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Communicated for the Bankers' Magazine. The object of this paper is not (as might be warranted from its caption) to discuss the propriety or the terms of those laws which mankind, with great uniformity and universality, have submitted to; as regulating the usance of money and the price which should be paid for its occasional transfer and employment. Such a discussion would open, of course, the whole question of usury; a very extensive subject, and one which invokes a multitude of statements and considerations, foreign it might seem to its financial aspect, in clearing up the ethical principles by which, for instance, a merely constructive offence is (as with us in Maryland) visited with a penalty more surefooted and more heavy than what is very often inficted upon crimes of undoubted fraud or personal violence. Nor is it intended to offer here, any speculations upon the merits or permanence of a regime that retains, in the face of many and extensive mutations of commerce in other regards, a price for the usance of money confessedly below the average value (or perhaps it would be more correct to say, the average demand) of that article in our market. For such speculations would involve, too, sundry ethical considerations in judging of the social advantages or otherwise of a system, one of whose prominent effects is the stimulating of perverted ingenuity to evade its application and thus to prevent it from being fairly and uniformly carried out.
These topics, then, are set aside for the present; and what follows, belongs merely to the technical part of the subject--the mode in which the interest of money is and ought to be calculated with an indication of how systematically and totally the design, if not the very terms, of the existing laws in this regard, are frustrated by the methods habitually accepted and in practice. These laws are, in the first instance and specially, those which obtain in Maryland, where the limit of interest on money has been, since a long time, six per cent. per annum ; but the indications, it is manifest, may be equally applied, under suitable modifications, to the laws of other States and countries where different rates to be sure but similar previsions have been introduced.
The interest on money, then, is with us calculated upon the natural or more properly calendar days; each one of which is assumed to be the sto part of the natural or tropical year. And in addition to the number of days expressed or implied upon the face of the obligation for the money had and received, interest is farther calculated upon an allowance of three days of grace and also for one day more; making in all four days more than what is apparent from the obligation or promissory note to pay. This extra fourth day seems to be justified in the presumption that the lender (not being prophetic) cannot certainly know in advance that the obligation will be redeemed; nor is he ordinarily possessed of such knowledge until, it may be, the afternoon of the third day. It is, therefore, hardly competent for him to make positive arrangements for the disposal of the money so replaced, among other parties until the said fourth day; and as such disposal may not in fact take effect until the fifth day, it appears to be fair that the first borrower should be charged with the annount of the otherwise possibly lost usance for one day. This, at least, appears to be the practice with Banks and regular Banking-houses trading in money. As for more private, and so to speak, amateur operations, where such rigid punctuality is not always exhibited nor perhaps bargained for, days of grace are accepted or not according to circumstances; most generally, however, the interest is calculated not from the date of the loan to the date of re-payment; as would indeed be the judicial adjustment in case of legal process in behalf of a Bank or Banking-house upon an obligation unredeemed at maturity. But neither amateurs nor regular dealers doubt that the days reckoned in the count of interest are each the sto of the year. What would be the decision of a Court of Law upon this point, strenuously argued before it, remains to be seen. Finally, it is the custom of Banks and regular dealers at least, though perhaps of a minority only of private lenders, to require the interest calculated in the foregoing manner to be paid in advance. Such, it is believed, is a correct statement of the method in which interest is calculated and paid. How it ought to be, can only be judged by a comparison with the prescriptions of the statutes.
Now, in general, these statutes, so far as belonging to the present point, only require that interest shall not exceed the rate of six per centum per annum; and that it shall not be so calculated as to charge interest upon interest, i. e. that it shall be rated upon the actual principal had and received. All these prescriptions are, as we shall see, more or less substantially frustrated in the practice.
First of all, what is the year contemplated and intended to be recognized in the law ?-Undoubtedly it is the civil or calendar year, extending from the first of January, to the first of January; and which (although, to prevent fractions of days, it allows for every three con
secutive years of 365 days, a bissextile or leap year of 366 days) may yet be taken, throughout any century, for all purposes of calculation,
* except the refinements of Astronomy, at the average of 365 days, to adjust itself to the revolutions of the natural or tropical years. And this is so plain that it would without demur be recognized in the case of any contract, the written obligation for which purported on its face to be for twelve months or one year; the months would be unanimously twelve calendar months, some of 31 days and some of 30; and the year would be the calendar year of 365 or 366 days, according as it happened or not to be divisible by 4 without remainder. If the said contract purported to extend over as much as four years, then the average year would necessarily be of 3654 days. But all this reality and necessity is in great measure frustrated; because in point of fact ninetenths at least of all the obligations passed for money lent are upon a specific number of days, not years or months; and even when months are recited upon the face of the instrument, it is easy to see that since the long and short months do not alternate regularly, nearly as often as not the count turns to the disadvantage of the borrower. It may then be affirmed upon this point, that in consequence of the assumed financial year being shorter than the legal calendar year, the habitual rate of interest is in reality greater than the prescribed legal rate. In point of fact, the 6 per centum per annum of the law becomes by this means 630 per cent.
Again the addition to the days of grace serves to make a farther increment in this rate. It is of course perfectly proper that the three days of grace should yield an interest to the lender; because the borrower has the option (and generally avails of it) to retain the money until towards the close of business hours on the third day; but on the fourth day he has no such option. However sair, then, interest accruing for this day may be between the parties; however justified it may be
* The Gregorian reformation of the Calendar was, as is well known, intended to adapt as accurately as possible the civil to the natural year, and thus cure the irregularity which had become quite conspicuous in the unseasonable recurrence of certain annual ecclesiastical festivals. But partly from the inadequate astronomical knowl. edge at the time (1582) and partly from the inherent asynchronousness of the two periods in question, the artificial and natural cycles do not perfectly coincide. In the course of one century, the intercalation of twenty-five leap years make the civil count longer than the true interval by 7-9ths of a day. This was sought to be corrected by providing that of every four centenary years, one only should be bissextile, and the three other common years of 365 days "Such a correction leaves the calendar of every 400 years, however, still too long by 1-9th of a day: Delambre, more than fifty years ago, proposed to correct this excess perfectly by making the year 3600 and its multiples, coinmon years, instead of bissextile as they would be by the Gregorian system. This system, which in the circuitous way I have been obliged to explain it, may appear rather complicated, is in fact very simple. All years whose date is divisible by 4 without remainder are bissextile, unless at the beginning of a new century of the centenary years, only those are bissextile whose number expressing the centuries is in like manner divisible by 4 without remainder. Thus 1848 which divided by 4 leaves no remainder is a leap-year; 1849 is not: the year 1600 was a leap-year, because 16 (centuries) divided by 4 leaves no remainder; in like manner the year 2000 will be a leap-year; but 1900 will not be. The year 3600 will be, according to the present calendar, bissextile; but it ought not be in order to make the cycles syn. chronize. All this serves to shew, however, what was said in the text, that within every century 365; days corresponds with a true year for all civil purposes.
by a due regard to the circumstances of the lender; or, however sanctioned by long and unanimous usage; it certainly receives no countenance from the terms of the law or from its scope which is that the lender should be entitled to interest for the whole period that the money had been out of his control but no longer. The increment of the rate of interest arising from this method of calculating, is in the ratio of the specified number of days plus 3 to the same number plus 4: it varies, of course, with the actual number; and when its ratio is multiplied into the proportion already given of the inaccurate year to the legal year, we have for any given number of days a rate of interest discordant, in the sense of excess, from the rate prescribed by law. This will be more apparent by the following table containing various numbers of days usually specified on the face of obligations, and the corresponding rates of interest actually accruing upon such obligations in every case. Obligation for Actual rate of Interest. Obligation for Actual rate of Interest. 10 days: 6,56 per cent. 90 days:
6,15 20 days: 6,35 120 days:
5,14 30 days: 6,27 180 days:
6,12 60 days: 6,18 360 days:
6,10 It is easily seen that the rate of interest gradually diminishes as the number of days, i. e. the length of time, increases; and in so far, short notes are disadvantageous to the borrower and proportionally lucrative to the lender. It can be as easily imagined that there would be limits at both extremities of the scale : in point of fact, the maximum limit, where the rate is the highest, occurs when the fractional number representing the days is infinitely small; and the minimum limit, where the rate is the lowest, when the number of days is infinitely great. In the first, the rate attains the limit of 8,12 per cent.; in the latter, it decends as low as 6,0875 per centum. In either, however, it is more than the rate prescribed in the law.
Again what is the rate per annum so prescribed; and how is the phrase to be construed and understood ?—There can be but little doubt that
* This will be more apparent to the mathematical reader by the expression of the formula. Thus the interest on any principal sum A being at any rate r per year of 365,25 days and the specified days being any number n with a constant allowance of 3 days of grace, if we call the principal and interest at maturity a, we shall have this equation :
The same symbols remaining, only assuming the year to be 360 days and allowing 4 days of grace, we shall have in like manner
:) Now a : al::r: R= the actual rate of interest accruing. Dividing by the factors common to both terms, we have
365,25. n +4 R=1.
1,014583 n + 4,0581 560.0 + 3
n + 3. It is evident that R is at its maximum when n= 0; and that it is at its minimum when the days of grace become = 0, as they do when n is infinite.
the word rate here means ratio; and as little that this last, if respect is to be had to the authority of those who first used the term in its technical sense, implies a quotient not a difference. It is the integral or fractional number of times that a given quantity is contained in any other given quantity. Thus the ratio of 6 to 10 is said to be (as 1 is to) 13; the difference between the two numbers is 4, which expresses nothing as regards any scale and, with respect to the harmony of numbers, is entirely barren. For this same difference occurs between an infinity (one may say) of other numbers whose ratios are very different. Thus 4 is the difference between 8 and 12, also; whose ratio is however not lg but 14: it is the same between 16 and 20 whose ratio is 14; and so on. It is true that we sometimes hear the phrase "arithmetical ratio”; but it is applied to a series of progressions by differences whose harmony is established upon other statements; and it is besides, even there, but a loose way of expression.
That this was also the perception (however vaguely appreciated and unskilfully carried out in practice) of the law, is evident from the very term it makes use of. What does six per centum imply but six for every hundred ? and what does this show but an idea of multiples and quotients as distinguished from differences ? It is true that at the period of the origin of the present law or its prototype, the analytic apparatus at the disposal of not only commercial men but even of professed mathematicians, was so deficient as to have made the calculation according to this idea exceedingly laborious; but Archimedes and Euclid had not lived so much in vain as to leave the world and its men of business without the possession of the idea. Shrinking, it may be, from the tedium of the necessary calculation and appalled at the intricacy of its processes as then existing, they resorted to an approximation which was the more readily adopted on the one hand because it was to the advantage of the lender, and acceded to on the other because the borrowers were very needy. For its maintenance at the present time, when proper arithmetical processes offer no difficulty, there is no reason for indicating such an invidious contrast; it is retained, one may suppose because it is very convenient and because it has been sanctioned by long usage. This last, however, if we argue from analogy, is precisely the reason which modern Reformers marching under the banner of Rotation, &c. will not be likely long to admit.
The law then intends that 100 dollars or unitary pieces of whatever denomination, shall produce to the lender 106 dollars or units at the end of the year; and no more. The ratio of the principal then to the priocipal and year's interest is 100 to 106; and the ratio of the year's interest to the principal is 6 to 100 or, as we say ordinarily, six per cent. In order that it may be a ratio and not a mere arbitrary increment, the term must be so involved as that the growth of the interest (which, we say commonly and say truly, is going on while we sleep) shall be continual and progressive; the aggregate of principal and interest at any epoch within the year must be always such as that if placed at interest at the same rate for the remainder of the year, it should still equal but not surpass 106 for every 100, at the year's end. That this is so might be inferred from the general motives at the