Ch. V. Interpretation of the Foreign Exchanges.

Foreign Exchanges an unerring mercantile and monetary barometer. Auch, they clearly point to the disturbing currents. (85)

„Favourable“ or „unfavourable states of the exchanges“.  Zusatz von Marx.
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Ausdrücke des Merkantilsystems ursprünglich
, ihre original basis the theory that the object of commerce is to attract gold. (85) The phrase accurate enough from the monetary or banking point of view. All engagement involve payments in gold or in paper convertible in gold. (86) When the stock of gold is evidently adequate, it is even in a banking point of view erroneous to consider a further accumulation advantageous or desirable. (86, 87) Nach Goschen »the phrase legitimately« expresses »the anxiety or confidence of the banking world as to the means of meeting their legal obligations«. (87) Nach demselben Herrn: [»]Political economists … are correct in their statement that, as regards the country at large and the interchange of commodities, exports and imports are always balanced  Zusatz von Marx.
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(!)
 … . But merchants and bankers are influenced by the feeling, that at any given moment they may be under greater liabilities for imports than they can temporarily meet, owing to the system of credit which disturbs the coincidence of payments for exports and imports, though their value may be actually equal; and further, by the anxiety as to the possibility of meeting these liabilities in that specific mode of payment to which they are pledged, namely, in gold or convertible notes.« ([87,] 88)

Exchanges favourable to any particular country … mean … that bills of that country upon foreign cities are difficult of sale, whilst bills drawn upon it from abroad are at a premium, indicating an eventual influx of specie. Exchanges unfavourable … when foreign bills are in great demand, and when, consequently, their value seems likely to be so enhanced as to render the export of bullion an unavoidable alternative. (88)

It is the price of short bills, not of those which have some time to run, which determines the course of bullion shipments. Bei long bills die rate of interest und question of credit exercise an additional influence. If there is a demand for bills upon any particular town, the price of all such bills, whether short or long, will rise. Wenn aber rate of interest at a very high point in such town, price of long bills would not rise in same proportion as that of short; for the purchaser must bear the discount, which has to be deducted from the long bill before it can become equally available with the short bill; and for any increase in this discount he requires to be compensated by a so much cheaper price. Ditto for risk which he will run until the bill be ultimately paid. ([88,] 89)

As an index of the general position of trade, the value of short bills is the more important; whereas the rates given for long paper, as compared with those for bills on demand, point mainly to the rate of interest, and partially to the state of credit. (89, 90) Natürlich anders wo long bills only are to be obtained to any amount. (90) Bei dem state of exchanges between Hamburg und London, f.i., neben der balance of trade, nie to forget the difference of value which would result from a premium on silver, the currencies of the 2 countries being dissimilar. So bei Russian exchanges … indicate not only the enormous indebtedness to foreign creditors, sondern auch depreciated currency. (91)

Extraordinary course of the American exchanges at the beginning of 1861. A large efflux of bullion from Europe to U. States took place, and various theories were started. Hauptgrund war indebtedness of Europe to U. St. Wurde als Grund angegeben growing troubles in the States (which were leading to a panic) and the presumed speculations of English capitalists.

The specie shipments were hurried and intensified by the Americans drawing sooner than usual against their claims on England, by suspending their orders for English manufactures, by the forced and unnatural increase of exportation even of articles not wanted in Europe. But the primary cause of the fall of the exchanges which led to the flow |100 of bullion to America lay in the immense excess of their exports of wheat and flour, following, too, on a cotton crop of unprecedented extent. (92) Die falschen Deuter des Efflux looked principally to the stock of gold in New York, the speculations in American securities, and the operations of capitalists. (93)

Stress was continually laid upon the fact that the stock of gold was accumulating in New York and was decreasing here, and it was argued that consequently the gold must return. To bring about this result, one of the following events would have to occur. It would return for payment of debt, aber die Yankees waren die creditors. Oder it would be remitted against fresh orders for English manufactures or for American stocks held in English hands. Diesem entsprach nicht der state of mercantile confidence in America (nämlich dem entering upon new mercantile transactions.) Oder gold would be sent as a loan to English capitalists, in the expectation that money would, as was certainly probable, become dearer here than in America. (93, 94)

Falsches Argument von vorn herein that, because in 1857 the bullion exported to America was immediately returned, the same result would be witnessed in 1861. In 1857 the Americans had incurred enormous debts to Europe; in  Bei Goschen Druckfehler: 1863
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1861
Europe had incurred enormous debts to her. On the former occasion the export of specie to the States was unnatural and artificial. In latter case the export of bullion was unavoidable. It was only hurried, because the American creditor, finding himself in the midst of a most dangerous political crisis, became suddenly urgent to receive all that was due to him, and to forestall, rather than to delay, the settlement of his claim. He drew his bills and forced them on the market with the eagerness of panic. Few buyers were to be found requiring them as remittances in discharge of European liabilities; for, trade had been curtailed, no new orders had been given, and, before the crisis commenced, the unusual prosperity of the Western States, in consequence of vast crops of grain, had made it possible for remittances against previous transactions to be sent earlier than usual. Thus, the bills were bought up in New York, not by such as had liabilities to discharge, but by such as were willing to advance the value of the bills till their equivalent in gold could be procured from England. This was the office of the New York banks, and by far the greater quantity of the bullion shipments consisted in what may be called the anticipated proceeds of these bills. Without the influence of panic, a high rate of interest on this side might have delayed the export of the proceeds, at least till the maturity of the bills. If these proceeds had remained longer on this side, they would either have constituted a loan to the banker to whom they were remitted, or have been invested in some kind of merchandise, and returned in that form rather than in that of gold. (94–96)

There was no monetary ground of panic, 1861, in the U. St. Quite the contrary. Sellers of bills might foresee a difficulty in disposing of them above the specie point and consequently up to that point press their bills upon the market. (96) The panic in America during the winter 1861 was attributable solely to political causes, which rendered all who had bills for sale eager to underbid each other for the sake of immediate payment, and to accept a price far below what they would have realised if they had had their bills exchanged into gold in England. … It is a rare occurrence to see alarm felt at an unusually favourable situation of the exchanges. (97)  Kommentar von Marx.
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Göschen is currency principle Esel.
 Zusatz von Marx.
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Er sagt:
»It was this urgency to secure themselves money at any price which induced the New York merchants to export every kind of produce, which normally, owing to the increase of the currency, would have risen in value in the States, to European markets, where prices were sure to fall owing to the decreasing currency.« (97)

 Zusammenfassung von Marx in eigenen Worten.
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Wer zahlt die costs of bullion transport? To whom are favourable exchanges unfavourable etc?

The American exporters of grain and cotton were the very class who (1861), in the first instance suffered most from the situation, in so far as the expense of the costly transmission of specie, with all the losses attached to it, would fall upon them. The English debtors may be argued not to have suffered any loss, because to them it was immaterial how they paid their bills at maturity – whether by handing their amount over to their neighbours, to whom the Americans would, in normal times, have remitted bills upon them; or by shipping it in gold by order and for account of their American creditors. But … the charge on the exporter often falls on the consumer of the product exported|101 To the extent the interests of the exporter become identical with those of the foreign country. For, that which adds to the cost of the article which he exports, must be borne either by him or by the consumer of his produce; and it is their joint interest that no such addition should be made. The cost of the transmission of bullion is an addition of this nature; and therefore it is contrary to the interest of the exporter, and the country to which he exports, that such an expense should have to be incurred. (98, 99)

A condition of the exchanges which leads to the importation of specie in any country favours the importers and consumers of that country, but causes an additional charge to the export trade. However, the extra charge upon this export trade having ultimately, on the above supposition, to be paid by foreign countries, it may be maintained that the state of the exchanges indicated is, in a certain sense, favourable to the country in question, and unfavourable to the foreigners with which it trades. (99)

Assume (what is partially true) that each country fetches from the other what it requires; in other words, that the export trade of a country is managed upon the order system. Cotton and grain may be sent from the States, not for account of American sellers, but of English buyers who have given their orders. If the article is bought by a foreign buyer in the place of its production, any sudden extra charge upon exportation must be borne by him. Thus a sudden fall in the exchanges, which makes his bill upon his London house less valuable, or causes the whole cost of the transmission of bullion from England to pay for his purchases to fall upon him, becomes unfavourable to the country to which he belongs, and for which he is buying, and not to that from which he is buying. Conversely, the Americans who give orders to English manufacturers are able, during the same period of low exchanges, to buy up bills on England which will pay for their goods, at a cheaper rate than usual, and are able to save the expense of the transmission of bullion, which, during normal times, generally falls on a portion of the American importers. As far as facility and economy in paying for the products of other countries are concerned, a state of the exchanges which renders it possible to purchase bills to pay for them, cheaply and easily, may correctly be designated as favourable. (99, 100)

Rise of bills of extraordinary extent and rapidity in America 1862–63. Unfavourable Exchange: Dieser Fall nicht zu erklären aus den normal elements der fluctuation of Exchanges. The sudden transmission of capital from America to Europe, and the continuance of a demand for importations from abroad, while the cotton export was stopped by the blocked blockade of the southern ports, accounts only bis zum Fall to the specie limit, but not beyond. Die Ursache darüber hinaus die depreciation of currency in America. Act suspending specie payment in the U. St., and authorising the issue of inconvertible Gvt paper money. Thus it became possible for the Foreign Exchanges to rise, not a few percents, but 50 or 100 or even 200 P.Ct. In the Southern States the exchange on London actually rose to 400 P.Ct. (101, 102)

In the Northern states the rise actually delayed far beyond the time when it was expected to occur. Ursachen: During the first months of the issue of the Gvt. paper, the private banks called in their notes to a very great extent, daher die aggregate currency nicht so much increased as expected. The area over which the American currency extends is so vast that the effects of an over-issue of paper would be less rapidly felt. The general contraction of credit lead to the absorption of a considerable amount of currency, ditto the enormous war expenditure. In the West a considerable dearth of currency had previously existed, and there was, consequently, a gap to be filled up. (103) Aber bald, in little more than a year, the exchange advanced from 110 to 180. … The price of foreign bills in New York, and the price of gold, constantly rose and fell together. Before the depreciation of the currency, the actual par of exchange for bills of exchange on England was 109. When gold rose, the foreign bills rose as much beyond 109, as gold rose above par, leaving the same margin (and the same variations within that margin), between the premium on gold and the price of sterling bills, as that which, in normal times, existed between the nominal par of exchange and the actual mean premium on |102 English bills. But this margin, which was 9 P.Ct. before, having itself to be calculated in depreciated currency, become apparently, but only apparently, greater. (104, 105)

The basis of the calculation – before the depreciation – 40$ = £9, so that 1$ = 4s. 6d. But as this assumed par of exchange does not coincide with the actual value  Kommentar von Marx.
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⦗soll heissen amount⦘
of the gold in the $ and the £, the £9 being worth 9 P.Ct. more than 40$, gold for gold (by which the value of the $ is reduced to about 4s. 11/2d.) the calculation has to be rectified, when bills on England are bought, by 9$ being added to every 100$ of the purchase money. (105.  Kommentar von Marx.
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Wären 40$ = £9, so 100$ = 221/2£. Aber in der That 109$ = 221/2£. oder 4327/45$ = 9£.
)  Goschen: „as long as a gold currency existed on both sides of the Atlantic“. – Gemeint ist die Greenback-Währung, eine nicht durch Edelmetalle gedeckte Papiergeldwährung, in den Vereinigten Staaten während des Amerikanischen Bürgerkriegs.
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Vor der issue des paper
, wenn equilibrium of exchanges between U. St. und England, bills on London stood at 109. This was the mean specie point, modified, either upwards or down wards, by the state of indebtedness, rate of interest, in fact, supply and demand. Nach der depreciation, diese 9% Premium in gold, would also be increased in exact proportion to the premium on gold. If, before the issue of paper money, the purchaser of a bill on England paid 100$ + 9$ for it, he would, if the premium on gold had risen to 50 P.C., have to pay 150 (instead of 100) + 131/2$ (instead of 9), or 1/2 as much again as what we may call the correcting premium. Thus, if the price of bills, when gold stood at 150, was 1631/2, this price would correspond to 109 when there was no premium on gold. The price might rise to 165 or fall to 161, according as there was supply or demand, but the mean point would be ascertained by the process described. (106, 107)

Disturbing causes were introduced by legislative enactments which interfered with the free commerce of gold, and consequently tended to vary occasionally the relative value between bills and gold, by encumbering all operations in the latter with certain charges and inconveniences. Taxes on transactions in gold would have the same force as increased charges on specie shipments, and would thus have a tendency to widen the margin between the premium on gold and the premium on bills. (107)

Besides the taxes imposed on operations in gold, other circumstances induced those who had occasion to buy either foreign bills or gold, to give a preference to the former, so that a somewhat artificial demand arose. Z.B. fears were continually entertained that the export of gold might at any time be prohibited directly or indirectly; preference therefore given to bills of which the export could not be forbidden. Or again, if gold or bills were to be purchased in order to be hoarded or held some little time before being used as remittances, interest would be lost upon gold but earned upon bills; for when these came to be sold, so would be worth so much more, as being nearer their maturity. Former charges and risks incident upon the holding of gold, not of bills. Thus many considerations would tend to widen the margin between gold and bills, and create violent perturbations at particular moments which could not be accounted for simply by the depreciation of the currency. (107, 108)

According as the Americans have remitted their funds to this country, in order to secure a portion of their fortune against the contingency of progressive depreciation, so has there been a demand for bills upon England.  Kommentar von Marx.
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(Umgekehrt: A supply of bills upon England was thereby created.)
Immense sums are said to have been remitted to English bankers by American correspondents, because this was clearly the safest course by which to secure their fortunes against loss and at the same time to earn a moderate interest. In America every species of banking investment was subject to daily depreciation, and such fortunes as consisted in securities payable in dollars, were rapidly melting away. Investments in gold were largely resorted to, but were dangerous, on account of the Government action, and unremunerative, owing to the loss of interest. Remittances to foreign countries combined the advantage of security with that of remunerative employment for capital, and many Mill. £. St. have been sent to Europe for this purpose. Gewisser Theil davon direkt über Kalifornien. Dadurch the great risks on the transmission of gold from California to New York avoided. Without these bullion remittances the demand for bills must have been even greater than it was; for the Americans required funds in England, not only for the purposes mentioned, but also for the payment of the large quantities of military stores purchased in this country, and for European manufactures. No cotton bills obtainable in New York, owing to the blockade, and fewer cornbills existing, owing to the reduction of that trade |103 in consequence of plentiful harvests in Europe, no doubt the demand for bills, notwithstanding the Californian remittances, has been great, and this demand has increased the premium on sterling bills. (109–111)

Rapid fall of bills (Foreign) following on the battle of Gettysburg and the opening up of the Mississippi: Premium on gold fell rapidly. Nicht von contraction of greenbacks. The conversion of some portion of greenbacks was a measure operating in that direction, but it was accompanied by fresh issues which neutralised that effect. Besides, this conversion was in operation before the fall, even at the time when the premium was rising. (112) Goschen erklärts aus »the belief suddenly springing up that the quantity of paper money would really be reduced, either by a further more effectual conversion, or by a redemption in bullion at a shorter date than appeared possible during the darker period of Northern prospects.[«] (113 112)

This belief induced persons, who had hoarded gold from a fear of a further depreciation of the currency (und had been before somewhat alarmed by the measures taken against this very hoarding by the Government) to sell their stock of gold as far fast as possible, giving up the idea of a further rise. The Gvt. too contributed by somewhat artificial means, to a premature decline in the premium on gold, by throwing large sums on the market which it had been able to accumulate und zuvor accumulated for this very purpose. (113) [»]An advance in gold again took place, which has since, with many fluctuations, made further progress.« (114. Note geschrieben December, 1863) They owe less to Europe than at any other previous time in late years, and the large deposits they have made in Europe, give them the power of regaining a great portion of the gold they have lost. (114)

When specie is being exported, it is sometimes supposed to be merely what is called an Exchange Operation, undertaken by a certain class of speculators, whose business it is to make a profit out of the variations in the price of foreign bills at different moments, buying them when they are cheap and selling them at a profit, and sometimes sending bullion abroad to buy up bills on their own country, if the prices should be temporarily below or touching specie point. Gold will of course not be exported so long as these speculators in exchange, or cambists, as they are called, can procure short bills. They wish to place funds at a certain spot. As long as they can procure short bills in the quantities they desire – as long, that is to say, as there are sufficient foreign debts owing to their own country, payable immediately, which can be transferred to them, and which they can pass on to others – they will not export gold. An efflux of gold accordingly proves, whoever the exporters may be, that the supply of short bills on other countries is being exhausted … that the balance of indebtedness is temporarily against the country in question. (117, 118)

It is often supposed that gold is never exported unless to give a profit to those who despatch it. Fallacy. The expression so often used  Zusatz von Marx.
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(in den money articles der Zeitungen z.B.)
, that the rates of exchange in any country are at such a point that no profit is to be made on shipments of gold to it, … do not prove that the despatch of bullion may not be natural and necessary. It must be sent by those who are in debt to that country, if they cannot find bills. … The exchanges may remain exactly at specie point for a long time, offering no prospects of profits to any cambists, yet compelling the constant flow of bullion in order to discharge liabilities. (118, 119)

Profits on Exchange operations: They can habitually be realised by those who, when they observe that there is a prospect of the demand for bills exceeding the supply, purchase in anticipation in order to sell at a higher price when the natural buyers, who require the bills for remittance, enter the market later on. Even when the exchanges reach the specie point, profits, though on a very limited scale, are made by those who, by having establishments identical with their own in foreign cities, and having a machinery, specially organised for the purpose, are able, by the avoidance of commission and the reduction of charges, to make bullion shipments at a cheaper cost than the actual merchants or manufacturers who have the remittances to make. They despatch the gold and sell the bills drawn against this gold to those who require to send funds abroad, realizing a fractional profit for the convenience which they afford. … As far as the exchanges and the |104 principles which determine them, are concerned, it is perfectly indifferent whether the debtors to foreign countries – importers, merchants, or consumers – remit gold themselves, or pay a slight profit to cambists and money dealers, who, shipping it in large quantities, retail the bills drawn there against to such as require to remit. (119, 120)

It is only in perfectly abnormal times that large profits are to be made on specie shipments, and only when the countries to which the shipments are to be made, lie at a very considerable distance; so that those who have the sagacity to ship in time, or before others deem it necessary, have the advantage of being able to buy up bills below the specie point, owing to the urgent necessity of the sellers of the bills to receive the equivalent immediately … Where there can be immediate action and reaction and immediate communication, as between London and Paris, there can be scarcely any further profits upon shipments of gold beyond those which can be effected by an economy of charges. Only those who have a machinery for the purpose can gain a profit which; in reality, is a kind of commission paid by the rest of the community. At a distance, there is much more margin; as, where months may elapse before bills can, by their natural process, be converted into coin, those who can undertake to give this coin on the spot can often make their own terms. (120, 121)

The limits, therefore, clear within which the natural action of the exchanges may be checked or intensified by the operations of cambists. In the case of a gradual fall in the exchanges in a distant country, where, if left to themselves, they might recede below specie point, because the unfortunate drawers  Goschen: of
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on
bills, being unable to wait the arrival of specie for their own account, might require the equivalent immediately, it might modify the position very much if speculators in foreign bills had foreseen the occurrence, and sent out specie to anticipate their wants, securing to themselves a moderate profit, but saving the drawers from a much heavier loss. (121, 122)

The influence of credit or discredit – at any time of panic or other temporary derangement of confidence – the discount at which bills are then sold will not be mistaken for the result of an adverse balance of trade or a depreciated currency. (123) Sudden movements in exchanges, either upwards or downwards, may reflect the position of the rate of interest in different countries, not only in the case of long bills – but also in the case of bills on demand themselves, as indicating that a high or low rate of interest is causing certain movements of capital from one country to another. The most general fact of which the exchanges are the sign, is the degree of intensity to which the demand of bills on a foreign country exists, for whatever purpose this demand may arise. It is clear that such a demand may be caused as much by a desire to remit to that country for the sake of employing it at a high rate of interest, as for the purpose of paying a debt. [(123, 124)]

 Feller/Odermann, S. 196.
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Zinsrechnung.

Berechnet auf 100, nach Procenten. Die Anzahl der Einheiten, die man auf 100 nimmt = Zinsfuß.

Einfache Zinsen, wenn Zinsen vom Entlehner des Kapitals zu bestimmten Terminen gezahlt werden; er zahlt zu einer bestimmten Zeit das geliehne Kapital unverändert zurück.

Zusammengesezte Zinsen, Zinseszinsen, Zins vom Zins, wenn Entlehner die fällig werdenden Zinsen zum Kapital schlägt, kapitalisirt, u. nun das vermehrte Kapital verzinst. Selten in kaufmännischer Rechnung.

A) Einfache Zinsen. A) Einfache Zinsen.

I)  Feller/Odermann, S. 197.
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Aufsuchung der Zinsen eines Kapitals.

Zinsfuß versteht sich gewöhnlich auf 1 Jahr, bei Discontgeschäften zuweilen für den Monat.

Der Zeitraum aber, für welchen die Zinsen eines gegebnen Kapitals zu berechnen sind, lassen läßt sich ausdrücken nach Jahren, Monaten, Wochen, Tagen.

a) Zinsen nach Jahren.

Wenn Zinsfuß auf 1 Jahr berechnet u. die Zinsen eines gegebnen Kapitals für 1 Jahr zu berechnen sind, so kommt, die Zeit nicht in Betracht u. es handelt sich nur um Aufsuchung der Procente vom 100. Wäre der Zinsfuß ein monatlicher, so multiplicirt man ihn × 100, wodurch er auf einen jährlichen reducirt wird.

Wie viel die jährlichen Zinsen von 843 834 Th. à 3%?

100 : 843 834 = 3 : x. x = 25,02. Oder: 1% = 8,34
3 = 25,02 Th.

Sind die Zinsen für mehrere Jahre zu berechnen, so geschieht die Berechnung zunächst für 1 Jahr u. das erhaltene Resultat wird dann mit der Anzahl der Jahre multiplicirt. Oder man multiplicirt den Zinsfuß mit der Anzahl der Jahre; so ist 41/2% in 2 J. = 41/2× 2% = 9% in 1 J.; od. = 1% in 9 Jahren.

Beispiele.

Wie viel betragen die Zinsen von 456 Rth à 3% in 7 J.

4,56 = 1% in 1 J.
3 × 4,56 = 13,68 = 3% in 1 J.
95,76 Th. = 3% in 7 J.

Zinsen von 945f. à 31/3% in 4 J.?

31/3% = 1/30 des Kapitals.
945/30 = 31f. 30xr = 31/3% in 1 J.
× 4
126fl. = 31/3% in 4 J.

Zins von 485 Fs. 50 cts. à 31/2% in 4 J.?

31/2% in 4 J. = 14% in 1 J.
4,855 = 1%
× 14
67,970 Fcs. = 67 Fcs. 97 cts.

Zins von 1326 M.B. 8β. à 5% in 21/2 J.?

5% in 21/2 J. = 121/2% in 1 J.
121/2% = 1/8 des Kapitals.
1326 M.B. 8β 8 = 165 M.B. 13β.

Bestehn Kapital, Zinsfuß u. Zeit aus unbequemen Zahlen, so Regel Multiplex anzuwenden: Z.B. wie viel Zins von α) 819 Th. à 42/3% in 13/4 J.? u. von β) 56f. à 61/2% in 3/4 J?

α) 100 : 819 = 42/3% : x β) 100 : 56 = 61/2% : x
1 : 13/4 1 : 3/4
x =  Zwischenschritt von Marx ergänzt.
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819×14×7 100×3×4
= 7×273×7 100×2 = 66,885 Th.
x = 2,73f.|

128

b) Zinsen nach Monaten.

Man rechnet nach Jahr; nimmt dann aus diesem Resultat denselben Theil, welchen die gegebnen Monate aus einem J. bilden. Oder Monate als Bruch vom Jahr betrachtet, Zinsfuß × mit diesem Bruch.

α) Zins von 964 Th. à 5% in 5 Mt? β) Zinsen von 520 Th. à 3% in 4 M.?
9,64 × 5 1 Pct p. Jahr. 4 Mt. = 1/3 J.
48,20 = 5% in 1 J. 1/3 × 3% = 1%.
16,066 = 5% in 4 Mt. (1/3 J.) 1% von 520 Th.= 5,20 Th.
4,017 = 5% in 1 Mt. (1/4à 4 Mt.)
20,083

Oder Regel Multiplex anzuwenden.

Zinsen von 429 Th. à 31/2% in 19 Monaten?

100 Th : 429 Th = 31/2% : x (Je mehr Kapital, desto mehr Zinsen.
12 : 19 = (Je mehr Zeit, desto mehr Zinsen
x =23,77 Th.

c) Zinsen nach Wochen.

früher (vor 1851) in Augsburg unter den Bankiers üblich.

d) Zinsen nach Tagen.

Im kaufmännischen Verkehr Zinsen meist nach Tagen gerechnet. Dabei nimmt man 1 J. = 360 T., jeden Monat = 30 T. Selbst wenn man bei Ermittlung der Anzahl Tage, für welche die Zinsen zu berechnen sind, jeden Monat zu der Anzahl der Tage berechnet, die er wirklich hat, versteht sich doch der Zinsfuß immer für 360 T. Ausnahmen: England, Englische Colonien, u. Amerika. Hier versteht sich der Zinsfuß für 365 T. Man rechnet also auch jeden Monat zu der Anzahl der Tage, die er wirklich hat.

Demnach ist für jeden Fall, wo die Zinsen nach Tagen zu berechnen sind, dreifache Lösung möglich, wie folgt für: Zins von 1832 Th. à 4% von 7 Feb. bis 11 Sept. 1855?

α) Zinsfuß für 365 Tage β) Zinsfuß für 360 T. γ) Zinsfuß für 360 Tage.
1 Mt. = so viel Tage als er hat. 1 Mt. = so viel Tage als er hat. 1 Mt.= 30 Tage.
100 : 1832 Th. = 4% : x 100 Th. : 1832 Th = 4% : x 100 Th. : 1832 Th. = 4% : x
365 Tage : 216 T. = 360 T. : 216 T. 360 T. : 213 T. =
x = 43 Th. 11 Sgr. x = 43 Th. 29 Sgr. x = 43 Th. 16 Sgr. 8 Pf

Der Wahrheit  Zusatz von Marx.
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(!)
kommt man am nächsten u. auch am bequemsten zu 360 T. = Jahr, u. Monat = 30 T.

Wenn man den Hauptansatz

γ) 100 Kapital : gegebenen Kapital = Zinsfuß : x
360 Tage : gegebne Tagen

mit dem Zinsfuß in 360 × 100 = 36,000 dividirt, so erhält man, da die meisten der im Handel gebräuchlichen Zinsfüsse ohne Rest in 36,000 enthalten sind, einen Quotienten, den man folgendermaassen zur Zinsenberechnung benutzt: Man multiplicirt das Kapital mit den Tagen und dividirt das Produkt durch den Quotienten, den der Zinsfuß giebt.

 Die Rechnung ist ein Zusatz von Marx.
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Nämlich: x =
Gegebnes Kapital × mit gegebnen Tagen × mit Zinsfuß 100 (Kapital) × 360 Tage = (Gegebnes Kap. × gegeb. Tage.) × mit Zinsfuß 36000 = Geg. Kapit. × Gg. Tage 36000/Zinsfuß .

Diese als Divisoren zu benutzenden Quotienten sind z.B. für 1% = 36000 1 = 36000. für 4% =  36,000 4 = 9000. etc

Z.B. Zinsen von 948 Th. à 4% in 148 Tagen? 948×148 9000 = 15 Th. 18 Sgr.

Berechnung von Zinsen mehrerer Kapitalien.

α) Gleicher Zinsfuß u. Gleiche Zeit: Addirt die Kapitalien. Berechnet von der Summe in gewöhnlicher Weise.

Zins von 960 Th, 430 Th., 500 Th. u. 1250 Th. in 9 Monaten à 4%?

Summe der Kapit. = 3140 Th. à 9 Mt. à 4% = 94,2 Th.

β) Ungleicher Zinsfuß u. Gleiche Zeit:  Feller/Odermann, S. 211: Die Berechnung
Schließen
Methode
beruht auf dem Grundsatz, daß Zinsen von 100f. à 5% = Zins. von 500f. à 1%; Zinsen von 100f. in 4 Mt. = Zinsen von 400f. in 1 Mt, ferner Zinsen von 100f. à 4% in 3 J. = Zinsen von 4 × 3 × 100 fcs. in 1 J. Man multiplicirt daher jedes Kapital mit seinem Zinsfuß, wodurch Kapitalien entstehn, die à 1% ausgeliehn sind, u. berechnet nun von deren Summe die Zinsen für die gegebne Zeit.

Z.B. Zinsen von 920 Th. à 4%, 760 Th. à 3%, 184 Th. à 31/2% in 11/2 Jahren?

920 Th. à 4% = 3680 Th. od. 6604 Th. à 1% in 11/2 J. x = 6604×1 1/2 = 99,06 Th. Zinsen.
760 à 3 = 2280
184 … 31/2 = 644

γ) Gleicher Zinsfuß u. Ungleiche Zeit: Die gegebnen Zeiten auf gleiche Benennung zu bringen; hierauf multiplicirt man jedes Kapital mit der ihm zugehörigen Zeit, wodurch Kapitalien entstehn, von deren Summe die Zinsen für 1 Zeit, d.h. für 1 J., 1 Mt. u.s.w. zu berechnen sind.

Z.B. Zinsen für 900f. in 7 Mt., 840f. in 61/2 Mt., 650f. in 3/4 J., u. 1245f. in 20 T. à 5%?

900f. in 7 Mt. = 6300f. in 1 Mt.
840  Feller, Odermann, S. 212: 61/2
Schließen
6
=
5460
650 9 = 5850
1245 2/3 = 830
18440 in 1 Mt à 5%. x = 76f. 50xr.

 Eigene Berechnung des Zwischenschritts von Marx.
Schließen
Nämlich:

100 : 18440 = 5% : x
12 M. : 1
x =  18440×5 1200 = 18440 240 .

δ) Ungleicher Zinsfuß u. Ungleiche Zeit. Man bringt die Zeitbestimmungen auf gleiche Benennung, multiplicirt jedes Kapital × seiner Zeit u. seinem Zinsfuß, berechnet von der Summe der Produkte Zinsen à 1% für 1 Zeit.

Beispiel: Wie viel beträgt Zinssumme von 490 Mc. Banco à 3% in 9 Mt, 860 à 4% in 11/4 J;

642 à 6% in 65 T.; 2000 à 3/8 pr. Ct. p. Mt in 10 Monaten?

490 à 3% in 9 Mt. = 13,230 Mc. B. à 1% in 1 Mt.
860 à 4 15 = 51,600
642 à 6 21/6 = 8346
2000 … 41/2 10 = 90000
x =  163176 1200 = 135 Mc. Bco. 15β.

II)  Feller/Odermann, S. 212.
Schließen
Aufsuchung des Kapitals.

Bei Aufsuchung der Zinsen eines Kapitals kommen nur direkte Verhältnisse vor, bei Aufsuchung von Kapital, Zinsfuß u. Zeit dagegen direkte u. indirekte.

Kapital u. Zinsen in direktem Verhältniß. ( Feller/Odermann, S. 212: je mehr Zinsen, desto mehr Capital
Schließen
Je mehr Kapital desto mehr Zinsen
) Kapital u. Zinsfuß in indirektem Verhältniß (Je grösser Zinsfuß, desto kleiner kann Kapital sein etc) Kapital u. Zeit in indirektem Verhältniß (Je grösser Zeitlänge, desto kleiner Kapital etc)

Beispiele.

Wie groß Kapital, dessen jährliche Zinsen à 5% 165 Th. betragen?: 5 : 165 = 100 : x. x = 3300 Th. Oder da 165/5 = 33, so muß das Kapital = 33 × 100 = 3300 sein.

Welches Kapital bedarf man, um à 5% dieselben Zinsen zu geben, welche 3200f. à 4% geben? 5 : 4 = 3200 : x; x = 2560f. Je grösser der Zinsfuß, desto kleiner das Kapital.

Welches Kapital bringt in 4 J. dieselben Zinsen, wie 1680 M.B. in 3 J.? 4 J. : 3 = 1680 : x; x = 1260. Je mehr Zeit, desto weniger Kapital.

Welches Kapital brachte in 4 Monaten, à 5%, 64f. Zinsen?

4 Mt. : 12 M. = 100f. Cpt. : x (Je weniger Zeit, desto mehr Kapital)
5f. Zins : 64 fcs Z (Je mehr Zinsen, desto mehr Kapital.)
x =  Zwischenschritt von Marx.
Schließen
1200×64 20 = 60 × 64
= 3840fl. 
|

129

III)  Feller/Odermann, S. 214.
Schließen
Aufsuchung des Zinsfusses.

Wenn Zinsfuß = x Zinsen, die 100 in 1 J. od. 12 M. od. 360 (resp. 365) T. giebt, so bleibt die Frage bei Aufsuchung des Zinsfusses:

x Zinsen geben 100 in 1 Jahr u.s.w.? wenn gegebnes Kapital in gegebner Zeit gewisse Zinsen giebt. Dann sind alle Verhältnisse direkt. Denn ist 100 kleiner od. grösser als das gegebne Kapital so giebt es weniger od. mehr Zinsen. Ist die Zeit (1 J. u.s.w.), die 100 aussteht > [bzw.] < als Zeit für welche das gegebne Kapital ausgeliehn ist, so giebt 100 weniger, mehr Zinsen.

Betrachtet man den Zinsfuß aber als den Maaßstab, nach welchem ein Kapital für eine gewisse Zeit ausgeliehn war od. werden soll, so sind die Verhältnisse indirekt.

Denn je grösser od. kleiner, im Vergleich zu 100, das gegebne Kapital, desto kleiner, grösser kann der Zinsfuß sein.

Je grösser, kleiner, im Vergleich zu der zu 100 gehörigen Zeit, die Zeitlänge, für welche das gegebne Kapital ausgeliehn, desto kleiner, grösser Zinsfuß.

Zu den Zinsen steht jedoch der Zinsfuß in direktem Verhältniß. Je mehr Zinsen, desto grösser, je weniger Zinsen, desto kleiner Zinsfuß.

Beispiele.

Zu welchen Zinsen (x%) ist ein Kapital von 450 Th. ausgeliehn, dessen jährliche Zinsen 18 Th.? 450 : 100 = 18 : x. x = 4%. Direkt: Je kleiner Kapital (100) desto kleiner Zinsen. Indirekt: Je grösser Kapital (450), desto kleiner Zinsen.

Zu welchem Zinsfuß muß ein Kapital ausgeliehn werden, das in 9 Mt. dieselben Zinsen geben soll, die es in 11/4 J. zu 3% gegeben hat? 9 Mt. : 15 = 3% : x. x = 5%. Indirekt: Je weniger Zeit, desto grösser Zinsfuß.

Zu wie viel % müssen 960f. ausgeliehn werden, wenn sie in derselben Zeit die Zinsen geben sollen, wie 840f. à 6%? 960 : 840 = 6 : x. x = 51/4%. Indirekt: Je grösser Kapital, desto kleiner Zinsfuß.

Zu wie viel % ist ein Kapital ausgeliehn, das 120 Th. Zinsen bringt, während es früher à 5%, 1331/3 Th. Zinsen gab? 1331/3 : 120 = 5 : x. x = 41/2%. Direkt: Je weniger Zinsen, desto kleiner Zinsfuß.

Wenn man in 41/2 J. von 850f. Kapital 153f. Zinsen erhoben hat, zu welchem Zinsfuß war dieß Kapital ausgeliehn?

850 : 100 = 153 : x
41/2 J. : 1
x = 4%

Wenn von 450 Th. in 11/2 J. dieselben Zinsen erhoben werden, das Kapital von 765 Th. in 9 Monaten à 6% gab, zu wie viel % erstres Kapital ausgeliehn?

450 : 765 = 6 : x Indirekt Je kleiner Kapital, desto grösser kann Zinsfuß sein
18 : 9 Mt Indirekt. Je mehr Zeit, desto kleiner muß Zinsfuß sein.
x = 5,1%.

IV)  Feller/Odermann, S. 217.
Schließen
Aufsuchung der Zeit.

Zeit steht zu Zinsen in direktem Verhältniß: Je mehr\weniger Zinsen desto mehr\weniger Zeit.

Zeit steht zu Kapital in indirektem Verhältniß: Je grösser Kapital, desto weniger Zeit u. vice versa.

Zeit steht zu Zinsfuß in indirektem Verhältniß: Je grösser Zinsfuß, desto weniger Zeit u. vice versa.

Beispiele.

Wie lang stand ein Kapital aus, das 54 Th. Zinsen gab, wenn gleich grosses andres Kapital in 31/4 J. 52 Th. Zinsen brachte? Direkt: Je mehr Zinsen, desto mehr Zeit. 52 Th. : 54 Th. = 31/4 J. : x. x = 33/8 J.

Welcher Zeitlänge bedarf man, um bei gleichem Zinsfuß mit 364f. Kapital so viel Zinsen zu gewinnen, als mit 390f. in 91/3 Monaten?: 364 : 390 = 91/3 Mt : x. x = 10 Mt. Indirekt: Je weniger Kapital, desto mehr Zeit.

Wie viel J. müssen 1000 M.B. ausstehn, um à 4% ebenso viel Zinsen zu geben, als sie à 41/2% in 2 J. 8 Mt. gebracht haben? 4% : 41/2% =  Jahres- von Marx in Monatsangaben umgerechnet.
Schließen
32 Mt : x. x = 36 Mt.
od. 3 J. Indirekt: Je kleiner Zinsfuß, desto mehr Zeit.

Wie lange haben 2650 Th. ausgestanden, wenn Zinsen davon à 41/2% 397 Th. 15 Sgr. betragen?

2650 Th : 100 Th. = 1 J. : x Indirekt: Je mehr Kapital, desto weniger Zeit.
41/2%: 3971/2 Direkt: Je mehr Zinsen, desto mehr Zeit.
x = 31/3 J.

Wie lange müssen 1960 Th. ausstehn, eh sie à 3% dieselben Zinsen bringen, wie 1260 à 31/2% in 91/3 Mtn?

1960f. : 1260f. = 91/3 Mt. : x Indirekt: Je mehr Kapital, desto weniger Zeit.
3% : 31/2% Indirekt: Je kleiner der Zinsfuß, desto mehr Zeit
x = 7 Mt.

Ein Kapital von 1780 Mark Banco gab in 225 T. 44 M.B. 8β Zinsen. Wie lange müssen 1125 M.B. ausstehn, um 361/2 M.B. Zinsen zu geben?

1125 M. : 1780 M. = 225 T. : x Indirekt: Je weniger Kapital, desto mehr Zeit.
441/2 Zins : 361/2 Direkt Je weniger Zinsen, desto weniger Zeit.
x = 292 Tage.

V)  Feller/Odermann, S. 219.
Schließen
Aufsuchung eines um die Zinsen vermehrten Kapitals.

Man kann diese Aufgabe nicht in einem Satz, aber auf doppeltem Weg lösen.

1) Was betragen 1260 Th. in 61/2 Mt. an Kapital u. Zinsen à 4%?

α) Man berechnet erst Zinsen auf 100. 12 Mt. : 61/2 Mt = 41/2 4 : x. x = 21/6. %. Das Kapital also in 61/2 Monat = 1021/6 u. nun: 100 : 1260 = 1021/6 : x. x = 1287,3.

β) Oder man sucht erst die Zinsen von 1260 Th. in 61/2 M. = 4%. Man findet 27,3 Th. Zinsen. Zum Kapital addirt = 1287,3.

2) Welchen Werth haben, nach 186 Tagen, 980f. Kapital à 5% an Kapital u. Zinsen?

α) 360 : 186 = 5 : x
x = 27/12
+ 100
= 1027/12

 Kommentar von Marx.
Schließen
Dieß 100 + Zins à 5% in 186 Tagen.

b) 100 : 980 = 1027/12 : x
x = 1005f. 19xr.

Daraus folgt umgekehrt, daß 1005f. 19xr nach 186 Tagen fällig, einen jetzigen baaren Werth haben von 980f., ein Schluß, der der Discontorechnung zu Grund liegt.|

130

VI)  Feller/Odermann, S. 220.
Schließen
Aufsuchung der Zinsen oder des Kapitals, welche in einem, Kapital u. Zinsen darstellenden, Werth enthalten sind.

Nach 7 Mt. erhält man an Kapital u. Zinsen für ein à 5% ausgeliehnes Kapital 967 Th. 12 Gr. 5 Pf. Wie viel betragen die in dieser Summe enthaltnen Zinsen?

12 Mt. : 7 M. = 5% : x
x = 211/12%
10211/12 Th. : 967.5/12 Th. = 21/12 211/12 : x
x = 275/12 Th. Also das ursprüngliche Kapital = 940.
Oder soll das ursprüngliche Kapital von vorn herein gefunden werden, so: 10211/12 Th. : 96711/12 9675/12  Th. = 100 : x. x = 940.



VII)  Feller/Odermann, S. 221.
Schließen
Aufsuchung eines mittleren Zinsfusses für mehrere Kapitalien.

a) Gleiche Kapitalien u. gleiche Zeiten.

Man addirt die verschiednen Zinsfüsse u. dividirt ihre Summe durch die Anzahl der Kapitalien.

Welches ist der mittlere Zinsfuß von 4 gleichen Kapitalien zu 3, 31/2, 4 od. 5%? x = 3+3,5+4+5 4 15,5 4 = 37/8%.

b) Ungleiche Kapitalien u. gleiche Zeiten.

Jedes Kapital ist hier mit dem ihm zugehörigen Zinsfuß zu multipliciren, u. die Summe dieser Producte durch die Summe der Kapitalien zu dividiren. Der Quotien Quotient = mittlere Zinsfuß.

Welches ist der mittlere Zinsfuß folgender auf 3 Monate ausgeliehner Kapitalien:

2000 Th. à 3%, 4000 Th à 4%, 6000 à 41/3% u. 1500 Th. à 6%?

2000 × 3 = 6000
4000 × 4 = 16,000
6000 × 41/3 = 26,000
1500 × 6 = 9000
13,500 in 57,000 = 42/9%.

Probe.

2000 à 3% in 3 Mt.= 15 Th.
4000 à 4% 3 do 40
6000 à 41/3 3 do 65
1500 à 6 3 do 22. 15 Sg.
1421/2 Th.

Aber 13,500 zum mittleren Zinsfuß von 42/9% = 1421/2 Th.

Der Grund dieses Verfahrens: Multiplicirt man jedes Kapital mit seinem Zinsfuß, so verwandelt man dadurch sämmtliche Beträge in Kapitalien gelegt à 1%, u. es kommt die Verschiedenheit der Zinsfüsse nicht mehr in Betracht. Da nun aber der Zinsfuß nicht für die Summe der Producte, sondern für die Summe der Kapitalien gefunden werden soll, so hat man folgenden Regel de Trisatz zu bilden: Summe der Kap. : Summe der Producte = 1% : x, oder da 1 nicht multiplicirt, x = Summe d. Producte Summe d. Kapitalien .

(da: Je kleiner das Kapital, desto grösser der Zinsfuß.)

c) Gleiche Kapitalien u. Ungleiche Zeiten.

Erst macht man die Zeiten gleichnamig, wenn sie es nicht schon sind. Dann multiplicirt man den Zinsfuß jeden Kapitals mit der ihm zugehörigen Zeit, u. d. dividirt die Summe der Producte durch die Summe der Zeiten.

Von 4 gleichen Kapitalien ist A auf 6 Mt. à 4%, B auf 5 Mt. à 3%, C auf 4 Mt. à 41/2% u. D auf 1/4 J. à 5% ausgeliehn. Welches ist der mittlere Zinsfuß dieser Kapitalien?  Anmerkung von Marx.
Schließen
1/4 J. = 3 Mt. Also D auf 3 Mt. à 5%.

6 Mt. à 4% = 1 Mt. à 24% 72/18 = 4% mittlerer Zinsfuß
5 3 = 1 15
4 41/2 = 1 18
3 5 1 15
18 M. 72

Probe

Jedes der 4 gleichen Capitalien sei = 600

600 Th à 4% in 6 Monaten = 12 Th. Zinsen.
600 à 3 5 = 7,5
600 à 41/2 4 = 9
600 à 5 3 = 7,5.
36 Th. Zinsen.

 Kommentar von Marx.
Schließen
⦗Nehmen wir die Summe der Monate = 18 u. dividiren sie durch die Anzahl der verschiednen Zeiten, = 4, so Durchschnitt = 18/4 = 41/2 Mt. In dieser Durchschnittsumlaufzeit bringt die Summe der Kapitalien = 600 × 4 = 2400 à 4%, 36 Th.⦘ Die Probe ist anders; daß jedes einzelne Kapital für seine Umlaufszeit zum mittleren Zinsfuß berechnet wird. Es zeigt sich dann:

600 Th. in 6 Mt. = 12 Th. Zinsen
600 5 = 10
600 4 = 8
600 3 = 6
2400 = 36.


d) Ungleiche Kapitalien, Ungleiche Zeiten.

Da in diesem case, neben dem durchschnittlichen Zinsfuß eine mittlere Verfallzeit aufzufinden ist, gehört dieß in die später kommende Terminrechnung (Sieh p. [132–134)]

B)  Feller/Odermann, S. 223.
Schließen
Berechnung Zusammengesezter Zinsen.

Es verdoppelt sich ein Kapital mit Zinseszinsen zu 3% in 23,45 J., zu 40 J. 4% in 17,673 J.; es verdreifacht sich in 37,161 J.; 28,011 J. u.s.w.

Die Arithmetik liefert hier nur weniger u. schwerfällig. Die complicirtren Aufgaben nur durch Anwendung der Logarithmen zu lösen.

Beispiele.

A) Wie groß wird ein Kapital von 850 Th., bei jährlicher Zinseszuschreibung mit Zinseszinsen a 5% nach 5 J.?

1) Durch die Kettenregel. 2) Durch Regel de Tri
1 Th. = 850 Th. Kapital. 100 : 850 = 105 : x x = 892,5 Ende des 1 J.
100 = 105 nach dem 1. J. 100 : 892,5 = 105 : x x = 937,125 Ende des 2 J.
100 = 105 2 J. 100 : 937,125 = 105 : x x = 983,9813 Ende des 3 J.
100 = 105 3 J. 100 : 983,9183 ,9813 = 105 : x x = 1033,1804 Ende des 4 J.
100 105 4 J. 100 : 1033,1804 = 105 : x x = 1084,8394 Ende des 5 J.
100 105 5 J
x = 1084,8393 Th  |
131

Wäre die Zinsenzuschreibung halbjährlich erfolgt: so:

x Th = 850 Th.
1) 100 = 102,5 nach 1 Halbjahr
2) 100 = 102,5 2
3) 100 = 102,5 3
4) 100 = 102,5 4
5) 100 = 102,5 5
6) 100 = 102,5 6
7) 100 = 102,5 7
8) 100 = 102,5 8
9) 100 = 102,5 9
10) 100 = 102,5 10
x = 1088,0718.

Zweites Beispiel  Kommentar von Marx.
Schließen
(umgekehrt)

Wie groß war das Stammkapital, das nach 5 J. mit jährlicher Zinszuschreibung von 5%, auf 1084,8394 Th. angewachsen ist?

1) Kettenregel. 2) Regel de Tri.
x Th. = 1084,8394 Th. 105 : 1084,8394 1084,8393 = 100 : x. x = 1033,1803.
105 = 100 105 : 1033,1803 = 100 : x. x = 983,9812.
105 = 100 105 : 983,9812 = 100 : x x = 937,125.
105 = 100 105 : 937,125 = 100 : x x = 892,5
105 = 100 105 : 892,5 = 100 : x. x = 850 Th.
105 = 100
x = 850 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.