The Theory of Interest

Fisher, Irving
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First Pub. Date
New York: The Macmillan Co.
Pub. Date
1st edition.


§1. Introduction


AT the close of the preceding chapter, the rate of interest was described as the percentage premium on present goods over future goods of the same kind. Does the kind of goods affect the premium? This important question—usually overlooked—may well engage our attention at the very outset. The number, or figure, expressing the rate of interest in terms of money does depend upon the monetary standard employed.


It is perfectly true, as is often pointed out, that when a man lends $100 this year in order to obtain $105 next year, he is really sacrificing not $100 in literal money but one hundred dollars' worth of other goods such as food, clothing, shelter, or pleasure trips, in order to obtain, next year, not $105 in literal money, but one hundred and five dollars' worth of other goods. But this fact does not remove the money factor from our problem. The money factor affects the rate of interest in many ways. The one here considered is that which occurs through a change in the value of the monetary standard.


If the monetary standard were always stable with reference to goods, the rate of interest, reckoned in terms of money, would be the same as if reckoned in terms of goods. When, however, money and goods change with reference to each other—in other words, when the money standard appreciates or depreciates in value in terms of goods—the numbers expressing the two rates of interest, one reckoned in terms of money and the other reckoned in terms of goods, will be quite different. Moreover, the former, or money rate, the only rate quoted in the market, will be influenced by the appreciation or depreciation.

§2. Assuming Foresight


The influence of such changes in the purchasing power of money on the money rate of interest will be different according to whether or not that change is foreseen. If it is not clearly foreseen, a change in the purchasing power of money will not, at first, greatly affect the rate of interest expressed in terms of money. Instead, if the change is in the direction of appreciation, it will injure the debtor, because to repay the principal of his debt will cost him more goods than either he or his creditor anticipated when the debt was contracted.


In so far as the appreciation is foreseen, any increased burden to the debtor in the principal may be somewhat offset by a reduction in the rate of interest. This is a fact which has seldom been recognized.*15 The assumption has been tacitly made that contracting parties are powerless to forestall gains or losses caused by an upward or downward movement of the monetary standard even when that movement is foreseen.


It is theoretically just as possible to make allowance for an expected change in the unit of value as it would be for an expected change in any other unit. If, by legislation, the unit of length were to be changed, and its change were set for a certain future date, contracts running beyond that date would surely be modified accordingly. Or suppose that a yard were defined (as legend tells us it once was) as the length of the king's girdle. If the king were a child, everybody would then know that the "yard" would probably increase with the king's age, and a merchant who should agree to deliver one thousand "yards" ten years hence would make his terms correspond to his expectations.


It would be strange, if, in some similar way, an escape could not be found from the effects of changes in the monetary yardstick, provided these changes were known in advance. To offset a foreseen appreciation, therefore, it would be necessary only that the rate of interest be correspondingly lower, and to offset a foreseen depreciation, that it be correspondingly higher.*16


Near the close of the last century, during the uncertainty as to the adoption or rejection of "free silver," a syndicate offered to buy from the United States government some $65,000,000 of bonds either on a 3 per cent basis in gold, or a 3¾ per cent basis in coin. Everyone knew that the additional ¾ per cent in the latter alternative was due to the mere possibility that coin might not be maintained at full gold value, but might sink to the level of the value of silver. If the alternative had been between repayment in gold and—not merely a possible but a certain—repayment in silver, the additional interest would obviously have exceeded ¾ per cent. It was stated, after the World War, that an American banking firm, when asked by a German concern for a loan in marks, offered to lend at 100 per cent per annum. The offer was rejected—fortunately for the American firm which, as it turned out, would actually have lost, and lost heavily, because the subsequent rapid depreciation of the mark far exceeded the compensatory effect of even so high an interest rate.


The exact theoretical relation between the rates of interest measured in any two diverging standards of value and the rate of foreseen appreciation or depreciation of one of these two standards relatively to the other has been developed by me with many numerical illustrations in a special monograph*17 and also in my first book on interest.*18 The two rates of interest in the two diverging standards will, in a perfect adjustment, differ from each other by an amount equal to the rate of divergence between the two standards.*19 Thus, in order to compensate for every one per cent of appreciation or depreciation, one point would be subtracted from, or added to, the rate of interest; that is, an interest rate of 5 per cent would become 4 per cent, or 6 per cent, respectively.

§3. Limitations of Theory


We next inquire what limits, if any, are imposed on the two rates of interest in the respective standards and the rate of divergence between the two standards. From what has been said it might seem that, when the appreciation is sufficiently rapid, the rate of interest in the upward-moving standard, in order to equalize the burden, would have to be zero or even negative. For instance, if the rate of interest expressed in gold is 4 per cent, and if wheat appreciates relatively to gold at 4 per cent also, the rate of interest expressed in wheat, if perfectly adjusted, would theoretically have to sink to zero! But zero or negative interest is practically almost impossible. If it were definitely foreknown that wheat was to appreciate as fast as 4 per cent when the rate of interest in money is 4 per cent, wheat would be hoarded and so many people would want it that its present price would tend instantly to come within 4 per cent of its next year's price. This would, from that instant, prevent the rate of interest in terms of wheat from passing below the zero mark.


For instance, if interest is 4 per cent, it is impossible that wheat should be worth $1 today and $1.10 next year foreknown today by everybody. For, if such prices were possible, holding for a rise would give a sure return of 10 per cent (neglecting storage charges and other costs of carrying). The result of such perfect knowledge of next year's price would be that the lowest possible price of present wheat would then be the expected $1.10 discounted at 4 per cent, or about $1.06.


This very limitation on the possible rate of interest—that it cannot theoretically sink below zero—carries with it a theoretical limitation on the possible rate of (foreknown) appreciation of any good.


It is important to emphasize the fact that these limits imposed on the rates of interest and appreciation imply the possibility of hoarding wheat, or other durable commodities, including money, without loss. If money were a perishable commodity, like fruit, the limits would evidently be pushed into the region of negative quantities. One can imagine a loan expressed in strawberries or peaches, contracted in summer and payable in winter, with negative interest.*20 Analogously we may regard the storage and other costs of carrying wheat as permitting, to that extent, a negative rate of interest in terms of wheat. It follows that even the rate of interest in terms of money may be negative when money is in sufficient danger of being lost or stolen, as during a riot or invasion.


But as long as our monetary standard is gold or other imperishable commodity, so that there is always the opportunity to hoard some of it, no rate of interest expressed therein is likely to fall to zero, much less to fall below zero. This principle is a special case of a more general principle of opportunity which will be developed later.

§4. Real and Money Interest


The theoretical relation existing between interest and appreciation implies, then, that the rate of interest is always relative to the standard in which it is expressed. The fact that interest expressed in money is high, say 15 per cent, might conceivably indicate merely that general prices are expected to rise (i.e., money depreciate) at the rate of 10 per cent, and that the rate of interest expressed in terms of goods is not high, but only about 5 per cent.


We thus need to distinguish between interest expressed in terms of money and interest expressed in terms of other goods. But no two forms of goods can be expected to maintain an absolutely constant price ratio toward each other. There are, therefore, theoretically just as many rates of interest expressed in terms of goods as there are kinds of goods diverging from one another in value.


Is there, then, no absolute standard of value in terms of which real interest should be expressed? Real income, a composite of consumption goods and services, in other words, a cost of living index in accordance with the principles set forth in Chapter I, affords a practical objective standard. By means of such an index number we may translate the nominal, or money rate of interest, into a goods rate or real rate of interest, just as we translate money wages into real wages. The cost of living plays the same rôle in both cases although the process of translating is somewhat different and more complicated in the case of interest from what it is in the case of wages, for the reason that interest involves two points of time, instead of only one; so that we must translate from money into goods not only in the present, when the money is borrowed, but also in the future, when it is repaid.


Income is the most fundamental factor in our economic lives. The derivation of the value of every durable agent or good involves the discounting or capitalizing of income as one of the steps. Consequently, a rate of interest in terms of fundamental income itself would seem to come as near as we can practically come to any basic standard in which to express a real rate of interest.


But, in actual practice, it is the rate in terms of money with which business men deal and hereafter the rate of interest, unless otherwise specified, will in this book be taken to mean this money rate.


The money rate and the real rate are normally identical; that is, they will, as has been said, be the same when the purchasing power of the dollar in terms of the cost of living is constant or stable. When the cost of living is not stable, the rate of interest takes the appreciation and depreciation into account to some extent, but only slightly and, in general, indirectly. That is, when prices are rising, the rate of interest tends to be high but not so high as it should be to compensate for the rise; and when prices are falling, the rate of interest tends to be low, but not so low as it should be to compensate for the fall.*21


The principle of interest being relative to the standard used in loan contracts would be more in evidence if it were customary to make loan contracts in terms of other standards than money. The rate is actually expressed in loan contracts in terms of money and only translated into terms of goods, if at all, after the contract has been fulfilled, when it is too late to stipulate compensations for the rise or fall in monetary value. If the money rate of interest were perfectly adjusted to changes in the purchasing power of money—which means, in effect, if those changes were perfectly and universally foreseen—the relation of the rate of interest to those changes would have no practical importance but only a theoretical importance. As matters are, however, in view of almost universal lack of foresight, the relation has greater practical than theoretical importance. The business man supposes he makes his contracts in a certain rate of interest, only to wake up later and find that, in terms of real goods, the rate is quite different.


The real rate of interest in the United States from March to April, 1917, fell below minus 70 per cent! In Germany at the height of inflation, August to September, 1923, the real rate of interest fell to the absurd level of minus 99.9 per cent, which means that lenders lost all interest and nearly all their capital as well; and then suddenly prices were deflated and the real interest rate jumped to plus 100 per cent.*22

Notes for this chapter

A brief outline of the history and theory of appreciation and interest is given in the Appendix to Chapter V of The Rate of Interest.
Since, because of ignorance and indifference, appreciations and depreciations are, as a matter of fact, never fully foreknown and their relation to interest and other business phenomena only dimly perceived, they are only partially provided against in the rate of interest itself. As I have tried to show in Stabilizing the Dollar, in The Money Illusion, and in other writings, the best remedy is to standardize, or stabilize, the dollar as we have standardized every other important unit of measure employed in business.
Appreciation and Interest, Publications of the American Economic Association, Third Series, Vol. XI, No. 4, Aug., 1896, pp. 331-442.
The Rate of Interest, Appendix to Chapter V.
This is strictly true only when the rate of interest in each standard is reckoned momently, or continuously. If, as in practice, the rate is reckoned quarterly, semi-annually, or annually, this equation is slightly altered. For the mathematical demonstration of this proposition, see Appendix to Sec. 3, Chapter V, of The Rate of Interest. For the significance of "continuous reckoning," see The Nature of Capital and Income, Chapter XII; also Appendix to Sec. 12 of Chapter XIII.
Böhm-Bawerk, The Positive Theory of Capital, pp. 252 and 297; Landry, L'Intérêt du Capital, p. 49.
That the appreciation or depreciation of money does actually influence the rate of interest, even though feebly, is now well recognised by those who have given attention to the subject. See Professor Marshall's testimony, Indian Currency Report, p. 169; and Johnson, Money and Currency. Boston, Ginn & Company, 1905.
The need to show income and capital accounts in terms of value instead of money units is now coming to be recognized by progressive accountants. For a clear and complete statement of this new principle in accounting, the reader is referred to Ernest F. DeBrul. Unintentional Falsification of Accounts. National Association of Cost Accountants Bulletin, Vol. IX. Pp. 1035-1058. New York, National Association of Cost Accountants, 1928. The same theory is expounded by Henry W. Sweeney in his doctor's dissertation, Stabilized Accounting, accepted by Columbia University but not yet published. See also his article, German Inflation Accounting, in the Journal of Accountancy, February, 1928, pp. 104-116; Dr. Walter Mahlberg. Bilanztechnik and Bewertung bei Schwankender Währung. Leipzig, G. A. Gloeckner, 1923; E. Schmalenbach. Grundlagen Dynamischer Bilanzlehre. Leipzig, G. A. Gloeckner, 1925; Lucien Thomas. La Tenue des Comptabilités en Période d'Instabilité Monétaire. Paris, éditions d'experta, 1927; Lucien Thomas. La Révision des Bilans à L'Issue de la Période d'Instabilité Monétaire. Paris, éditions d'experta, 1928. Also compare Dr. F. Schmidt, Die Industriekonjunktur—ein Rechenfehler! Zeitschrift für Betriebswirtschaft, Jahrg. 1927, and Ist Wertänderung am ruhenden Vermögen Gewinn oder Verlust?, Zeitschrift für Betriebswirtschaft, Jahrg. 1928.

Part I, Chapter 3

End of Notes

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