Definition. INTEREST is the annual sum or rate per cent. which the borrower of a capital agrees, or is bound, to pay to the lender for its use.
It was generally supposed, previously to the middle of last century, that, in the event of all legislative enactments regulating the rate of interest being repealed, its increase or diminution would wholly depend on the comparative scarcity or abundance of money; or, in other words, that it would rise as money became scarce, and fall as it became more plentiful. But this opinion has been successfully controverted. And it has been shown that the rate of interest, in advanced communities, is not determined by the abundance of the currency, but by the average rate of profit derived from the employment of capital. No doubt it most frequently happens that loans are made in currency; but this is of no consequence. There is obviously no substantial difference between A furnishing B with 100 bushels of corn, or 100 yards of cloth, to be repaid at the expiration of a specified period by the delivery of 104 or 105 bushels, or 104 or 105 yards, or with as much money, at 4 or 5 per cent., as would purchase the corn or cloth.
And it is easy to perceive that, as crowds of passengers may be successively conveyed by the same carriage, so the same sum of money may serve to negotiate an infinity of loans. Suppose A lends to X, L1000, with which the latter buys from B an equivalent amount of commodities; that B, having no use for the money, lends it to Y, who pays it away for produce to C, who again lends it to Z, and so on. It is plain that X, Y, Z have received loans of commodities or produce from A, B, C worth three times (and they might have been worth thirty or three hundred times) as much as the money employed in settling the transactions. According as the supply of currency, compared with the business it has to perform, is greater or less, we give a greater or less number of guineas or livres, notes or assignats, for the articles we wish to obtain. It is not, however, by the fact of the price of such articles being high or low, but by the advantage or profit which the borrowers expect to derive from their possession, that the interest or compensation to be paid to the lenders for their use is determined. It may perhaps be supposed in the case of goldsmiths and jewellers, that when the quantity of metallic money is increased, they will obtain the raw material of their business with greater facility. But this is not always the case; and, though it were, it would not, in any degree, affect the rate of interest. No coins are ever sent to the melting pot unless the currency be degraded or depreciated; that is, unless it be deficient in weight, or relatively redundant in quantity. And it is plain that the inducement to offer a high or a low rate of interest for loans of money, which it is intended to work up into plate or other articles, will not depend on the supply of such money, but on the profit to be derived from its conversion into goods, a circumstance wholly unconnected with the scarcity or abundance of coin.
It, therefore, appears that, speaking generally, the rate of interest depends on the profit that may be made by employing capital in industrious undertakings, and not on the prices paid for the articles of which it consists. The latter are affected by every change in the value of money, whereas the former is little if at all affected by these changes, and is determined by the productiveness of industry. A low or a high rate of profit is uniformly accompanied by a low or a high rate of interest. Money, as every one knows, is cheaper in the United States and in Australia, than in England; but the ordinary rate of profit being higher there than here, interest, despite the lower value of money, is also higher. Extraordinary as it may seem, it is nevertheless true, that, during the half dozen years ending with 1856, the current rate of interest in San Francisco, where bullion is so very abundant as to be almost a drug, has varied from 1½ to 2 and 3 per cent. a month, or from 18 to 24 and 36 per cent. per annum. And though it were allowed that from a third to a half of this rate should be viewed as a premium to compensate the insecurity prevalent in California, still the residue would amount to three, four, or five times the ordinary rate of interest in England. In farther corroboration of these statements, we may mention that the low rate of interest in Holland during the greater part of the 17th, and the whole of the 18th century, was not owing to any peculiar abundance or cheapness of money, but to the high rate of taxation and the difficulty of investing capital with a profit. And to this latter circumstance we owe the low rate of interest in this country towards the middle of last century and at several late periods. It is not, in short, by the amount or value of the currencies of different countries; but by the means which they respectively enjoy for the profitable employment of capital or stock, that their profits and interest are governed.
That a rise or fall in the value of money can have no direct influence over interest, is plain from the fact of the interest being itself paid in the money that has risen or fallen. But, at the same time, a sudden increase in the supply of money, may undoubtedly have a temporary effect in depressing interest. Importers of bullion may not be able to lay it out advantageously in purchases, and may, in consequence, be disposed to have it coined and lent, though at a low rate. We incline, however, to think that the influence of considerations of this sort is but inconsiderable. Lenders will not take less for loans than the borrowers are willing to offer, and the offers of the latter must be determined not merely by the amount of money seeking investments, but partly also, and in a still greater degree, by the profit that may be made by its employment. When there is a rapid influx of money, loans for short periods are usually obtainable at low rates. This, however, is not generally the case with loans for lengthened periods. The lenders are willing to accept a reduced interest for a short term, till they can look about for some more profitable means of investment. But the interest on loans on mortgage, or for lengthened periods, is always proportioned to the rate of profit at the time; and, supposing the security to be unexceptionable, is but little affected by anything else.
The profits made in industrious undertakings are, for the most part, distributed into gross and nett profits. Thus, if from the total returns, whether annual or otherwise, obtained in any business or employment, we deduct all sorts of outlays necessarily incurred in carrying it on, including the wages or remuneration due to the undertakers for their skill and trouble in superintending the business and a sum to compensate the risks provided against by insurance, the residue is the nett profit of, or return to, the capital employed. And it is on this latter portion that interest depends, or rather with which it is usually identical. Lenders having nothing to do with the employment of capital, are not entitled to any peculiar advantage that may arise from it. But they are entitled to all that can fairly be considered as the return to the capital they have lent, after the risks, salaries, and necessary emoluments of those who undertake its employment, are deducted; and this much, speaking generally, they will get, and no more. Whatever else may be realized by the employment of capital in industrial pursuits, belongs to the borrowers, and forms the fund out of which they are remunerated. In coming to this conclusion, we are supported by the authority of Mr Tooke. "The rate of interest," says he, "is the measure of the nett profit on capital. All returns beyond this on the employment of capital, are resolvable into compensations, under distinct heads, for risk, trouble, or skill, or for advantages of situation or connection."
Whatever, therefore, may at any time occasion a sudden glut of money or capital, may lower the rate of nett profit and interest. But that very circumstance, by increasing the demand for capital, will eventually raise the rate to its proper level; and the glut having disappeared, profits and interest will depend on the productiveness of industry.
Besides such variations as are proportioned to variations in the ordinary rate of profit, and which equally affect all loans, the rate of interest varies according to the security for the repayment of the principal, and the duration of the loan. Hence the powerful influence which the character of the borrower, the purpose for which he borrows, and the nature of the business in which he is engaged, have over interest. Careful, skilful, and intelligent parties always borrow, *ceteris paribus*, on lower terms than those of an opposite description. The spendthrift, the idle, and the unskilful, can with difficulty obtain loans on any terms; and those who deal with them and stipulate for a high rate of interest to cover their risk, frequently find that their guarantee is inadequate, and that they would have better consulted their own advantage by lending to respectable parties on the usual terms. The nature of the employment in which borrowers are engaged has also, as now stated, a powerful effect in determining the rate of interest. Wherever there is risk, it must be compensated. A sum lent on mortgage over a valuable estate is not exposed to any risk. But a sum lent to a manufacturer or merchant engaged in a hazardous business, is exposed to a high degree of risk; and the interest payable on the latter, insomuch as it must include a premium to compensate this extra risk, may be twice or three times as much as that paid on the mortgage.
We should mistake, however, if we supposed that this circumstance places those who carry on peculiarly hazardous businesses in a comparatively disadvantageous situation. Competition will not permit taking everything into account, a greater or a less amount of nett profit to be permanently obtained in one branch of industry than in another. The produce realized by those who engage in employments of more than ordinary hazard is generally sold at prices that yield the ordinary rate of profit, with a surplus sufficient to guarantee their stock against the extra risk to which it is exposed. Were it otherwise, everybody would decline placing their property in a state of comparative danger, and undertakings of a hazardous nature would not be entered into. But it very frequently happens, that the manager of a hazardous branch of industry, paying from 10 to 12 per cent. for loans, realizes larger nett profits than the purchaser of an estate with money borrowed at 3 or 4 per cent.
Supposing the security to be equal, capital lent for a fixed and considerable period always fetches a higher rate of interest than that which is lent for short periods, or which may be demanded at the pleasure of the lender. There are but few modes of safely employing loans of which the duration is so uncertain, so that they are frequently worth very little; and hence the rate of interest is, in the majority of cases, in part at least, determined by the length of the loan; for, when that is considerable, it may be productively employed in a variety of businesses, in which it would not otherwise be prudent to invest it, at the same time that the borrower has time to prepare for its repayment. But this principle has only a slight influence over loans for terms beyond three, or at most five, years; for a loan for either of these terms, but especially the latter, may be employed in a great variety of ways, and would bring nearly as much interest as it would do were it for ten or twelve years. It is farther to be observed, that large classes of borrowers prefer the less interest which they get for advances at short dates to the higher rate which they might get were they for longer terms. Most people wish to have the full command of their capital. Merchants and manufacturers who lend on mortgage would in so far deprive themselves of the means of extending their business, and of speculating. And though sometimes, perhaps, this might be for their advantage, yet the flattering opinion which most people entertain of their own sagacity and good fortune, would but seldom permit them to doubt that it was a very serious disadvantage. Hence the low rates at which banking companies who pay the sums deposited with them on demand, and governments overwhelmed with debt, are able to borrow. A stockholder's mortgage, or claim on the revenue of a country, maybe immediately converted into cash at the current prices. And, however much the majority of the creditors of a deeply indebted country may be impressed with a conviction of its inability to discharge the various claims upon it, each individual, confident in his own good fortune and foresight, flatters himself that he, at all events, will foresee the coming tempest, and be able to sell out before a public bankruptcy.
It is evident, from these statements, that in addition to the security for loans and their duration, the rate of interest will, to a considerable extent, depend on the facilities afforded for enforcing or carrying out the stipulations in contracts. And hence a main cause of its reduction as society is more and more improved. Generally, it may be said that a speedy, cheap, and effectual process for securing the payment of debts, has a powerful tendency to lower—and a slow, costly, and ineffectual process, to raise—the rate of interest. In most countries, extraordinary means are taken to compel payment of bills; and this is a principal cause of the low rate at which they are commonly discounted. The easy enforcement of contracts constitutes, in truth, an important portion of the security for a debt. By a good security, is not meant a guarantee that a loan will ultimately be made good, but that it will be punctually paid when due; or, if the loan be of a kind that a little delay in its payment is usually given, that that delay will not be exceeded, and that it will be paid within the customary term. A security which should insure the final payment of a debt, but which should not insure its payment when due, or shortly thereafter, is not a good, but a bad security. It is indispensable to the transacting of business safely, cheaply, and expeditiously, that there should be as little doubt as possible either in regard to the payment of loans or the term when they are to be paid. If either of these points be doubtful, the lender will insist on an indemnity for the consequent risk. And it therefore appears that the summary proceedings taken to enforce payment of bills, and such like debts, are in truth and reality more for the advantage of the borrowers than of the lenders. They reduce the rate of interest; and the hardship, such as it is, which they occasionally inflict on the borrower, does not occur in one case out of five hundred; while their powerful influence in depressing interest tells in every case.
In Greece the rate of interest was not regulated by law; and it consequently varied with all the causes of variation above alluded to. Generally, however, it was what we should reckon very high, amounting, in most cases, to from 10 to 18 per cent., and upwards. This high rate of interest was not occasioned by a high rate of profit, but by the uncertainty of the laws, and the facilities which they afforded to fraudulent debtors to defeat the just claims of their creditors. The interest on money lent on *bottomry*, or on the security of the ship or cargo, or both, was rated at so much per voyage. It therefore depended on the place to which the ship was to sail, the season of the year, the chance of meeting pirates or enemies' ships, etc. Usually it was ex-
---
1 This, however, is not a common practice; most companies stipulating that notice of the withdrawal of deposits shall be given some eight or ten days previously.
2 It is not, of course, any part of our business to inquire into the methods most proper to be taken to enforce payment of debts. But, how paradoxical sooner it may appear, we believe it would not be difficult to show that the putting of most descriptions of small debts, or of debts under L30 or L40, out of the pale of the law, would be advantageous. It would tend to prevent the abuse of credit by the lower classes, to whom it is extremely pernicious, and to make habits of economy and punctuality more valuable than at present. tremely great, varying from 30 to 50 or 60 per cent. The bankers and money lenders of Athens, though of low origin, being mostly freedmen or aliens, appear to have been considered as eminently trustworthy, and entitled to the public confidence. But they were, notwithstanding, quite as unpopular, and for no better reasons, as the Jews and Lombards of the Middle Ages. We are surprised that so learned a writer as Boeckh should have been so imbued with the vulgar prejudice against them as to state that they drew upon themselves the "merited hatred of all classes." He should have known that it has not been the covetousness of bankers, but that bad laws administered by interested judges, by making loans insecure, and driving parties of the highest respectability from the banking business, have been alone to blame for the exorbitant usury of ancient as well as of modern times. Had contracts been properly enforced, the probability is that interest would have been as low in Greece as in England.
Instead, however, of leaving the rate of interest to be adjusted by the free competition of the parties, on the principles thus briefly explained, or endeavouring to reduce it by facilitating the enforcement of contracts, most governments have interfered, either entirely to prohibit the taking of interest, or to fix certain rates which might be legally exacted, while any excess over them was declared to be usury, and prohibited under the severest penalties. In the ages in which these enactments had their origin, the precious metals were the only species of money, and were considered quite peculiar. Being used in a double capacity—as standards by which to ascertain the values of different articles, and as the equivalents for which they were most frequently exchanged—they acquired a fictitious importance in the estimation, not merely of the vulgar, but of persons of the greatest discernment. The fact, that to buy and to sell is merely to barter one commodity for another, to exchange a quantity of corn, or cloth, or beef, for a quantity of gold or silver, and vice versa, was entirely overlooked. The attention was gradually transferred from the money's worth to the money itself. And the wealth of states and of individuals was not measured by the amount of their disposable produce, or by the quantity or value of the articles with which they could afford to purchase the precious metals, but by the quantity or value of these metals actually in their possession. For these and other reasons, money has been considered as a merchandise par excellence. And we need not, therefore, be surprised at the measures to which the prevalence of such exaggerated opinions almost necessarily led; or that vigorous efforts should have been made to protect those who were unprovided with so powerful an instrument from becoming a prey to their more fortunate neighbours. Individuals might freely dispose of their corn, cattle, land, etc. But it was supposed that the demand for money might be so great, as to enable the lenders, unless restrained in their exactions, to ruin the borrowers, and engross the whole property of the country.
Another cause of the prejudice against stipulating for interest grew out of the dislike entertained to accumulation. It is a consequence of economy, or of a saving of income; and this, in rude ages, is considered indicative of a sordid disposition, and as being positively hurtful. Prodigals and spendthrifts were long, and perhaps still continue to be, the favourites of the public. Before the nature and functions of capital were properly understood, it was believed that it could not be increased without injury to individuals, and that whatever advantage it might give to one party must occasion an equal disadvantage to others. Our ancestors did not know that those who, by their economy, accumulate stock, add to their own wealth, without diminishing that of any one else; nor did they know that, when expended, as is almost always the case, in the support of productive industry, this stock affords the means of producing an increased income. But reckoning, as they did, that the savings of individuals were so much withdrawn from income in which the public would otherwise have participated, it was natural enough that they should endeavour to limit the advantage derivable from their employment.
Much, also, of the prejudice against bargaining for interest, prevalent in the middle ages, may be traced to the authority of certain texts of Scripture, which were understood to prohibit its exaction. It is, doubtful, however, whether they will really bear that interpretation. And supposing that they did, nothing could be more irrational than to regard the municipal regulations of a people placed in such peculiar circumstances as the Jews, as general and fixed principles, applicable in all ages and countries.
But, whatever may have led to the efforts so generally made to limit or suppress interest, it is abundantly certain that, instead of succeeding in their object, they had an opposite effect. If a borrower consider it for his advantage to offer 6, 7, or 8 per cent. for a loan (and otherwise he would not make the offer), why should the legislature prohibit him from offering, and the lender from receiving, more than 3, 4, or 5 per cent.? An interference of this sort, besides being uncalled for and unnecessary, is in a high degree prejudicial. Restrictive laws, instead of reducing, uniformly raise the rate of interest. They cannot be so framed as to prevent borrowers from engaging underhand, to pay a higher rate of interest than is fixed by statute. And if the lenders had implicit confidence in the secrecy and solvency of the borrowers, they might accommodate them with the sums wanted, without requiring any additional interest, because of the illegality of the transaction. But cases of this sort are extremely rare. Gratitude, and a sense of benefits received, are but slender securities for honourable conduct. Numberless unforeseen events occur to weaken and dissolve the best cemented friendships; and a transaction of this kind would afford an additional source of jealousies and divisions. In such matters, indeed, men are more than usually sharp-sighted, and are little disposed to trust to moral guarantees for the security of their property. But though neither the threatenings of the law, nor the inducements which it held out to dishonest debtors to recede from the stipulations into which they had entered, were able to prevent, or even greatly to lessen, what are termed usurious bargains, they rendered them more oppressive. They obliged the lenders to demand, and the bor-
---
1 Boeckh's Public Economy of Athens, vol. i., pp. 164-191. 2 Michaelis On the Laws of Moses, vol. ii., 336. English translation. It is a remarkable fact that the famous reformer Calvin was one of the first to emancipate himself from the prejudices formerly so prevalent, especially among religious people, against taking interest. He comments as follows on the statement of Aristotle, that as money did not produce money, no return could be equitably claimed by the lender:—“Pecunia non parit pecuniam. Quid maro? quid dossae? est aut locutionis pensionem percipio? An ex tectis et parietibus argentum propriis nascitur? Sed et terra producta, et mari advenitique quaestiones deinde producent, et habitationes commoditas cum certa pecunia parari commutative solet. Quod si igitur plus ex negotiatione lucri percipi possit, quam ex fundi ejusmodi proventa: an feretur qui fundum sterilum fortasse colono locaverit ex quo mercedem vel proventum percipiat, qui ex pecunia fructum aliquem perciperit, non feretur? et quia pecunia fundum acquirit, annua pecunia illa generat aliorum annuum pecuniarium? Unde vero mercatores lucrari? Ex ipsius, inquire, diligentia atque industria. Quis dubitet pecuniam vacuam inutili modo esse? neque quis a me non rogat, vacuam apud se habere a me accipiam cogitat. Non erga ex pecunia illa lucrum accedit, sed praestantia. Hinc igitur rationes subtiles quidem sunt, et speciem quandam habent, sed ubi propria expenduntur, salpes concident. Nam igitur conclusio judicandum de usuaria esse, non ex particulari aliquo Scripturae loco, sed tantum ex acquisitatis regula.” (Quoted by Dugald Stewart in his Notes to his Preliminary Dissertation to the Encyclopaedia Britannica.)
rowers to undertake to pay a rate of interest sufficient to yield the current rate of net profit at the time, with a further sum to balance the risk of entering into what the law made an illegal transaction. This latter sum being, of course, proportioned to the greater or less magnitude of the risk to be provided against, it increased or diminished according as the laws for the prevention of usury were enforced or relaxed.
Whenever, under the old system, the market rate of interest rose above the statutory rate, the free transfer of capital was obstructed. Parties could no longer look merely to their own advantage. And loans which might have been obtained for 6, 7, or 8 per cent., had there been no hazard from anti-usurious statutes, were raised, on its account, to 8, 10, and 12 per cent. It is, therefore, plain that if the means taken to put down usury were not wholly responsible for its existence, they, at all events, added largely to its amount.
These conclusions do not rest on theory only, but are supported by a wide and uniform experience. In Rome, during the republic, the ordinary rate of interest was excessively high. The debtors, or plebeians, were every now and then threatening to deprive their creditors, who were generally of the patrician order, not only of the interest, but of the principal itself. Repeated instances occurred to show that these were not mere empty threats; and the patricians indemnified themselves, by a corresponding premium, for the dangers to which they were exposed. "Des continuels changements," says Montesquieu, "soit par des loix, soit par des plebisites, naturaliserent à Rome l'usure: car les cranciers, voyant le peuple leur débiteur, leur législateur, et leur juge, ne curent plus de confiance dans les contrats. Le peuple, comme un débiteur décrédié, ne tentoit à lui prêter que par des gros profits; d'autant plus que, si les loix ne venaient que de temps en temps, les plaintes du peuple étoient continuelles, et intimidentoient toujours les créanciers. Cela fit que tous les moyens bonnés de prêter et d'emprunter furent abolis à Rome, et qu'une usure affreuse toujours foudroyée, et toujours renaissante, s'y établit. Le mal venoient de ce que les choses n'avoient pas été négociées. Les loix extrêmes dans le bien font naître le mal extrême; il fallut payer pour le prêt de l'argent, et pour le danger des peines de la loi."
In Mohammedan countries, notwithstanding the prohibition in the Koran, the ordinary rate of interest is at least three or four times as great as its ordinary rate in Europe. "L'usure augmente dans les pays Mahometans à proportion de la sévérité de la défense: le prêteur s'indemnise du péril de la contrevention."
During the middle ages, when interest was excessively high, the rate of profit was probably little, if at all, higher than at present. But it should be observed that a very great majority of the loans of these ages were but little influenced by its amount. They were not made to be invested, but to be spent. The great barons and other landed proprietors were the principal borrowers. And in nineteen out of every twenty instances, the sums which they borrowed were expended in the maintenance of crowds of idle retainers, in warfare, or in prodigalities of some sort or other. And while the borrowers belonged generally to what we should now call the spendthrift class, and there were no efficient means of compelling them to abide by their engagements, the lenders were but few in number, and mostly Jews and Italians, the objects of the most unreasonable prejudices. Under such circumstances, it would be folly to suppose that the rate of interest should depend in any considerable degree on the rate of profit. The numbers, position, and character of the borrowers, compared with the fewness, position, and character of the lenders, and the risk to which the latter were exposed in entering into such transactions, occasioned the excessively high rate of interest. Of the 50 and even 100 per cent. which borrowers then frequently engaged to pay as interest, not more than 10 or 12 per cent. can properly be said to have been given for the productive services of loans. The rest must be considered as occasioned partly by the extreme scarcity of disposable capital and the carelessness of the borrowers, and partly, and principally, as a bonus to compensate the lenders for the imminent hazard of losing the principal.
In England, as in most other countries, Christians were, after the Conquest, absolutely prohibited, both by the civil and the ecclesiastical law, from bargaining for interest. But as Jews, according to the Mosaic law, were allowed to lend at interest to a stranger, its exaction by them was first connived at, and subsequently authorized by law. And the same privilege was afterwards extended to the Italian or Lombard merchants. In consequence of this exemption, many Jews early settled in England, and engrossed a large share of the trade of the kingdom. But despite their industry and general good conduct, the prejudices against them, and against the business in which they were mostly engaged, were so very strong that they and their families were regarded as slaves of the crown, by whom they were plundered, to an extent and under pretences which would now appear incredible. To such an extreme, indeed, were these oppressive practices carried, that a particular office, called the exchequer of the Jews, was established, for receiving the sums extorted from them in fines, customs, tallages, forfeitures, &c. They were, in consequence, obliged to charge an enormous rate of interest, or, as Madox expresses it, "to fleece the subjects of the realm as the king fleeced them." Hence, while only from 7 to 10 and 12 per cent. interest was paid in countries where sounder principles prevailed, the rate charged in England was three, four, and even five times as great.
But in the end the disorders occasioned by this ruinous system became so obvious, that, notwithstanding the deeply-rooted prejudices to the contrary, a statute was passed in 1546 (37 Hen. VIII., cap. 7), legalizing interest to the extent of 10 per cent. per annum; because, as is recited in the words of the act, the statutes "prohibiting interest altogether have so little force, that little or no punishment hath ensued to the offenders." In the reign of Edward VI., the horror against interest seems to have revived in full force; for, in 1552, the taking of any was again prohibited, "as a vice most odious and detestable," and "contrary to the word of God." But, in spite of this denunciation, the rate of interest, instead of being reduced, immediately rose to 14 per cent., and continued at this rate until, in 1571, an act was passed (13th Eliz., cap. 8) repealing the act of Edward VI., and reviving the act of Henry VIII., allowing 10 per cent. interest. In the preamble to this act it is stated, "That the prohibiting act of King Edward VI. had not done so much good as was hoped for; but that
---
1 Esprit des Lois, liv. xxii., c. 21. 2 Deuteronomy, cap. xxxiii., v. 20. 3 At Verona, in 1228, the interest of money was fixed by law at 124 per cent. Towards the end of the fourteenth century, the republic of Genoa paid only from 7 to 10 per cent. to her creditors; and the average discount on good bills at Barcelona, in 1439, is stated to have been about 10 per cent. But whilst interest in Italy and Catalonia, where a considerable degree of freedom was allowed to the parties bargaining for a loan, was thus comparatively moderate, it was, despite its total prohibition, incomparably higher in France and England. Matthew Paris mentions that, in the reign of Henry III., the debtor paid 10 per cent. every two months. And this, though impossible as a general practice, may not have been very far from the average interest charged on the few loans that were then contracted for (Hallam's Middle Ages, vol. iii., p. 402). 4 Madox's History of the Exchequer, vol. i., pp. 221-261, 4to, 1769. 5 Ibid., liv. xxi., c. 19. Interest, rather the vice of usury hath much more exceedingly abounded, to the utter undoing of many gentlemen, merchants, occupiers, and others, and to the importable hurt of the commonwealth." This salutary statute was opposed, even by those who should have known better, with all the violence of superstitious fanaticism. Dr John Wilson, a man famous in his day, and celebrated for the extent of his learning, informed the House of Commons, of which he was a member, that "it was not the amount of the interest taken that constituted the crime; but that all lending for any gain, be it ever so little, was wickedness before God and man, and a damnable deed in itself, and that there was no mean in this vice any more than in murder or theft." To quiet the consciences of the bishops, a clause was inserted, declaring usury to be forbidden by the law of God, and to be in its nature sin, and detestable. This statute was limited to a period of five years; but, "forasmuch as it was, by proof and experience, found to be very necessary and profitable for the commonwealth of this realm," it was, in the same reign, made perpetual (39th Eliz., cap. 18).
In the 21st of James I., the legal rate of interest was reduced to 8 per cent., by an act to continue for seven years only, but which was made perpetual in the succeeding reign (3d Car. I., cap. 4). During the commonwealth, the legal rate of interest was reduced to 6 per cent., a reduction which was afterwards confirmed by the 12th Car. II. And, finally, in the reign of Queen Anne, a statute (12th Anne, cap. 16) was framed, reducing the rate of interest to 5 per cent., at which it stood till 1839.
In the preamble to this statute, it is stated that, "whereas the reducing interest to 10, and from thence to 8, and thence to 6, in the hundred, hath from time to time, by experience, been found very beneficial to the advancement of trade and the improvement of lands, it is become absolutely necessary to reduce the high rate of interest of 6 per cent. to a nearer proportion to the interest allowed for money in foreign states." It was for these reasons enacted, that all bargains or contracts stipulating for a higher rate of interest than 5 per cent. should be utterly void. And "that all persons who should after that time receive, by means of any corrupt bargain, loan, exchange, chevizance, or interest, of any wares, merchandise, or other thing whatever, or by any deceitful way or means, or by any covin, engine, or deceitful conveyance for the forbearing or giving day of payment, for one whole year, for their money or other thing, above the sum of L5 for L100 for a year, should forfeit, for every such offence, the treble value of the moneys or other things so lent, bargained," &c.
In Scotland, previously to the Reformation, no interest could be legally charged. But that great event, by weakening the force of those religious prejudices, which had chiefly dictated the prohibition of interest, led to the adoption of more liberal opinions on the subject, and to the enactment of the statute of 1587 (11th Parl., Jac. VI., cap. 52), which legalized interest to the extent of 10 per cent. In 1633 the legal rate was reduced to 8 per cent., and in 1661 to 6 per cent. The statute of Anne, reducing the rate of interest to 5 per cent., extended to both kingdoms.
The statutes prohibiting the taking of interest in Ireland were not repealed until 1635, when the statute 10th Car. I., cap. 22, gave liberty to stipulate for any rate not exceeding 10 per cent. In 1704 this rate was reduced to 8 per cent.; in 1722 it was reduced to 7 per cent.; and in 1732 it was further reduced to 6 per cent.
In France the rate of interest was fixed at 5 per cent. so early as 1665; and this, a few short intervals only excepted, continued to be the legal rate till the Revolution. Laverdy, in 1766, reduced it from 5 to 4 per cent. Instead, however, of the market rate being proportionally reduced, it was raised from 5 to 6 per cent. Previously to the promulgation of the edict, loans might have been obtained on good security at 5 per cent.; but an additional per cent. was afterwards required to cover the illegality. This caused the speedy abandonment of the measure.
The same thing happened in Livonia in 1786, when the Empress Catherine reduced interest from 6 to 5 per cent. Hitherto, says Storch (in loco citato), those who had good security to offer were able to borrow at 6 per cent.; but henceforth they had to pay 7 per cent. or upwards. And such will be found to be invariably the case, when the legal is less than the market rate of interest.
It has been observed by Adam Smith, that the statutory regulations, reducing interest in England, were made with great propriety. Instead of preceding, they followed the fall which was gradually taking place in the market rate of interest; and, therefore, did not contribute, as they would otherwise have done, to raise that which they were intended to reduce. Sir Josiah Child, whose treatise, recommending a reduction of interest to 4 per cent., was originally published in 1668, states, that the goldsmiths of London, who then acted as bankers, could obtain as much money as they pleased, upon their servants' notes only, at 4½ per cent.
The supposed insecurity of the revolutionary establishment, and the novelty of the practice of funding, occasioned the payment of a high rate of interest for a large portion of the sums borrowed by the public in the reigns of William III. and Anne. But private persons, of undoubted credit, could then borrow at less than 5 per cent. During the reign of George II. the market rate of interest fluctuated from 3 to 4 and 4½ per cent.
Smith mentions that the increased means of profitably investing capital acquired during the war, terminated by the peace of Paris in 1763, raised the market rate of interest to a level with the statutory rate, or perhaps higher. But it was not until the subsequent European war that any very material or general inconvenience was found to result from the limitation of interest to 5 per cent.
It is necessary, however, to observe, that this remark applies exclusively to loans negotiated by individuals who could offer unexceptionable security; for, since the act of 1714, persons engaged in employments of more than ordinary hazard, or whose character for prudence and punctuality did not stand high, or who could only offer inferior security, were unable to borrow at 5 per cent., and were consequently compelled to resort to a variety of schemes for defeating or evading the enactments in the statute. The most common device was the sale of an annuity. Thus, supposing an individual whose personal credit was indifferent, and who had only the liferent of an estate to give in security, wished to borrow, he sold an annuity to the lender sufficient to pay the interest stipulated for, which, because of the risks and odium attending such transactions, was always higher than the market rate, and also to pay the premium necessary to insure payment of the principal at the death of the borrower. It is curious to observe, that though the sale of an irredeemable life annuity, at a rate exceeding legal interest, was not reckoned fraudulent or usurious, yet, so late as 1743, Lord Hardwicke held that, in their less exceptionable form, or when they were redeemable, their sale could be looked upon in no other light than Interest: as an evasion of the statute of usury, and a loan of money. But the extreme inexpediency of this distinction soon became obvious, and the law was changed. The great extension of the traffic in annuities, and the advantage of giving as much publicity as possible to such transactions, led to various inquiries and regulations respecting them in the early part of the reign of George III. In consequence, the sale of irredeemable annuities became nearly unknown; and it was ruled, that the sale of a redeemable annuity could not be impeached, though it appeared on the face of the deeds that the lender had secured the principal by effecting an assurance of the borrower's life.
During the greater part of the French revolutionary war, the usury laws operated to the prejudice of all classes of borrowers. The great extent and high interest of the public loans, the facility of selling out of the funds, the regularity with which the dividends were paid, and the temptations to speculation arising from the fluctuations in the price of funded property, diverted so large a portion of the floating capital of the country into the coffers of the treasury, that it was next to impossible for private individuals to borrow at the legal rate of interest, except from the trustees of public companies, or through the influence of circumstances of a very peculiar nature. Hence, the proprietors of unencumbered freehold estates, of which they had the absolute disposal, were very generally obliged, when they had occasion for loans, to resort to those destructive expedients which had formerly been the resource only of spendthrifts and persons in desperate circumstances.
The evidence annexed to the "Report of the Committee of 1818 on Usury Laws," sets their impolicy and pernicious influence in a clear light. Mr Suggden, now Lord St Leonards, stated, that when the market rate of interest was above the legal rate, the landed proprietor was compelled to resort to some shift to evade the usury laws. He had "known annuities granted for three lives, at 10 per cent., upon fee-simple estates, unencumbered, and of great annual value, in a register county. He had also known annuities granted for four lives; and more would have been added, but for the danger of equity setting aside the transaction on account of the inadequacy of the consideration. Latterly, many annuities were granted for a term of years certain, not depending upon lives." On being asked whether, were there no laws limiting the rate of interest, better terms could or could not have been obtained, he answered, "I am decidedly of opinion that better terms could have been obtained; for there is a stigma which attaches to men who lend money upon annuities, that drives all respectable men out of the market. Some leading men did latterly embark in such transactions, but I never knew a man of reputation in my own profession lend money in such a manner, although we have the best means of ascertaining the safest securities, and of obtaining the best terms."
"The laws against usury," said Mr Holland, of the house of Messrs Baring Brothers and Company, "drive men in distress, or in want of money, to much more disastrous modes of raising it than they would adopt if no usury laws existed. The man in trade, in want of money for an unexpected demand, or disappointed in his returns, must fulfil his engagements, or forfeit his credit. He might have borrowed money at 6 per cent., but the law allows no one to lend it to him; and he must sell some of the commodity he holds, at a reduced price, in order to meet his engagements. For example, he holds sugar which is worth 80s.; but he is compelled to sell it immediately for 70s. to the man who will give him cash for it, and thus actually borrows money at 12½ per cent., which, had the law allowed him, he might have borrowed from a money dealer at 6 per cent. It is known to every merchant that cases of this kind are common occurrences in every commercial town, and more especially in the metropolis. A man in distress for money pays more interest, owing to the usury laws, than he would if no such laws existed; because now he is obliged to go to some of the disreputable money lenders to borrow, as he knows the respectable money lender will not break the laws of his country. The disreputable money lender knows that he has the ordinary risk of his debtor to incur in lending his money, and he has further to encounter the penalty of the law, for both of which risks the borrower must pay. If no usury laws existed, in common cases, and where a person is respectable, he might obtain a loan from the respectable money lender, who would then only have to calculate his ordinary risk, and the compensation for the use of his money."
The committee admitted the force of this evidence by agreeing to the following resolutions:—1st. That it is the opinion of this committee, that the laws regulating or restraining the rate of interest have been extensively evaded, and have failed of the effect of imposing a maximum on such rate; and that, of late years, from the constant excess of the market rate of interest above the rate limited by law, they have added to the expense incurred by borrowers on real security, and that such borrowers have been compelled to resort to the mode of granting annuities on lives; a mode which has been made a cover for obtaining a higher rate of interest than the rate limited by law, and has farther subjected the borrowers to enormous charges, or forced them to make very disadvantageous sales of their estates. 2d. That it is the opinion of this committee, that the construction of such laws, as applicable to the transactions of commerce as at present carried on, have been attended with much uncertainty as to the legality of many transactions of frequent occurrence, and consequently been productive of much embarrassment and litigation. 3d. That it is the opinion of this committee, that the present period, when the market rate of interest is below the legal rate, affords an opportunity peculiarly favourable for the repeal of the said laws."
In spite, however, of the recommendation of the committee, and the cogent evidence on which it was founded, the popular prejudice continued so strong, that it was not till 1839 that a statute was passed, the 2d and 3d Vict., cap. 37, which exempted all bills of exchange and promissory notes, not having more than twelve months to run, and all contracts for sums above L10, from the operation of the usury laws.
It was supposed, or at all events argued, that the repeal of the usury laws would tempt such individuals as had money to lend, to indulge in those mean and discreditable practices which characterize the lowest class of money dealers. But it was more reasonably contended, that in the event of the rate of interest being left to be adjusted by the free competition of the parties, there would be little employment for inferior dealers. Except when the market rate of interest was below the legal rate, the usury laws prevented all persons, whose credit was not extremely good, from obtaining loans from capitalists of the highest character, and forced them to have recourse to those who were less scrupulous. Supposing the market rate of interest to be 6 or 7 per cent., an individual in ordinarily good credit may, now that the usury laws are abolished, easily obtain a loan at that rate. But when the law declared that no more than 5 per cent. should be taken, and, consequently, affixed a species of stigma to those lenders who bargained for a higher rate, the rich and more respectable capitalists being excluded from the market, borrowers were obliged to resort to those of an inferior character, who, in addition to the premium for the risk of entering into an illegal transaction, received an indemnification for the odium which, in such cases, always attaches to the lender. It is idle to attempt to secure individuals
---
1 "Considerations on the Rate of Interest," by E. B. Suggden, Esq., Pamphlet, vol. viii., p. 278. against the risk of imposition in pecuniary, more than in any other species of transactions. And, although the object had been desirable, it could not be obtained by such inadequate means. The usury laws generated the very mischief they were intended to suppress. Instead of diminishing, they multiplied usurious transactions, and aggravated the evils they were designed to mitigate or remove.
Nothing can be more unreasonable than the clamour against money lenders, because of their exacting a comparatively high rate of interest from prodigals and spendthrifts. This is the most proper and efficient check that can be put upon extravagance. Supposing the security of a prodigal and an industrious man to be nearly equal, and this is but seldom the case, the capitalist who lends to the latter, in preference to the former, confers a service on the community. He prevents those funds which ought to be employed in supporting useful labour, and in adding to the public wealth, from being wasted in frivolous or pernicious pursuits.
But, perhaps, it will be said, that this is mistaking the object of the usury laws; that they were not intended to force capitalists to lend to spendthrifts on the same terms as to industrious persons, but to protect the prodigal and unwary from the extortion of usurers, by making any stipulation between them for more than a given rate of interest null and void. But why all this solicitude about the least valuable class of society? Why fetter the circulation of capital amongst those who would turn it to the best account, lest any portion of its chance to fall into the hands of those who would squander it away? If the prevention of prodigality be of sufficient importance to justify the interference of the legislature, prodigals should be put under an interdict; for this is the only way in which it is possible to restrict them. It is not by borrowing money at high interest, but by contracting debts to dealers, on whose charge there is no check, that spendthrifts run through their fortunes. Bentham has justly observed, that so long as a man is looked upon as one who will pay, he can much more easily get the goods he wants than the money to buy them with, though he were content to give for it twice or three times the ordinary rate of interest. How contradictory, then, to permit prodigals to borrow (for it was really borrowing) the largest supplies of food, clothes, &c., at 20, 30, or even 100 per cent. interest, at the same time that we prohibited them, and every one else, from borrowing money at more than 5 per cent.? Instead of being of any service, this restriction was evidently injurious to the prodigal. It narrowed his choice, and drove him to a market where no disgrace is attached to the exaction of the most exorbitant interest, and where he could scarcely escape being ruined.
The outcry which is sometimes raised against capitalists for taking advantage of the necessities of industrious individuals, is seldom much better founded than that which is raised against them for taking advantage of the prodigal or simple. Parties borrow according to their character for sobriety and punctuality in meeting their engagements, and according to the presumed state of their affairs at the time. To say that a capitalist takes advantage of the necessities of individuals, is, in most cases, equivalent to saying that he refuses to lend to persons in suspicious or necessitous circumstances, on the same terms he would do were they in good credit, or were there no doubt of their solvency. And were he to act otherwise, would he be considered fit to be entrusted with the management of his affairs?
But, as already seen, whatever may be the extortion of lenders, the usury laws did not check it. On the contrary, they compelled the borrowers to pay, over and above the common rate of interest, a premium to indemnify the lenders for the risks incurred in breaking them. They attempted to remedy what was not an evil, and what, consequently, should not have been interfered with; and in doing this they necessarily created a real grievance. The wisdom of an act of parliament which should compel the underwriters to insure a gunpowder magazine and a salt warehouse on the same terms would not be very evident. Yet it would not be more absurd than to enact that the same rate of interest shall be charged on capital lent on good, on indifferent, and on bad securities. "It is in vain, therefore," to use the words of Locke, "to go about effectually to reduce the price of interest by a law; and you may as rationally hope to set a fixed rate upon the hire of houses or ships, as of money. He that wants a vessel, rather than lose his market, will not stick to have it at the market rate, and find means to do it with security to the owner, though the rate were limited by law; and he that wants money, rather than lose his voyage or his trade, will pay the natural interest for it, and submit to such ways of conveyance, as shall keep the lender out of reach of the law."
The case of Holland furnishes a striking proof of the correctness of the theory we have been endeavouring to establish. The rate of interest has been, for a very long period, lower in Holland than anywhere else in Europe; and yet it is the only country in which usury laws have been altogether unknown, where capitalists are allowed to demand, and borrowers to pay, any rate of interest. Notwithstanding all the violent changes of the government, and the extraordinary disturbance of her financial concerns since 1790, the rate of interest in Holland has continued comparatively steady. During the whole of that period, persons who could offer unexceptionable security have been able to borrow at from 2 to 5½ per cent.; nor has the average rate of interest charged on capital, advanced on the worst species of security, ever exceeded 6 or 7 per cent., except when the government was negotiating a forced loan. But, in this country, where the law declared that no more than 5 per cent. should be taken, the rate of interest for money advanced on the best landed security varied, in the same period, from 5 to 16 or 17 per cent., or above five times as much as in Holland.
In France, the usury laws were abolished at the Revolution; and it is stated that their abolition was not attended by any rise of interest. According to the Code Napoleon, only 6 per cent. is allowed to be charged on commercial loans, and 5 per cent. on those made on the security of real property. There is, however, no difficulty in evading the law. This is usually done by giving a bonus before completing the transaction, or, which is the same thing, by framing the obligation for the debt for a larger sum than is really advanced by the lender. None of the parties particularly interested can be called to swear to the fact of such bonus being given; so that the transaction is unpunishable, unless a third party, privy to the settlement of the affair, be produced as a witness.
In Hamburg, the rate of interest is quite unrestricted; or, if there be a written law restraining it, it has become obsolete. The rate, therefore, varies according to circumstances. Occasionally it has been at 7, 8, and even 10 per cent.; and in 1799, a period of great mercantile embarrassment and insecurity, it was as high as 14 per cent. Generally, however, the rate of discount on good bills does not exceed 3 or 4 per cent.
---
1 "Considerations of the Lowering of Interest and Raising the Value of Money, 1691" (Works, vol. ii., p. 7, 4to, 1777). 2 Strictly speaking, this applies only to the state of Holland previously to the Revolution in 1795. The enactments of the Code Napoleon were subsequently introduced; but it appears, from the Report of the Parliamentary Committee on the Usury Laws, that they have not been acted upon. 3 Storch, Économie Politique, tom. iii., p. 187. 4 Report on Usury Laws, p. 46. In Russia, the legal rate of interest is 6 per cent. But as Russia is a country capable of much improvement, and where there are very great facilities for the advantageous employment of capital, the market rate of interest is invariably higher than the statute rate, and the law is constantly and easily evaded.
In the United States, the legal rate of interest varies in the different states of the Union. In Alabama and Texas it is 8 per cent.; in New York, South Carolina, Georgia, Michigan, and Wisconsin, 7 per cent.; in Louisiana, 5 per cent.; and in all the other states, 6 per cent. The penalties for taking a higher rate than that allowed by law, vary in the different states, being much less in some than in others. We are not aware whether any legal rate of interest has been established in California; but, as already seen, the interest charged on bills in San Francisco has varied of late years from 1½ to 3 per cent. per month.
The previous statements apply only to the cases of interest arising out of loans made by one party to another. But there are cases in which interest may become due without being stipulated for, by unnecessary or unjustifiable delays in the payment of debts, or by trustees, agents, or other parties coming into possession of property belonging to others, &c., and in these it is necessary, to obviate litigation, that the interest to be charged should be fixed by law. This legal rate had better be somewhat below the ordinary market rate, and may be adjusted from time to time as circumstances may require. But, except in cases of this sort, there is no more reason for interfering to regulate the rate of interest, than there is for interfering to regulate premiums of insurance, or the prices of commodities.
**Distinction of Simple and Compound Interest.**—When a loan is made, it is usual to stipulate that the interest upon it should be regularly paid at the end of every year, half-year, &c. A loan of this sort is said to be at simple interest. It is of the essence of such loan, that no part of the interest accruing upon it should be added to the principal to form a new principal; and though payment of the interest were not made when it becomes due, the lender would not be entitled to charge interest upon such unpaid interest. Thus, suppose, L.100 were lent at simple interest at 5 per cent., payable at the end of each year; the lender would, at the end of 3 or 4 years, supposing him to have received no previous payments, be entitled to L.15 or L.20, and no more.
Sometimes, however, money or capital is invested so that the interest is not paid at the periods when it becomes due, but is progressively added to the principal; so that at every term a new principal is formed, consisting of the original principal, and the successive accumulations of interest upon interest. Money invested in this way is said to be placed at compound interest.
It appears only reasonable, when a borrower does not pay the interest he has contracted for at the period when it is due, that he should pay interest upon such interest. This, however, is not allowed by the law of England; nor is it allowed to make a loan at compound interest. But this rule is easily evaded, by taking a new obligation for the principal with the interest included, when the latter becomes due. Investments at compound interest are also very frequent. Thus, if an individual buy into the funds, and regularly buy fresh stock with the dividends, the capital will increase at compound interest; and so in any similar case.
**Calculation of Interest.**—Interest is estimated at so much per cent. per annum, or by dividing the principal into 100 equal parts, and specifying how many of these parts are paid yearly for its use. Thus 5 per cent., or 5 parts out of 100, means that L.5 are paid for the use of L.100 for a year, L.10 for the use of L.200, L.2, 10s. for the use of L.50 for the same period, and so on.
Suppose, now, that it is required to find the interest of L.210, 13s. for 3½ years at 4 per cent. simple interest. In this case we must first divide the principal, L.210, 13s. into 100 parts, 4 of which will be the interest for 1 year; and this being multiplied by 3½ will give the interest for 3½ years. But instead of first dividing by 100, and then multiplying by 4, the result will be the same, and the process more expeditious, if we first multiply by 4, and then divide by 100. Thus,
| Principal | Rate per cent. | |-----------|---------------| | L.210 | 4 |
| L. | s. d. | |-------------|--------------| | 100) 842 | 12 (8 8 6) | | 20 | 31 | | 8.52 | | | 12 | 25 5 6 | | 6.24 | 4 4 3 | | 4 | | | 96 | L.29 9 92 |
It is almost superfluous to observe, that the same result would have been obtained by multiplying the product of the principal and rate by the number of years, and then dividing by 100.
Hence, to find the interest of any sum at any rate per cent. for a year, multiply the sum by the rate per cent. and divide the product by 100.
To find the interest of any sum for a number of years, multiply its interest for one year by the number of years; or, without calculating its interest for one year, multiply the principal by the rate per cent. and that product by the number of years, and divide the last product by 100.
When the interest of any sum is required for a number of days, they must be treated as fractional parts of a year; that is, we must multiply the interest of a year by them, and divide by 365.
Suppose that it is required to find the interest of L.210 for 4 years 7 months and 25 days, at 4½ per cent.
| Principal | Rate per cent. | |-----------|---------------| | L.210 | 4½ |
| L. | s. d. | |-------------|--------------| | 100) 842 | 12 (8 8 6) | | 20 | 31 | | 8.52 | | | 12 | 25 5 6 | | 6.24 | 4 4 3 | | 4 | | | 96 | L.29 9 92 |
The interest for 1 year, L.9½ x 4 = L.37.90 do. for 4 years.
The interest for 25 days is \( \frac{9.45 \times 25}{365} = \frac{236.25}{365} = \frac{6472}{365} \); that is, it is equal to the interest for a year multiplied by the fraction \( \frac{25}{365} \).
Division by 100 is performed by cutting off two figures to the right.
Many attempts have been made to contrive more expeditious processes than the above for calculating interest. The following is one of the best:
Suppose it were required to find the interest upon L.172 for 107 days at 5 per cent.
This forms what is called in arithmetical books a double rule of three question, and would be stated as follows:
| L. Days | L. Days | |---------|---------| | 100x365 | 5 :: 172x107 : L.2, 10s. 4½d., the interest required.
Hence, to find the interest of any sum for any number of days at any rate per cent., multiply the sum by the number of days, and the product by the rate, and divide by 36,500 (365 x 100); the quotient is the interest required.
When the rate is 5 per cent., or 1-20th of the principal, all that is required is to divide the product of the sum multiplied by the days by 7300 (365, the days in a year, multiplied by 20).
Five per cent. interest being found by this extremely simple process, it is usual in practice to calculate 4 per cent. interest by deducting 1-5th; 3 per cent. by deducting 2-5ths; 2½ per cent. by dividing by 2; 2 per cent. by taking the half of 4, and so on.
---
1 Report on Usury Laws, p. 46; and Storck, tom. iii., p. 207. In calculating interest upon accounts-current, it is requisite to state the number of days between each receipt or payment, and the date (commonly the 31st of December) to which the account-current is made up. Thus, L172 paid on the 15th of September, bearing interest to the 31st of December, 107 days. The amount of such interest may, then, be calculated as above explained, or by the aid of tables.
The 30th of June is, after the 31st of December, the most usual date to which accounts-current are made up, and interest calculated.
It is desirable, in calculating interest on accounts-current, to be able readily to find the number of days from any day in any one month to any day in any other month. This may be done with the greatest ease by means of the following Table:
| Jan. | Feb. | March | April | May | June | July | Aug. | Sept. | Oct. | Nov. | Dec. | |------|------|-------|-------|-----|------|------|------|-------|------|------|-----| | 1 | 32 | 60 | 91 | 121 | 152 | 182 | 213 | 244 | 274 | 305 | 335 | | 2 | 33 | 61 | 92 | 122 | 153 | 183 | 214 | 245 | 275 | 306 | 336 | | 3 | 34 | 62 | 93 | 123 | 154 | 184 | 215 | 246 | 276 | 307 | 337 | | 4 | 35 | 63 | 94 | 124 | 155 | 185 | 216 | 247 | 277 | 308 | 338 | | 5 | 36 | 64 | 95 | 125 | 156 | 186 | 217 | 248 | 278 | 309 | 339 | | 6 | 37 | 65 | 96 | 126 | 157 | 187 | 218 | 249 | 279 | 310 | 340 | | 7 | 38 | 66 | 97 | 127 | 158 | 188 | 219 | 250 | 280 | 311 | 341 | | 8 | 39 | 67 | 98 | 128 | 159 | 189 | 220 | 251 | 281 | 312 | 342 | | 9 | 40 | 68 | 99 | 129 | 160 | 190 | 221 | 252 | 282 | 313 | 343 | | 10 | 41 | 69 | 100 | 130 | 161 | 191 | 222 | 253 | 283 | 314 | 344 | | 11 | 42 | 70 | 101 | 131 | 162 | 192 | 223 | 254 | 284 | 315 | 345 | | 12 | 43 | 71 | 102 | 132 | 163 | 193 | 224 | 255 | 285 | 316 | 346 | | 13 | 44 | 72 | 103 | 133 | 164 | 194 | 225 | 256 | 286 | 317 | 347 | | 14 | 45 | 73 | 104 | 134 | 165 | 195 | 226 | 257 | 287 | 318 | 348 | | 15 | 46 | 74 | 105 | 135 | 166 | 196 | 227 | 258 | 288 | 319 | 349 | | 16 | 47 | 75 | 106 | 136 | 167 | 197 | 228 | 259 | 289 | 320 | 350 |
By this Table may be readily ascertained the number of days from any given day in the year to another. For instance, from the 1st of January to the 14th of August (first and last days included), there are 226 days. To find the number, look down the column headed January, to No. 14, and then look along in a parallel line to the column headed August, you find 226, the number required.
To find the number of days between any other two given days, when they are both after the 1st of January, the number opposite the 1st day must, of course, be deducted from that opposite the second. Thus, to find the number of days between the 13th of March and the 19th of August, deduct from 231—the number in the Table opposite to 19 and under August—72, the number opposite to 13 and under March, and the remainder, 159, is the number required, last day included.
In leap years, one must be added to the number after the 28th of February.
When interest, instead of being simple, is compound, the first year's or term's interest must be found, and being added to the original principal, makes the principal upon which interest is to be calculated for the second year or term; and the second year's or term's interest being added to this last principal, makes that upon which interest is to be calculated for the third year or term; and so on for any number of years.
But when the number of years is considerable, this process becomes exceedingly cumbersome and tedious, and to facilitate it tables have been constructed, which are subjoined to this article.
The first of these tables (No. I.) represents the amount of L1 accumulating at compound interest, at 3, 3½, 4, 4½, and 5 per cent. every year, from 1 year to 70 years, in pounds and decimals of a pound. Now, suppose that we wish to know how much L500 will amount to in 7 years at 4 per cent. In the column marked 4 per cent., and opposite to 7 years, we find L1·315,932, which shows that L1 will, if invested at 4 per cent. compound interest amount to L1·315,932 in 7 years; and consequently, L500 will, in the same time, and at the same rate, amount to L500 x L1·315,932 or L677·966; that is L677, 19s. 4d.
For the same purpose of facilitating calculation, the present value of L1 due any number of years hence, not exceeding 70, at 3, 3½, 4, 4½, and 5 per cent. compound interest, is given in the subjoined table, No. II. The use of this table is precisely similar to the one above. Let it, for example, be required to find the present worth of L500 due 7 years hence, reckoning compound interest at 4 per cent.—opposite to 7 years, and under 4 per cent., we find L1·75291,781, the present worth of L1 due at the end of 7 years; and multiplying this sum by L500, the product being L379·9589, or L379, 19s. 2d., is the answer required.
N.B.—These Tables are taken from Tables of Interest, Discount, and Annuities, by John Smart, Gent., 4to., London, 1726. They are carried to 8 decimal places, and enjoy the highest character, both here and on the Continent, for accuracy and completeness. The original work is now become scarce.
(J. H. M.)
VOL. XII. ### Table II.—Showing the Present Value of Lr receivable at the End of any given Year, from 1 to 70, reckoning Compound Interest at 2\(\frac{1}{2}\), 3, 3\(\frac{1}{2}\), 4, 5, 6 per Cent.
| Years | 2\(\frac{1}{2}\) per Cent. | 3 per Cent. | 3\(\frac{1}{2}\) per Cent. | 4 per Cent. | 4\(\frac{1}{2}\) per Cent. | 5 per Cent. | 6 per Cent. | |-------|-------------------|----------|-----------------|-----------|-----------------|---------|---------| | 1 | 0.97560.976 | 0.97887.379 | 0.96615.357 | 0.95153.846 | 0.93663.750 | 0.92238.055 | 0.91339.623 | | 2 | 0.95181.440 | 0.94299.591 | -0.23141.070 | -0.21451.601 | 0.91517.595 | 0.90072.948 | 0.88999.644 | | 3 | 0.95825.329 | 0.95145.168 | -0.31095.270 | -0.28878.636 | 0.97470.061 | 0.96583.770 | 0.95916.928 | | 4 | 0.95050.306 | 0.88484.709 | -0.50241.160 | -0.45825.540 | 0.93586.414 | -0.23637.115 | 0.91361.247 | | 5 | 0.88843.429 | 0.86250.878 | -0.51471.917 | -0.29121.717 | 0.90241.150 | 0.75382.614 | 0.74725.317 | | 6 | 0.86211.087 | 0.83748.426 | -0.51136.034 | -0.31688.195 | 0.70758.957 | 0.74624.154 | 0.70498.634 | | 7 | 0.84184.824 | 0.81029.151 | -0.75699.185 | -0.29119.781 | 0.71842.816 | 0.71060.133 | 0.599H.533 | | 8 | 0.78748.597 | 0.76349.923 | -0.66634.466 | 0.119649.551 | 0.87039.856 | 0.69252.567 | 0.69214.687 | | 9 | 0.80723.236 | 0.70451.873 | 0.37373.269 | 0.26320.674 | 0.67508.999 | 0.64692.902 | 0.67919.446 | | 10 | 0.71816.540 | 0.72046.390 | 0.34019.881 | -0.75050.417 | 0.13832.958 | -0.43392.769 | -0.51391.325 | | 11 | 0.76214.473 | 0.73236.255 | 0.61809.551 | 0.49155.207 | 0.61619.874 | 0.48596.229 | -0.52978.750 | | 12 | 0.74522.591 | 0.70137.908 | -0.50958.130 | -0.59041.415 | 0.33866.386 | -0.55853.742 | -0.49342.093 | | 13 | 0.75420.035 | 0.69654.534 | 0.37137.000 | -0.40709.469 | 0.96128.116 | -0.68896.902 | -0.45738.402 | | 14 | 0.70177.720 | 0.66111.782 | -0.73175.706 | -0.47679.369 | 0.92997.284 | -0.67893.354 | -0.44359.054 | | 15 | 0.69045.026 | 0.64482.195 | -0.72180.360 | -0.55560.820 | 0.32506.690 | -0.61857.704 | -0.32008.090 | | 16 | 0.67362.030 | 0.62316.694 | -0.77267.591 | -0.56339.918 | 0.9440.932 | -0.66111.156 | -0.34553.132 | | 17 | 0.65719.518 | 0.60801.345 | -0.63721.630 | -0.51273.327 | 0.97371.636 | -0.56266.965 | -0.32318.093 | | 18 | 0.64116.668 | 0.58739.161 | -0.36208.105 | 0.40002.670 | 0.95073.179 | -0.47716.129 | -0.73896.644 | | 19 | 0.62553.772 | 0.57092.303 | 0.45156.709 | 0.45145.216 | 0.46335.162 | -0.3562.556 | -0.22700.606 | | 20 | 0.61027.694 | 0.55397.757 | 0.26338.636 | 0.32052.918 | 0.14638.368 | -0.1778.700 | -0.07839.508 |
...