impediment. If the cost is only 1/2%, there must be a profit of 2% p.a. in the rate of interest, or 1/2% on 3 months, before any advantage commences. If 1/2% the cost of sending money to England, and exchanges so favourable as to be able to draw it back without any cost at all, there must nevertheless be an excess of more than 2% in the London rate of interest over that in Paris, before the operation of sending gold over from France, merely for the sake of the higher interest, will pay. (144, 145)

Hence a slight increase in the rate of discount is, under some circumstances, – that is, when there is not a great supply of bills upon England – not sufficient to bring over gold from the Continent … if 6% will not do, 7 or 8% will. … The first few per cents. do little more than cover the possible expenses of the transmission of the bullion itself, a difference of 4% p.a. on 3 months bills being necessary to cover 1% expense; but as soon as the charges (or the risk of charges) – the loss in exchange (as they are usually called) – are covered, then every additional per cent. which is granted as discount becomes an actual and certain profit … the rate of discount must be advanced till that point is reached. (145, 146)

Fact jedoch that stets grosse supply of English bills auf dem Continent. When the English rate of interest advances, desire to take advantage of it, and remit capital to England for temporary investment. The transmission to England effected in bills, so long as they can be procured. Sellers of English bills (on Continent) enabled to make a higher price. Competition raises it, till remittances by means of bills become almost as expensive as a shipment of bullion itself. Thus the profit, which would be made by those who could buy bills at the usual exchange to remit to England for investment at the higher rate, is divided between those who sell the bill and those who buy and remit it. … As the supply of bills tends to become insufficient, gold is actually sent. (146, 147)

The Peculiar Foreign Billsnot representing any actual indebtednessrather influence the exchanges in an opposite direction. … The issue of bills representing no transaction in goods, but simply based upon credit, and consequently … illimitable … tends to depress the price of bills. … For the period during which they have to run (for, as soon as they have to be covered, their previous effect is neutralised at once), their issue may have a material effect upon the export of gold. Those who draw bills in this manner on credit, may be actuated by two different motives: either they may wish to use the secure the use of the money paid as the price of these bills, for legitimate or illegitimate purposes, during the 2 months which the bill has to run, that is till the time when they must part with the money to pay remittances, – or they believe that when their drafts come to maturity there will be a larger supply of bills on the market, and that then they will be able to make a profit by buying their remittances at a cheaper price than they obtained for their drafts. The issue of drafts drawn upon credit, and not against any debt – drafts by which the drawer incurs a debt, instead of securing himself the payment of a debt of another – is a measure by which the merchants of the country in which they are drawn may be temporarily relieved of making bullion remittances, if they are in debt, or make cheaper remittances if they want to give orders. (148, 149) In other cases – at the expiration of a certain time this will add to the difficulty, as an equal amount must again be withdrawn. (149, 150)

On the continent, this species of bills is often used as an engine for drawing gold from England, |109 in fact, as a mode of borrowing in the London market. Drafts are issued, payable 3 months after date; these are remitted to London, and there discounted, the proceeds being invested in gold, and shipped abroad. When the Exchanges are unfavourable to the Continent – i.e., when a bill on England commands a larger number of dollars or florins than usual – such bills create an artificial supply, and may prevent the price from running up to specie point. duo duo. due. due.(?)

 Feller/Odermann, S. 226.
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Discontrechnung.

Bei Verkäufen auf Zeit od. Credit, Trassiren auf lange Sicht u.s.w. hat der Schuldner die Bezahlung eines gewissen Betrags zu einer bestimmten Zeit zu leisten, ohne denselben bis dahin verzinsen zu müssen. Der Gläubiger schlägt die Zinsen, die er von seinem Kapital geniessen würde, in diesem Fall, wenn er es selbst benutzen könnte, zu diesem Kapital. Der Schuldbetrag also = Kapital + Zinsen für die gegebne Zeit. Trägt der Schuldner, im Einverständniß mit Gläubiger, seine Schuld vor der Verfallszeit ab, so die Zinsen abzuziehn für die Zeitlänge, um welche früher seine Verbindlichkeit erfüllt. Dieser Nachlaß od. Abzug vom Schuldbetrag = Discont. Das Bezahlen einer Schuld vor Verfallzeit, unter Abzug von Discont heißt Diskontiren. Diskontgeschäft: Wechsel, später fällig, gekauft unter Abzug des Diskonts für die Zeit, welche sie bis zum Diskont noch zu laufen haben.

Das zu discontirende Kapital ist kein reiner, sondern ein vermehrter Werth. Daher die Abrechnung der in demselben enthaltnen Zinsen nicht nach Procentsatz von, sondern auf 100 zu erfolgen. Bei Abrechnung nach Procenten auf 100 bringt die baare Zahlung, wenn sofort zu demselben Zinsfuß wieder angelegt, ebenso viel Zinsen als der durch das Diskontiren erfolgte Abzug beträgt. Z.B. 2060 Th. in 1 J. fällig, sollen mit 3% diskontirt werden.

So: 103 : 2060 = 3 : x. x = 60 u. 2060 – 60 = 2000. Diese Summe zu 3% sofort wieder zinsbar angelegt, giebt 100 : 200 = 3 : x. x = 6000/100 = 60 Th. – Würde dagegen der Diskont vom 100 berechnet, so hätte man: 100 : 2060 = 3 : x. x =  Zwischenschritt von Marx.
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6180/100
= 61,8. Die baare Zahlung wäre 2000 – 61,8 = 1998,2 Th., welche, zu 3% angelegt, nur 59,946 Th. Zinsen giebt, Verlust für Empfänger von 1,854 Th., den er nur dadurch ausgleichen könnte, daß er die erhaltene Summe zu höherem Zinsfuß, etwas 31/10% wieder ausliehe.

Obgleich durch die letztre Art den Diskont zu berechnen, Empfang im Nachtheil, doch kaufmännischer usus. Theils Rechnung bequemer, theils der Unterschied in kaufmännischen Geschäften nur selten von Bedeutung, denn Zeitraum, wofür diskontirt wird, meist kurz. Anders aber in Beziehung auf Discontgeschäft mit Nichtkaufleuten. Erwerbung von Grundstücken u.s.w.

 Diese Überschrift samt Überschriftenebene von Marx. Bei Feller/Odermann nur: 1) Einfacher Discont auf Hundert
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A) Einfacher Diskont.

I)  Feller/Odermann, S. 228.
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Einfacher Discont auf 100.

1) Aufsuchung des Diskont.

Wieviel beträgt der Diskont von 1200 Th, am 24. Sept. fällig, u. am 12. Juli mit 4% diskontirt?

Von 12. Juli – 24. Sept., Monat zu 30 T. = 72 T. Man berechnet  Zusatz von Marx.
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d’abord
, wie viel Zinsen geben 100 in 72 T. à 4%? 360 : 72 = 4 : x. | x = 4/5 P.Ct.

Kapital von 100 also in 72 T. werth, à 4% Th. 1004/5. Umgekehrt sind 1004/5 in 72 Tagen fällig = 100 baar, od. geben einen Diskont von 4/5%. Wieviel beträgt der Diskont von 1200? | 1004/5 : 1200 = 4/5: x. | x = 911/21 Th = 9 Th. 15 Sgr. 7 Pf.

Richtiger ist es aber, u. auch gewöhnlicher, bei Discont auf 100 das Jahr zu 365 T. zu rechnen, sowohl für Zinsfuß als Zeit, welche das Kapital noch zu laufen hat. Dann 12 Juli – 24 Sept. = 74 Tage, und:

365 : 74 = 4 : x. x = 296/365%. und daher: 100296/365 : 1200 = 296/365: x. x = 96009/9199 = 9. Th. 19 Sgr. 6 Pf.

Auch das diskontirte Kapital kann zur Auffindung des Diskonts gegeben sein. Dann: Wie viel der Diskont, wenn ein à 72 Tage à 4% diskontirtes Kapital mit 119010/21 bezahlt wird?

Der baare Werth 100 giebt 4/5 Discont; wie viel geben 119010/21? | 100 : 119010/21 = 4/5 : x. x = 911/21 Th.

2) Aufsuchung des diskontirten Kapitals.

Hier kann neben Zinsfuß u. Zeit, entweder das zu diskontirende Kapital oder der Diskont gegeben sein. Man berechnet wie oben die Zinsen von 100 Kapital in 72 Tagen à 4% = 4/5. Wenn 100 +4/5, nach 72 Tagen fällig, = 100 baar, was ist Baarwerth von 1200 Th., nach 72 Tagen fällig? 1004/5 : 1200 = 100 : x. x = 119010/21 Th.

Wie viel wurde für ein à 4% discontirtes Kapital gezahlt, wenn der Discont für 72 Tage 911/21 Th. betrug?

4/5 : 911/21 = 100 : x. x = 119010/21 Th.

3) Aufsuchung des zu diskontirenden Kapitals.

Hier kann, neben Zinsfuß u. Zeit, entweder das diskontirte Kapital od. der Diskont gegeben sein.

Wie groß ist das Kapital, welches nach Abzug von 4% Discont für 72 T., 119010/21 Th. übrig gelassen hat?

Zunächst Zinsen von 100 in 72 T. à 4% zu berechnen. = 4/5%. Dann: 100 : 119010/21 = 1004/5 : x. x = 1200 Th.

Wie groß ist das Kapital, das für 72 T. à 4% mit 911/21 Th. diskontirt worden ist?

100 = 4/5 Zinsen. Also: 4/5: 911/21 = 1004/5 : x. x = 1200 Th.

Als ein diskontirtes Kapital ist der Baarpreis einer Waare dann anzusehn, wenn er dem Preis derselben Waare auf Zeit entgegengesetzt wird u. die Ermittlung des letztern aus dem ersten entspricht der Ermittlung des zu discontirenden Kapitals aus dem diskontirten Kapital.

Ist also z.B. der Baarpreis einer Waare = 16 Th., so sollte derselbe für 3 Mt. Credit, wenn der Verkäufer sich 5% Zinsen rechnet sein: 100 : 16 = 1011/4 : x. x = 16,2 Th. Die Waare könnte zu diesem Preis auf 3 Monate od. baar mit 5% Discont pr J. verkauft werden, der Discont müßte dann aber auf 100 berechnet sein. Da aber im kaufmännischen Verkehr der Discont stets vom 100 berechnet wird, so später anzugebender Weg zur Ermittlung dieses Preises.

4) Aufsuchung des Zinsfusses.

Wie viel % beträgt der Diskont, wenn 1200 Th. für 72 Tage mit 911/21 Th. diskontirt worden sind?

Sowohl Zinsfuß als Zeit verstehn sich immer für 100 Reinwerth, welcher noch keine Veränderung nach gewissen % erlitten hat. Das gegebne zu discontirende Kapital, weil es die % für gewisse Zeit einschließt, ist daher nicht proportional zu 100, u. wird es erst, wenn man es von dem in ihm enthaltnen Diskont befreit hat.

(1200 Th ÷  Zusatz von Marx zur Erklärung des Zeichens.
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(minus)
911/12 Th.) : 100 Th. Kapital = 911/21 Th. Discont : x
72 Tage : 360
x = 4%

Lautete die Frage: Wie viel beträgt der Diskont, wenn nach Abzug von 911/12 Th. Discont für 72 Tage, 119010/21 Th. bezahlt worden sind, so bedürfte es natürlich keiner Abrechnung des Disconts.

5) Aufsuchung der Zeit.

Wie lange hat ein Kapital von 1200 noch zu laufen, welches à 4% mit 911/12 Th. discontirt wurde?

(1200 Th ÷ 911/12 Th) : 100 Th. Kp. = 360 Tage : x T.
4 Th. Discont : 911/21 Th. Discont.
x = 72 Tage


132

II)  Feller/Odermann, S. 231.
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Einfacher Discont von 100.

1) Aufsuchung des Diskont.

Wieviel beträgt discont von 1200 Th. pr. 72 T. à 4%? D’abord zu sehn wie viel 100 in 72 J. à 4% giebt: 360 : 72 = 4 : x. x = 4/5.

Dann: 100 : 1200 = 4/5: x. x = 9,6 Th.

Die Berechnung des Disconts vom 100 (wie auch für jeden der folgenden Fälle) stimmt mit der Berechnung der Zinsen vollkommen überein. Durch das Discontiren nach Discontfuß vom 100 erleidet der Empfänger der Baarzahlung stets grösseren Abzug als nach demselben Discontfuß auf 100.

Es kann auch hier zur Aufsuchung des Disconts das diskontirte Kapital gegeben sein. Z.B. Wieviel der Discont, wenn Kapital, für 72 T. à 4% discontirt, Baarwerth von 1190,4 Th. hat?

Zinsen von 100 in 72 Tagen = 4/5 (à 4%). Hence Baarwerth von 100 vor Verfall der 72 Tage = 100 – 4/5 = 991/5. u. 991/5 : 1190,4 Th. = 4/5 : x; x = 9,6 Th.

2) Aufsuchung des diskontirten Kapitals.

Dazu kann neben Zeit u. Zinsfuß  Feller/Odermann, S. 232: 1) das zu discontirende Capital; 2) der Discont
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das diskontirte Kapital
gegeben sein.

a) Wieviel 1200 Th. nach 4% Discontabzug pr 72 Tage? Man berechnet erst den Discontabzug = 9,6 Th. Dann 1200 Th – 9,6 Th = 1190,4 Th. Oder man ziehe den Discont für 100 in 72 T. = 4/5 von 100 ab = 991/5. Dann: 100 : 1200 = 991/5 : x. x = 1190,4 Th.

b) Wie viel betrug, das diskontirte Kapital, wenn der à 4% pr. 72 Tage berechnete Diskont = 9,6 Th.? 4/5 : 9,6 = 991/5 : x. x = 1190,4 Th.

Formeln zur Vereinfachung der Rechnung: Baarwerth von 800 Th. sei nach 41 Tagen fällig, bei Discont von 4% auf od. von 100.

Nach 360 : 41 = 4% : x, Zinsen in 41 Tagen = 41/90 u. daher:

α) Discont auf 100: α) 10041/90 : 800 = 100 : x od. 9041 : 800 = 9000 : x

β) Discont von 100: β) 100 : 800 = 9949/90: x od. 9000 : 800 = 8959 : x

Daher folgt: α) das nach einem Discontsatz auf 100 zu vermindernde Kapital findet man, wenn man es mit dem zum Discontfuß gehörigen Divisor multiplicirt, u. durch denselben aber um die gegebne Anzahl der Tage vermehrten Divisor dividirt. β) Das nach Discontfuß von 100 zu vermindernde Kapital, wenn man es mit dem um die Anzahl der Tage verminderten Divisor multiplicirt u. durch den Divisor dividirt.

3) Aufsuchung des zu diskontirenden Kapitals.

Ausser Zinsfuß u. Zeit kann hier α) Discont, od. β) discontirtes Kapital gegeben sein.

α) Wie groß Kapital, diskontirt à 4%, mit 9,6 Th. für 72 Tage?

4 Th. Discont : 9,6 Th. Discont = 100 Th. Kapital : x
72 Tage : 360 Tage
x = 1200 Th.

β) Wie groß Kapital, welches nach Abzug von 4% Discont für 72 Tage 1190,4 Th. übrig läßt?

Discont von 100 Th. für 72 Tage à 4% = 4/5 Th; 100 – 4/5 = 991/5. und: 991/5 : 1190,4 = 100 : 1200.

Discontirter Werth, wie bemerkt, entspricht dem Baarpreis einer Waare, ein zu discontirender Werth dem Preise einer auf Zeit od. Credit zu verkaufenden Waare. Nach dem Kaufmannsusus auch im Waarenhandel der Diskont nach dem Fuß vom 100 berechnet. Also Frage: Wie ist aus dem Preis einer gegen baar zu verkaufenden Waare der Preis derselben Waare auf Zeit zu bestimmen?

Z.B. Welches der Preis einer Waare Ziel 3 Mt. mit 5% Disct., wenn sie pr. Casse mit 16 Th. verkauft wird?

Auf 3 Mt. 5% = 5/4% = 11/4%; 100 T. in 3 Monaten also baar werth = 100 – 11/4 = 983/4 baar.

Für 16 Th. baar hat man also, Ziel 3 Mt. zu fordern: 983/4: 16 = 100 : x; x = 1616/79 Th. zu fordern.

Erbietet sich nun der Käufer, dem die Waare mit 1616/79 Th. Ziel 3 Mt. od. pr Kasse mit 5% Discont notirt wird, sofort beim Kaufe der Waare zur Baarzahlung, so erhält der Verkäufer in der That 16 Th. baar, denn 5% auf 16,16/79 Th. für 3 Mt. = 16/79 Th. Macht er aber erst später, z.B. ein Monat vor Verfall, von der Baarzahlung Gebrauch, so Verkäufer  Marxʼ Ausdruck.
Schließen
beschissen
. Discont auf 1616/79 Th. pr 1 Mt. à 5% giebt 16/237 Th. – Er erhält also 1616/237 Th. Diese an Zinsen für 1 Mt. à 5% geben nur 239/3555 Th. statt 240/3555 od. 16/237, die er als Discont zu gewähren hatte.

4) Aufsuchung des Zinsfusses.

Welches ist Zinsfuß, wozu 1200 Th. p. 72 Tage mit 9,6 Th. diskontirt worden?

1200 Th. : 100 Th = 9,6 Th Discont : x
72 : 360 Tagen
x = 4%

5) Aufsuchung der Zeit.

Für wie viel Tage wurde Kapital von 1200 Th. diskontirt, wenn 9,6 Th. Discont à 4% gerechnet wurden?

1200 Th. : 100 = 360 Tage : x
4 Dst : 9,6 D. =
x = 72 Tage.

B)  Feller/Odermann, S. 237.
Schließen
Zusammengesetzter Discont.

1) Welchen Werth hat am 6. Mai 1855 Forderung von 2000 Th, fällig am 6 August 1857, mit 4% Discont vom Discont? α) Discont vom auf 100. β) Discont vom 100.
x Kapital = 2000 Th. Kp. x Th. Kapital = 2000 Th. K.
104 = 100 (1. Jahr) 100 = 96 für 1 J.
104 = 100 (2 J.) 100 = 96 2 J.
101 = 100 (3 Mt.) 100 = 99 3 M.
x = 1830,804 Th.  Zusatz von Marx.
Schließen
(x für erstes Glied: 104 : 100 = 2000 : x)
x = 1824,788 Th.  Zusatz von Marx.
Schließen
(x für erstes Glied: 100 : 96 = 2000 : x)

2) Staatsschuld von 20 Mill. Th. soll jährlich um 1% so getilgt werden, daß sich dieß eine Procent immer auf den nach erfolgter Tilgung übrigbleibenden Kapitalbetrag bezieht. Auf welchen Betrag die Schuld reducirt nach 5 Jahren? Procente vom 100.

x Th Kapt. = 20.000000 Th.
100 = 99
100 = 99
100 = 99
100 = 99
100 = 99
x = 19,019800,998 Th.

Inhalt:

  • 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.