What is usury and lending at “interest” –

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Of Usury, from Brant’s Stultifera Navis (the Ship of Fools); woodcut attributed to Albrecht Dürer

Usury (play /ˈjuːʒəri/[1]) is the practice of charging excessive, unreasonably high, and often illegal interest rates on loans.[2][3]

Originally, when the charging of interest was still banned by Christian churches, usury simply meant the charging of interest at any rate (as well as charging a fee for the use of money, such as at a bureau de change). In countries where the charging of interest became acceptable, the term came to be used for interest above the rate allowed by law. The term is largely derived from Christian religious principles; Riba is the corresponding Arabic term and ribbit is the Hebrew word.

The pivotal change in the English-speaking world seems to have come with the permission to charge interest on lent money[4]: particularly the 1545 act “An Act Against Usurie” (37 H.viii 9) of King Henry VIII of England (see book references).


Historical meaning

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Banking during Roman times was different from modern banking. During the Principate, most banking activities were conducted by private individuals, not by such large banking firms as exist today; almost all moneylenders in the Empire were private individuals because anybody that had any additional capital and wished to lend it out could easily do so.[5]

The rate of interest on loans varied in the range of 4–12 percent; but when the interest rate was higher, it typically was not 15–16 percent but either 24 percent or 48 percent. The apparent absence of intermediary rates suggests that the Romans may have had difficulty calculating the interest due on anything other than mathematically convenient rates. They quoted them on a monthly basis, as in the loan described here, and the most common rates were multiples of twelve. Monthly rates tended to range from simple fractions to 3–4 percent, perhaps because lenders used Roman numerals.[6]

Moneylending during this period was largely a matter of private loans advanced to persons short of cash, whether persistently in debt or temporarily until the next harvest. Mostly, it was undertaken by exceedingly rich men who were prepared to take on a high risk if the profit looked good; interest rates were fixed privately and were almost entirely unrestricted by law. Investment was always regarded as a matter of seeking personal profit, often on a large scale. Banking was of the small, back-street variety, run by the urban lower-middle class of petty shop-keepers. By the 3rd century, acute currency problems in the Empire drove them into decline.[7] The rich who were in a position to take advantage of the situation became the money-lenders when the ever-increasing tax demands in the last declining days of the Empire crippled and eventually destroyed the peasant class by reducing tenant-farmers to serfdom. It was evident that usury meant exploitation of the poor.[8]

The First Council of Nicaea, in 325, forbade clergy from engaging in usury[9] (canon 17). At the time, usury was interest of any kind, and the canon merely forbade the clergy to lend money on interest above 1 percent per month (12.7% APR). Later ecumenical councils applied this regulation to the laity.[9][10]

Lateran III decreed that persons who accepted interest on loans could receive neither the sacraments nor Christian burial.[11] Pope Clement V made the belief in the right to usury a heresy in 1311, and abolished all secular legislation which allowed it.[12] Pope Sixtus V condemned the practice of charging interest as “detestable to God and man, damned by the sacred canons and contrary to Christian charity.”[12]

Theological historian John Noonan argues that “the doctrine [of usury] was enunciated by popes, expressed by three ecumenical councils, proclaimed by bishops, and taught unanimously by theologians.”[10]

Certain negative historical renditions of usury carry with them social connotations of perceived “unjust” or “discriminatory” lending practices. The historian Paul Johnson, comments:

Most early religious systems in the ancient Near East, and the secular codes arising from them, did not forbid usury. These societies regarded inanimate matter as alive, like plants, animals and people, and capable of reproducing itself. Hence if you lent ‘food money’, or monetary tokens of any kind, it was legitimate to charge interest.[13] Food money in the shape of olives, dates, seeds or animals was lent out as early as c. 5000 BC, if not earlier. …Among the Mesopotamians, Hittites, Phoenicians and Egyptians, interest was legal and often fixed by the state. But the Hebrew took a different view of the matter.[14]

The Hebrew Bible regulates interest taking. Interest can be charged to strangers but not between Hebrew.

Deuteronomy 23:19 Thou shalt not lend upon interest to thy brother: interest of money, interest of victuals, interest of any thing that is lent upon interest. Deuteronomy 23:20 Unto a foreigner thou mayest lend upon interest; but unto thy brother thou shalt not lend upon interest; that the LORD thy God may bless thee in all that thou puttest thy hand unto, in the land whither thou goest in to possess it.[15]

Israelites were forbidden to charge interest on loans made to other Israelites, but allowed to charge interest on transactions with non-Israelites, as the latter were often amongst the Israelites for the purpose of business anyway, but in general, it was seen as advantageous to avoid getting into debt at all to avoid being bound to someone else. Debt was to be avoided and not used to finance consumption, but only when in need. However, the laws against usury were among the many which the prophets condemn the people for breaking.[16]

Johnson contends that the Torah treats lending as philanthropy in a poor community whose aim was collective survival, but which is not obliged to be charitable towards outsiders.

A great deal of Jewish legal scholarship in the Dark and the Middle Ages was devoted to making business dealings fair, honest and efficient.[17]

Usury (in the original sense of any interest) was at times denounced by a number of religious leaders and philosophers in the ancient world, including Plato, Aristotle, Cato, Cicero, Seneca,[18] Aquinas,[19] Muhammad,[20] Moses,[21] Philo[citation needed] and Gautama Buddha[citation needed].[22]

For example, Cato in his De Re Rustica said:

“And what do you think of usury?” — “What do you think of murder?”

But one must always consider that usury, in historical context, has always been inextricably linked to economic abuses, mostly of the masses and of the poor; but sometimes of the financier and royalty, as bankrupt royalty has led to many a demise, thus frowning upon lending at interest or for a euphemistic “just profit”[clarification needed]. The main moral argument is that usury creates excessive profit and gain without “labor” which is deemed “work” in the Biblical context. Profits from usury are argued not to arise from any substantial labor or work but from mere avarice, greed, trickery and manipulation. In addition, usury is said to create a divide between people due to obsession with monetary gain. Most importantly, usury is the derivation of profit from biological time, which is linked to life, considered sacred, God-given and divine, leading to excessive worrying about money instead of God, thus subjugating a God-given sanctity of life to man-made artificial notions of material wealth.

Interest of any kind is forbidden in Islam. As such, specialized codes of banking have developed to cater to investors wishing to obey Qur’anic law. (See Islamic banking)

As the Jews were ostracized from most professions by local rulers, the church and the guilds, they were pushed into marginal occupations considered socially inferior, such as tax and rent collecting and moneylending. Natural tensions between creditors and debtors were added to social, political, religious, and economic strains.[23]

…financial oppression of Jews tended to occur in areas where they were most disliked, and if Jews reacted by concentrating on moneylending to non-Jews, the unpopularity — and so, of course, the pressure — would increase. Thus the Jews became an element in a vicious circle. The Christians, on the basis of the Biblical rulings, condemned interest-taking absolutely, and from 1179 those who practiced it were excommunicated. Catholic autocrats frequently imposed the harshest financial burdens on the Jews. The Jews reacted by engaging in the one business where Christian laws actually discriminated in their favor, and became identified with the hated trade of moneylending.[24]

Peasants were forced to pay their taxes to Jews who were economically coerced into becoming the “front men” for the lords. The Jews would then be identified as the people taking their earnings. Meanwhile the peasants would remain loyal to the lords.[citation needed]

In England, the departing Crusaders were joined by crowds of debtors in the massacres of Jews at London and York in 1189–1190. In 1275, Edward I of England passed the Statute of Jewry which made usury illegal and linked it to blasphemy, in order to seize the assets of the violators. Scores of English Jews were arrested, 300 were hanged and their property went to the Crown. In 1290, all Jews were expelled from England, and allowed to take only what they could carry; the rest of their property became the Crown’s. The usury was cited as the official reason for the Edict of Expulsion. However, not all Jews were expelled: it was easy to convert to Christianity and thereby avoid expulsion. Many other crowned heads of Europe expelled the Jews, although again conversion to Christianity meant that you were no longer considered a Jew (see the articles on marranos or crypto-Judaism).

The growth of the Lombard bankers and pawnbrokers, who moved from city to city was along the pilgrim routes.

Die Wucherfrage is the title of a Lutheran Church – Missouri Synod work against usury from 1869. Usury is condemned in 19th century Missouri Synod doctrinal statements.[25]

In the 16th century, short-term interest rates dropped dramatically (from around 20–30% p.a. to around 9–10% p.a.). This was caused by refined commercial techniques, increased capital availability, the Reformation, and other reasons. The lower rates weakened religious scruples about lending at interest, although the debate did not cease altogether.

The papal prohibition on usury meant that it was a sin to charge interest on a money loan. As set forth by Thomas Aquinas, the natural essence of money was as a measure of value or intermediary in exchange. The increase of money through usury violated this essence and according to the same Thomistic analysis, a just transaction was one characterized by an equality of exchange, one where each side received exactly his due. Interest on a loan, in excess of the principal, would violate the balance of an exchange between debtor and creditor and was therefore unjust.

Some have suggested that the development of double entry bookkeeping would provide a powerful argument in favor of the legitimacy and integrity of usury but this is an obvious non-sequitur. Business has always been accepted as a right and proper activity[26] by all cultures, including those that reject usury.

Religious context

The Old Testament

From the King James Version

[Exodus 22:25] If thou lend money to any of my people that is poor by thee, thou shalt not be to him as an usurer, neither shalt thou lay upon him usury.

[Leviticus 25:36] Take thou no usury of him, or increase: but fear thy God; that thy brother may live with thee.

[Leviticus 25:37] Thou shalt not give him thy money upon usury, nor lend him thy victuals for increase.

[Deuteronomy 23:19] Thou shalt not lend upon usury to thy brother; usury of money, usury of victuals, usury of any thing that is lent upon usury:

[Deuteronomy 23:20] Unto a stranger thou mayest lend upon usury; but unto thy brother thou shalt not lend upon usury: that the LORD thy God may bless thee in all that thou settest thine hand to in the land whither thou goest to possess it.

[Ezekiel 18:17] He withholds his hand from sin and takes no usury or excessive interest.


The following quotations are from the Hebrew Bible, 1917 Jewish Publication Society translation:

If thou lend money to any of My people, even to the poor with thee, thou shalt not be to him as a creditor; neither shall ye lay upon him interest. (Exodus, 22:25)[27]

And if thy brother be waxen poor, and his means fail with thee; then thou shalt uphold him: as a stranger and a settler shall he live with thee. Take thou no interest of him or increase; but fear thy God; that thy brother may live with thee. Thou shalt not give him thy money upon interest, nor give him thy victuals for increase. (Leviticus, 25:35-37)

Thou shalt not lend upon interest to thy brother: interest of money, interest of victuals, interest of any thing that is lent upon interest. Unto a foreigner thou mayest lend upon interest; but unto thy brother thou shalt not lend upon interest; that the LORD thy God may bless thee in all that thou puttest thy hand unto, in the land whither thou goest in to possess it. (Deuteronomy, 23:20-21)

New Testament

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Christ drives the Usurers out of the Temple, a woodcut by Lucas Cranach the Elder in Passionary of Christ and Antichrist.[28]

The New Testament contains references to usury, notably in the Parable of the talents:

“Thou oughtest therefore to have put my money to the exchangers, and then at my coming I should have received mine own with usury.”
“…Out of thine own mouth will I judge thee, thou wicked servant. Thou knewest that I was an austere man, taking up that I laid not down, and reaping that I did not sow. Wherefore then gavest not thou my money into the bank, that at my coming I might have required mine own with usury?”
Finally the master said to him ‘Why then didn’t you put my money on deposit, so that when I came back, I could have collected it with interest?’


Main articles: Riba and Islamic banking

The following quotations are English translations from the Qur’an:

Those who charge usury are in the same position as those controlled by the devil’s influence. This is because they claim that usury is the same as commerce. However, God permits commerce, and prohibits usury. Thus, whoever heeds this commandment from his Lord, and refrains from usury, he may keep his past earnings, and his judgment rests with God. As for those who persist in usury, they incur Hell, wherein they abide forever (Al-Baqarah 2:275)

God condemns usury, and blesses charities. God dislikes every disbeliever, guilty. Lo! Those who believe and do good works and establish worship and pay the poor-due, their reward is with their Lord and there shall no fear come upon them neither shall they grieve. O you who believe, you shall observe God and refrain from all kinds of usury, if you are believers. If you do not, then expect a war from God and His messenger. But if you repent, you may keep your capitals, without inflicting injustice, or incurring injustice. If the debtor is unable to pay, wait for a better time. If you give up the loan as a charity, it would be better for you, if you only knew. (Al-Baqarah 2:276-280)

O you who believe, you shall not take usury, compounded over and over. Observe God, that you may succeed. (Al-‘Imran 3:130)

And for practicing usury, which was forbidden, and for consuming the people’s money illicitly. We have prepared for the disbelievers among them painful retribution. (Al-Nisa 4:161)

The usury that is practiced to increase some people’s wealth, does not gain anything at God. But if people give to charity, seeking God’s pleasure, these are the ones who receive their reward many fold. (Ar-Rum 30:39)

Scholastic theology

The first of the scholastics, Saint Anselm of Canterbury, led the shift in thought that labeled charging interest the same as theft. Previously usury had been seen as a lack of charity.

St. Thomas Aquinas, the leading theologian of the Catholic Church, argued charging of interest is wrong because it amounts to “double charging”, charging for both the thing and the use of the thing. Aquinas said this would be morally wrong in the same way as if one sold a bottle of wine, charged for the bottle of wine, and then charged for the person using the wine to actually drink it. Similarly, one cannot charge for a piece of cake and for the eating of the piece of cake. Yet this, said Aquinas, is what usury does. Money is exchange-medium. It is used up when it is spent. To charge for the money and for its use (by spending) is to charge for the money twice. It is also to sell time since the usurer charges, in effect, for the time that the money is in the hands of the borrower. Time, however, is not a commodity that anyone can sell. (For a detailed discussion of Aquinas and usury, go to Thought of Thomas Aquinas).

Labor is time, or if preferred, is measured by time. Workers are paid by the hour, by the day, by the week, by the month, rarely by the quarter or year. Labor is not effort, energy, expenditure of fuel (food). It is nothing but one’s time. As an example of labor without the expenditure of energy: A security guard whose job is just to be there. Perhaps nothing happens and he can read a book, assemble model trains, or even sleep, as long as he wakes up when the alarm rings. He has spent not one calorie of energy for the employer above what it takes just to live. Yet he is paid (compensated) for his time, for his labor. Even share-croppers and pieceworkers are compensated for the time they spent adding value to the raw materials. The sharecropper hands over the agreed portion of the increase (crop; harvest) to the owner of the land or the leaseholder in return for whatever the landlord provided: the land, perhaps the seed, farming tools, supplies, etc. The pieceworker is compensated for the labor, the time he spent, in adding value to the raw materials: the tools, the supplies, the workspace, light, heat, etc., according to the agreement made with the boss (client). If one labors for compensation, what he is compensated for is his time. As an even exchange of value, he has neither gained or lost anything. He has merely converted something he was going to lose anyway, time from his life, which, as we all know, is limited though we do not know in advance what the limit is, into something else that he wanted. Whether he is paid in goods, services or money is irrelevant. Money is but a medium of exchange that is much more efficient than straight barter. Only a miser wants money for itself, just to possess it. Normal people want money because it allows them to convert one thing that they are willing to sacrifice into something else that they actively want.

This did not, as some think, prevent investment. What it stipulated was that in order for the investor to share in the profit he must share the risk. In short he must be a joint-venturer. Simply to invest the money and expect it to be returned regardless of the success of the venture was to make money simply by having money and not by taking any risk or by doing any work or by any effort or sacrifice at all. This is usury. St Thomas quotes Aristotle as saying that “to live by usury is exceedingly unnatural”. Islam likewise condemns usury but allowed commerce (Al-Baqarah 2:275) – an alternative that suggests investment and sharing of profit and loss instead of sharing only profit through interests. Judaism condemns usury towards Jews, but allows it towards non-Jews. St Thomas allows, however, charges for actual services provided. Thus a banker or credit-lender could charge for such actual work or effort as he did carry out e.g. any fair administrative charges. The Catholic Church, in a decree of the Fifth Council of the Lateran, expressly allowed such charges in respect of credit-unions run for the benefit of the poor known as “montes pietatis“.[29]

In the 13th century Cardinal Hostiensis enumerated thirteen situations in which charging interest was not immoral.[30] The most important of these was lucrum cessans (profits given up) which allowed for the lender to charge interest “to compensate him for profit foregone in investing the money himself.” (Rothbard 1995, p. 46) This idea is very similar to Opportunity Cost. Many scholastic thinkers who argued for a ban on interest charges also argued for the legitimacy of lucrum cessans profits (e.g. Pierre Jean Olivi and St. Bernardino of Siena).

Other contexts

Usury in literature

In The Divine Comedy Dante places the usurers in the inner ring of the seventh circle of hell. (Cultural attitudes have changed a great deal since the 14th century as the usurers’ ring was shared only by the blasphemers and sodomites.)

In the 16th century, it was necessary for Shylock to convert to Christianity and forsake usury before he could be redeemed in the climax of The Merchant of Venice. Thomas Lodge‘s didactic tirade against London moneylenders, An Alarum against Usurers containing tried experiences against worldly abuses tried to incite the educated class against the harm usurers seemed to induce in their victims.

By the 18th century, usury was more often treated as a metaphor than a crime in itself, so Jeremy Bentham‘s Defense of Usury was not as shocking as it would have appeared two centuries earlier.

In Honoré de Balzac‘s 1830 novel Gobseck, the title character, who is a usurer, is described as both “petty and great—a miser and a philosopher…”[31]

In the early 20th century Ezra Pound‘s anti-usury poetry was not primarily based on the moral injustice of interest but on the fact that excess capital was no longer devoted to artistic patronage, as it could now be used for capitalist business investment.[32]

Usury and the law

The Magna Carta commands, “If any one has taken anything, whether much or little, by way of loan from Jews, and if he dies before that debt is paid, the debt shall not carry usury so long as the heir is under age, from whomsoever he may hold. And if that debt falls into our hands, we will take only the principal contained in the note.”[33]

“When money is lent on a contract to receive not only the principal sum again, but also an increase by way of compensation for the use, the increase is called interest by those who think it lawful, and usury by those who do not.” (William Blackstone‘s Commentaries on the Laws of England).

In the United States, usury laws are state laws that specify the maximum legal interest rate at which loans can be made. Congress has opted not to regulate interest rates on purely private transactions, but it arguably has the power to do so under the interstate commerce clause of Article I of the Constitution.

Congress opted to put a federal criminal limit on interest rates by the Racketeer Influenced and Corrupt Organizations Act (RICO) definitions of “unlawful debt”, which make it a federal felony to lend money at an interest rate more than twice the local state usury rate and then try to collect that “unlawful debt”.[34]

It is a federal offense to use violence or threats to collect usurious interest (or any other sort). Such activity is referred to as loan sharking, but that term is also applied to non-coercive usurious lending or even to the practice of making consumer loans without a license in jurisdictions that require licenses.

Usury and royalties

Royalties are contractual obligations of the Issuer of the royalty, made for the benefit of the holder of the royalty. Royalties require the payment of an agreed percentage of revenue of the Issuer, for an agreed period of time. In the event a royalty is purchased from an Issuer, the future revenue upon which the royalty is based is unknown at the time of the original transaction. Therefore, the cumulative amount of the future royalty payments is also an unknown. Royalty payments are not interest and royalties expire without value at their maturity. To be usurious payments made and received for the use of funds must be considered interest for loaned funds which require repayment at the maturity of the loan. The value in gains by the use of the royalty should equal its payment value, excess cost or interest beyond its tangible value is illicit interest or usury.

Usury and slavery in present day

While the practice of direct slavery is widely banned across the world, in some places debt-slavery is still practiced.[35] A debtor who is found unable to repay a loan can be placed in a state of debt-slavery, a situation where-by their life and labors are directed by the lender until the debt is considered repaid.[36] Usury is often a major part of extending this slavery, not uncommonly assisting in extending the debt-slavery onto the children of the debtor, thus making slaves of multiple generations and promoting child labor.[37] Another form of or name for this practice is debt bondage.

Usury statutes in the United States

Each U.S. state has its own statute which dictates how much interest can be charged before it is considered usurious or unlawful.

If a lender charges above the lawful interest rate, a court will not allow the lender to sue to recover the debt because the interest rate was illegal anyway. In some states (such as New York) such loans are voided ab initio.[38]

However, there are separate rules applied to most banks. The U.S. Supreme Court held unanimously in the 1978 Marquette Nat. Bank of Minneapolis v. First of Omaha Service Corp. case that the National Banking Act of 1863 allowed nationally chartered banks to charge the legal rate of interest in their state regardless of the borrower’s state of residence.[39] In 1980, because of inflation, Congress passed the Depository Institutions Deregulation and Monetary Control Act to exempt federally chartered savings banks, installment plan sellers and chartered loan companies from state usury limits. This effectively overrode all state and local usury laws.[40][41] The 1968 Truth in Lending Act does not regulate rates, except for some mortgages, but requires uniform or standardized disclosure of costs and charges.[42]

In the 1996 Smiley v. Citibank case, the Supreme Court further limited states’ power to regulate credit card fees and extended the reach of the Marquette decision. The court held that the word “interest” used in the 1863 banking law included fees and, therefore, states could not regulate fees.[43]

Some members of Congress have tried to create a federal usury statute that would limit the maximum allowable interest rate, but the measures have not progressed. In July 2010, the Dodd–Frank Wall Street Reform and Consumer Protection Act, was signed into law by President Obama. The act provides for a Consumer Financial Protection Bureau to regulate some credit practices but has no interest rate limit.[44]

Usury statutes in Canada

Canada’s Criminal Code limits the interest rate to 60% per year.[45] The law is broadly written and Canada’s courts have often intervened to remove ambiguity.[46]

Ethical arguments for usury

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Freedom of trade

The primary ethical argument in defense of usury has been the argument of negative freedom against the “restraint of trade” since the borrower has voluntarily entered into the usury contract.[citation needed] Opponents note, however, that borrowers may be tricked into signing such contracts, assume there is a usury law cap on interest that does not exist, or be driven to accept such an interest rate out of necessity.[citation needed] At the same time however, except for related party transactions where feelings of compassion, guilt, etc., compel the lender to lend without interest, in un-related party transactions where neither the borrower nor the lender has any predetermined attachment to one another, there is no incentive for the lender to lend or for the borrower to repay the debt without usury.


A practical argument for usury in welfare economics is that charging interest is essential to guiding the investment process, based on the claim that profits are required to direct investments to their most productive use (solving the economic calculation problem). According to this argument, interest-driven investment is essential to economic growth, and therefore to the very existence of industrial civilization. This practical argument for the utility of usury treats all “unearned” returns to capital as interest; traditionally, guaranteed interest is usurious, whereas dividends from shared ventures are less so. In this tradition, the practical case against usury does not completely apply (although replacing debt market investments with stock market savings may not always be desirable). Officially, this is how capitalist Islamic states solve the calculation problem. An example of the ‘moral’ difference between dividend income and interest income is found in The Merchant of Venice: Shylock lends Antonio money for trade speculation, demanding repayment in flesh should Antonio’s project fail utterly (accepting none of the business risk).

Excessive rates

In addition to the defense of interest as such, the practice of charging high interest rates is defended by those who point out that such rates reflect the very fact that the loans are being given to creditors with a high risk of default (in a competitive debt market the interest spread simply covers the credit risk). Economists of the Austrian school say that there is no such thing as a “just” interest rate separate from the free market equilibrium determined by the time-preferences of individual lenders and debtors. (Other free market theorists take a similar view on the merit of an unregulated debt market, but may not explain the subjective estimate of a worthwhile interest-rate bargain through time preference.)

Adverse selection and enforcement methods

Some have defended the threat or use of force (legal or illegal) against non-payers (such as required by Shylock). This position is based on the idea that without force there will be a market failure—since very high interest loans will only be taken up by those intending to default. The need for enforcement stems from this adverse selection problem rather than any immorality inherent in moneylenders. See: “The market for lemons“.

Today’s credit reporting system in industrialized countries obviates much of the need for the use of force. Since all potential lenders can quickly learn of one’s delinquent status, non-payers may find an unwilling seller for many important goods, like apartment rentals, mortgages, renting of expensive equipment without a deposit, and in many cases, insurance or employment. In the minds of many debtors, such considerations outweigh fear of force brought against them.[citation needed]


Some low-interest charity loans (such as small business micro-loans) defend interest-charging[citation needed] since it allows for the indefinite administration of the charity, the replacement of defaulted loans, and in some cases, the creation of additional loan pools in other regions. These people say that the final “ethical result” of the interest rates justifies the means of charging them.[citation needed]

Avoidance mechanisms and interest-free lending

Islamic banking

Main article: Islamic banking

In a partnership or joint venture where money is lent, the creditor only provides the capital yet is guaranteed a fixed amount of profit. The debtor, however, puts in time and effort, but is made to bear the risk of loss. Muslim scholars argue that such practice is unjust.[47] As an alternative to usury, Islam strongly encourages charity and direct investment in which the creditor shares whatever profit or loss the business may incur (in modern terms, this amounts to an equity stake in the business).

Interest-free banks

The JAK members bank is a usury-free saving and loaning system.

Interest-free micro-lending

Growth of the internet internationally has enabled both both business micro-lending through sites such as kickstarter as well as through global micro-lending charities where lenders make small sums of money available on zero-interest terms. Persons lending money to on-line micro-lending charity Kiva for example do not get paid any interest,[48] although the end users to whom the loans are made may be charged interest by Kiva’s partners in the country where the loan is used.[49]

See also


Constructs such as ibid., loc. cit. and idem are discouraged by Wikipedia’s style guide for footnotes, as they are easily broken. Please improve this article by replacing them with named references (quick guide), or an abbreviated title. (October 2010)
  1. ^ from Medieval Latin usuria, “interest”, or from Latin usura, “interest”
  2. ^ Oxford Dictionaries
  3. ^ Longman Exams Dictionary
  4. ^ Eisenstein, Charles: Sacred Economics: Money, Gift, and Society in the Age of Transition
  5. ^ Zgur, Andrej: The economy of the Roman Empire in the first two centuries A.D., An examination of market capitalism in the Roman economy, Aarhus School of Business, December 2007, pp. 252–261.
  6. ^ Temin, Peter: Financial Intermediation in the Early Roman Empire, The Journal of Economic History, Cambridge University Press, 2004, vol. 64, issue 03, p. 15.
  7. ^ Young, Frances: Christian Attitudes to Finance in the First Four Centuries, Epworth Review 4.3, Peterborough, September 1977, p. 80.
  8. ^ Young, Frances: Christian Attitudes to Finance in the First Four Centuries, Epworth Review 4.3, Peterborough, September 1977, pp. 81–82.
  9. ^ a b Moehlman, 1934, p. 6.
  10. ^ a b Noonan, John T., Jr. 1993. “Development of Moral Doctrine.” 54 Theological Stud. 662.
  11. ^ Moehlman, 1934, p. 6-7.
  12. ^ a b Moehlman, 1934, p. 7.
  13. ^ Johnson cites Fritz E. Heichelcheim: An Ancient Economic History, 2 vols. (trans. Leiden 1965), i.104-566
  14. ^ Johnson, Paul: A History of the Jews (New York: HarperCollins Publishers, 1987) ISBN 0-06-091533-1, pp. 172–73.
  15. ^ The Hebrew Bible in English according to the JPS 1917 Edition. http://www.mechon-mamre.org/e/et/et0523.htm
  16. ^ Examples of debt: I Samuel 22:2, II Kings 4:1, Isaiah 50:1. Prophetic condemnation of usury: Ezekiel 22:12, Nehemiah 5:7 and 12:13. Cautions regarding debt: Prov 22:7, passim.
  17. ^ Johnson, p. 272.
  18. ^ “Usury – The Root of All Evil”. The Spirit of Now. Peter Russell.
  19. ^ “Thomas Aquinas: On Usury, c. 1269-71”. Fordham University.
  20. ^ “The Prophet Muhammad’s Last Sermon”. Fordham University.
  21. ^ Exodus 22:25
  22. ^ Historical Critique of Usury
  23. ^ http://www.newworldencyclopedia.org/entry/Anti-Semitism#Restrictions
  24. ^ Johnson, p. 174.
  25. ^ Official Missouri Synod Doctrinal Statements
  26. ^ Carruthers, Bruce G., Espeland Wendy Nelson, Accounting for Rationality: Double-Entry Bookkeeping and the Rhetoric of Economic Rationality, American Journal of Sociology, Vol. 97, No. 1. (July 1991), pp. 38-40
  27. ^ “When you lend money to My people, to the poor person [who is] with you, you shall not behave toward him as a lender; you shall not impose interest upon him.” (ORT translation with Rashi commentary)
  28. ^ The references cited in the Passionary for this woodcut: 1 John 2:14-16, Matthew 10:8, and The Apology of the Augsburg Confession, Article 8, Of the Church
  29. ^ “Session Ten: On the reform of credit organisations (Montes pietatis)”. Fifth Lateran Council. Rome, Italy: Catholic Church. 1515-05-04. Retrieved 2008-04-05.
  30. ^ Roover, Raymond (Autumn 1967). “The Scholastics, Usury, and Foreign Exchang”. Business History Review (The Business History Review, Vol. 41, No. 3) 41 (3): 257–271. doi:10.2307/3112192. JSTOR 3112192.
  31. ^ Honoré de Balzac (1830). Wikisource link to Gobseck. Trans. Ellen Marriage. Wikisource.
  32. ^ http://www.englit.ed.ac.uk/studying/undergrd/american_lit_2/Handouts/cmc_pound.htm
  33. ^ Annotated English translation of 1215 version
  34. ^ 18 U.S.C. § 1961 (6)(B). See generally, Racketeer Influenced and Corrupt Organizations Act
  35. ^ http://www.antislavery.org/english/resources/reports/download_antislavery_publications/bonded_labour_reports.aspx
  36. ^ http://www.hrw.org/en/reports/2006/07/27/swept-under-rug
  37. ^ http://hir.harvard.edu/courting-africa/child-slavery
  38. ^ NY Gen Oblig 5-501 et seq. and NY 1503.
  39. ^ Marquette Nat. Bank of Minneapolis v. First of Omaha Service Corp., 439 U.S. 299 (1978).
  40. ^ Usury rate limits Reference: Interest rate usury limits for U.S. states, ‘Lectric Law Library.
  41. ^ The Effect of Consumer Interest Rate Deregulation on Credit Card Volumes, Charge-Offs, and the Personal Bankruptcy Rate, Federal Deposit Insurance Corporation “Bank Trends” Newsletter, March, 1998.
  42. ^ FDIC, Truth in Lending Act.
  43. ^ ABA Journal, March 2010, p. 59
  44. ^ ibid
  45. ^ Criminal Interest Rate, R.S.C. 1985, chap. C-46, section 347, as amended by 1992, c. 1, s. 60(F) and 2007, c. 9, s. 1
  46. ^ Waldron, Mary Anne (2011). “Section 347 of the Criminal Code “A Deeply Problematic Law””. Uniform Law Conference of Canada. Retrieved 2012-01-01.
  47. ^ Maududi(1967), vol. i, pg. 199
  48. ^ Kiva Faq: Will I get interest on my loan?: “Loans made through Kiva’s website do not earn any interest. Kiva’s loans are not an investment and are not recommended as an investment.”
  49. ^ Kiva FAQ: Do Kiva.org’s Field Partners charge interest to the entrepreneurs?: “Our Field Partners are free to charge interest, but Kiva.org will not partner with an organization that charges exorbitant interest rates.”

Further reading

  • ‘In Restraint of Usury: the Lending of Money at Interest’, Sir Harry Page, The Chartered Institute of Public Finance and Accounts, London, 1985,
  • The Bibliography therein – particularly:
  • ‘The Idea of Usury: from Tribal Brotherhood to Universal Otherhood’, Benjamin Nelson, 2nd Edition, University of Chicago Press, Chicago and London, 1949, enlarged 2nd edition, 1969.
  • ‘Interest and Inflation Free Money: Creating an Exchange Medium That Works for Everybody and Protects the Earth’, Margrit Kennedy, with Declan Kennedy: Illustrations by Helmut Creutz; New and Expanded Edition, New Society Publishers, Philadelphia, PA, USA and Gabriola Island, BC, Canada, 1995.

External links

Wikiquote has a collection of quotations related to: Usury
Look up usury in Wiktionary, the free dictionary.

Debt instruments
Managing debt
Debt collection and evasion
Debt markets
Debt in economics



From Wikipedia, the free encyclopedia
  (Redirected from Interest (economics))
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For other uses, see Interest (disambiguation).
This article needs attention from an expert on the subject. Please add a reason or a talk parameter to this template to explain the issue with the article. WikiProject Economics or the Economics Portal may be able to help recruit an expert. (January 2009)

Interest is a fee paid by a borrower of assets to the owner as a form of compensation for the use of the assets. It is most commonly the price paid for the use of borrowed money,[1] or money earned by deposited funds.[2]

When money is borrowed, interest is typically paid to the lender as a percentage of the principal, the amount owed to the lender. The percentage of the principal that is paid as a fee over a certain period of time (typically one month or year) is called the interest rate. A bank deposit will earn interest because the bank is paying for the use of the deposited funds. Assets that are sometimes lent with interest include money, shares, consumer goods through hire purchase, major assets such as aircraft, and even entire factories in finance lease arrangements. The interest is calculated upon the value of the assets in the same manner as upon money.

Interest is compensation to the lender, for a) risk of principal loss, called credit risk; and b) forgoing other investments that could have been made with the loaned asset. These forgone investments are known as the opportunity cost. Instead of the lender using the assets directly, they are advanced to the borrower. The borrower then enjoys the benefit of using the assets ahead of the effort required to pay for them, while the lender enjoys the benefit of the fee paid by the borrower for the privilege. In economics, interest is considered the price of credit.

Interest is often compounded, which means that interest is earned on prior interest in addition to the principal. The total amount of debt grows exponentially, and its mathematical study led to the discovery of the number e.[citation needed]


History of interest

According to historian Paul Johnson, the lending of “food money” was commonplace in Middle East civilizations as far back as 5000BC. They regarded interest as legitimate since acquired seeds and animals could “reproduce themselves”; whilst the ancient Jewish religious prohibitions against usury were a “different view”.[3].

In the Roman Empire interest rates usually calculated on a monthly basis and set as multiples of 12, apparently for expedient calculation by the wealthy private individuals that did most of the moneylending.[4]

The First Council of Nicaea, in 325, forbade clergy from engaging in usury[5] which was defined as lending on interest above 1 percent per month (12.7% APR). Later ecumenical councils applied this regulation to the laity.[5][6] Catholic Church opposition to interest hardened in the era of scholastics, when even defending it was considered a heresy. St. Thomas Aquinas, the leading theologian of the Catholic Church, argued that the charging of interest is wrong because it amounts to “double charging“, charging for both the thing and the use of the thing.

In the medieval economy, loans were entirely a consequence of necessity (bad harvests, fire in a workplace) and, under those conditions, it was considered morally reproachable to charge interest.[citation needed] It was also considered morally dubious, since no goods were produced through the lending of money, and thus it should not be compensated, unlike other activities with direct physical output such as blacksmithing or farming.[7] For the same reason, interest has often been looked down upon in Islamic civilization, with most scholars agreeing that the Qur’an explicitly forbids charging interest.

Medieval jurists developed several financial instruments to encourage responsible lending and circumvent prohibitions on ursury, such as the Contractum trinius

Of Usury, from Brant’s Stultifera Navis (the Ship of Fools); woodcut attributed to Albrecht Dürer

In the Renaissance era, greater mobility of people facilitated an increase in commerce and the appearance of appropriate conditions for entrepreneurs to start new, lucrative businesses. Given that borrowed money was no longer strictly for consumption but for production as well, interest was no longer viewed in the same manner. The School of Salamanca elaborated on various reasons that justified the charging of interest: the person who received a loan benefited, and one could consider interest as a premium paid for the risk taken by the loaning party.

There was also the question of opportunity cost, in that the loaning party lost other possibilities of using the loaned money. Finally and perhaps most originally was the consideration of money itself as merchandise, and the use of one’s money as something for which one should receive a benefit in the form of interest. Martín de Azpilcueta also considered the effect of time. Other things being equal, one would prefer to receive a given good now rather than in the future. This preference indicates greater value. Interest, under this theory, is the payment for the time the loaning individual is deprived of the money.

Economically, the interest rate is the cost of capital and is subject to the laws of supply and demand of the money supply. The first attempt to control interest rates through manipulation of the money supply was made by the French Central Bank in 1847.

The first formal studies of interest rates and their impact on society were conducted by Adam Smith, Jeremy Bentham and Mirabeau during the birth of classic economic thought.[citation needed] In the late 19th century leading Swedish economist Knut Wicksell in his 1898 Interest and Prices elaborated a comprehensive theory of economic crises based upon a distinction between natural and nominal interest rates. In the early 20th century, Irving Fisher made a major breakthrough in the economic analysis of interest rates by distinguishing nominal interest from real interest. Several perspectives on the nature and impact of interest rates have arisen since then.

The latter half of the 20th century saw the rise of interest-free Islamic banking and finance, a movement that attempts to apply religious law developed in the medieval period to the modern economy. Some entire countries, including Iran, Sudan, and Pakistan, have taken steps to eradicate interest from their financial systems entirely.[citation needed] Rather than charging interest, the interest-free lender shares the risk by investing as a partner in profit loss sharing scheme, because predetermined loan repayment as interest is prohibited, as well as making money out of money is unacceptable. All financial transactions must be asset-backed and it does not charge any “fee” for the service of lending.

Types of interest

Simple interest

Simple interest is calculated only on the principal amount, or on that portion of the principal amount that remains unpaid.

The amount of simple interest is calculated according to the following formula:

I_{simp} = r \cdot B_0 \cdot m

where r is the period interest rate (I/m), B0 the initial balance and m the number of time periods elapsed.

To calculate the period interest rate r, one divides the interest rate I by the number of periods m.

For example, imagine that a credit card holder has an outstanding balance of $2500 and that the simple interest rate is 12.99% per annum. The interest added at the end of 3 months would be,

I_{simp} = \bigg( \frac{0.1299}{12} \cdot $2500 \bigg) \cdot 3 = $81.19

and they would have to pay $2581.19 to pay off the balance at this point.

If instead they make interest-only payments for each of those 3 months at the period rate r, the amount of interest paid would be,

I = \bigg(\frac{0.1299}{12}\cdot $2500\bigg) \cdot 3= ($27.0625/month) \cdot 3=$81.19

Their balance at the end of 3 months would still be $2500.

In this case, the time value of money is not factored in. The steady payments have an additional cost that needs to be considered when comparing loans. For example, given a $100 principal:

  • Credit card debt where $1/day is charged: 1/100 = 1%/day = 7%/week = 365%/year.
  • Corporate bond where the first $3 are due after six months, and the second $3 are due at the year’s end: (3+3)/100 = 6%/year.
  • Certificate of deposit (GIC) where $6 is paid at the year’s end: 6/100 = 6%/year.

There are two complications involved when comparing different simple interest bearing offers.

  1. When rates are the same but the periods are different a direct comparison is inaccurate because of the time value of money. Paying $3 every six months costs more than $6 paid at year end so, the 6% bond cannot be ‘equated’ to the 6% GIC.
  2. When interest is due, but not paid, does it remain ‘interest payable’, like the bond’s $3 payment after six months or, will it be added to the balance due? In the latter case it is no longer simple interest, but compound interest.

A bank account that offers only simple interest, that money can freely be withdrawn from is unlikely, since withdrawing money and immediately depositing it again would be advantageous.

Composition of interest rates

In economics, interest is considered the price of credit, therefore, it is also subject to distortions due to inflation. The nominal interest rate, which refers to the price before adjustment to inflation, is the one visible to the consumer (i.e., the interest tagged in a loan contract, credit card statement, etc.). Nominal interest is composed of the real interest rate plus inflation, among other factors. A simple formula for the nominal interest is:

 i= r + \pi

Where i is the nominal interest, r is the real interest and \pi is inflation.

This formula attempts to measure the value of the interest in units of stable purchasing power. However, if this statement were true, it would imply at least two misconceptions. First, that all interest rates within an area that shares the same inflation (that is, the same country) should be the same. Second, that the lenders know the inflation for the period of time that they are going to lend the money.

One reason behind the difference between the interest that yields a treasury bond and the interest that yields a mortgage loan is the risk that the lender takes from lending money to an economic agent. In this particular case, a government is more likely to pay than a private citizen. Therefore, the interest rate charged to a private citizen is larger than the rate charged to the government.

To take into account the information asymmetry aforementioned, both the value of inflation and the real price of money are changed to their expected values resulting in the following equation:

 i_t = r_{(t+1)} + \pi_{(t+1)} + \sigma

Here, i_t is the nominal interest at the time of the loan, r_{(t+1)} is the real interest expected over the period of the loan,  \pi_{(t+1)} is the inflation expected over the period of the loan and  \sigma is the representative value for the risk engaged in the operation.

Cumulative interest or return

[icon] This section requires expansion.

The calculation for cumulative interest is (FV/PV)-1. It ignores the ‘per year’ convention and assumes compounding at every payment date. It is usually used to compare two long term opportunities.[citation needed]

Other conventions and uses


  • US and Canadian T-Bills (short term Government debt) have a different calculation for interest. Their interest is calculated as (100-P)/P where ‘P’ is the price paid. Instead of normalizing it to a year, the interest is prorated by the number of days ‘t’: (365/t)*100. (See also: Day count convention). The total calculation is ((100-P)/P)*((365/t)*100). This is equivalent to calculating the price by a process called discounting at a simple interest rate.
  • Corporate Bonds are most frequently payable twice yearly. The amount of interest paid is the simple interest disclosed divided by two (multiplied by the face value of debt).

Flat Rate Loans and the Rule of .78s: Some consumer loans have been structured as flat rate loans, with the loan outstanding determined by allocating the total interest across the term of the loan by using the “Rule of 78s” or “Sum of digits” method. Seventy-eight is the sum of the numbers 1 through 12, inclusive. The practice enabled quick calculations of interest in the pre-computer days. In a loan with interest calculated per the Rule of 78s, the total interest over the life of the loan is calculated as either simple or compound interest and amounts to the same as either of the above methods. Payments remain constant over the life of the loan; however, payments are allocated to interest in progressively smaller amounts. In a one-year loan, in the first month, 12/78 of all interest owed over the life of the loan is due; in the second month, 11/78; progressing to the twelfth month where only 1/78 of all interest is due. The practical effect of the Rule of 78s is to make early pay-offs of term loans more expensive. For a one year loan, approximately 3/4 of all interest due is collected by the sixth month, and pay-off of the principal then will cause the effective interest rate to be much higher than the APY used to calculate the payments. [8]

In 1992, the United States outlawed the use of “Rule of 78s” interest in connection with mortgage refinancing and other consumer loans over five years in term.[9] Certain other jurisdictions have outlawed application of the Rule of 78s in certain types of loans, particularly consumer loans.[8]

Rule of 72: The “Rule of 72” is a “quick and dirty” method for finding out how fast money doubles for a given interest rate. For example, if you have an interest rate of 6%, it will take 72/6 or 12 years for your money to double, compounding at 6%. This is an approximation that starts to break down above 10%.

Market interest rates

Question book-new.svg This unreferenced section requires citations to ensure verifiability.

There are markets for investments (which include the money market, bond market, as well as retail financial institutions like banks) set interest rates. Each specific debt takes into account the following factors in determining its interest rate:

Opportunity cost

Opportunity cost encompasses any other use to which the money could be put, including lending to others, investing elsewhere, holding cash (for safety, for example), and simply spending the funds.


Since the lender is deferring consumption, they will wish, as a bare minimum, to recover enough to pay the increased cost of goods due to inflation. Because future inflation is unknown, there are three ways this might be achieved:

  • Charge X% interest ‘plus inflation’. Many governments issue ‘real-return’ or ‘inflation indexed’ bonds. The principal amount or the interest payments are continually increased by the rate of inflation. See the discussion at real interest rate.
  • Decide on the ‘expected’ inflation rate. This still leaves the lender exposed to the risk of ‘unexpected’ inflation.
  • Allow the interest rate to be periodically changed. While a ‘fixed interest rate’ remains the same throughout the life of the debt, ‘variable’ or ‘floating’ rates can be reset. There are derivative products that allow for hedging and swaps between the two.

However interest rates are set by the market, and it happens frequently that they are insufficient to compensate for inflation: for example at times of high inflation during e.g. the oil crisis; and currently (2011) when real yields on many inflation-linked government stocks are negative.


There is always the risk the borrower will become bankrupt, abscond or otherwise default on the loan. The risk premium attempts to measure the integrity of the borrower, the risk of his enterprise succeeding and the security of any collateral pledged. For example, loans to developing countries have higher risk premiums than those to the US government due to the difference in creditworthiness. An operating line of credit to a business will have a higher rate than a mortgage loan.

The creditworthiness of businesses is measured by bond rating services and individual’s credit scores by credit bureaus. The risks of an individual debt may have a large standard deviation of possibilities. The lender may want to cover his maximum risk, but lenders with portfolios of debt can lower the risk premium to cover just the most probable outcome.

Default Interest

Default interest is the interest that a borrower would pay if the borrower will not fulfill the loan covenants. The default interest is usually much higher than the original interest since it is reflecting the aggravation in the financial risk of the borrower. The default interest compensates the lender for the added risk.

Banks tend to add default interest to the loan agreements in order to separate between different scenarios.

Deferred consumption

Charging interest equal only to inflation will leave the lender with the same purchasing power, but they would prefer their own consumption sooner rather than later. There will be an interest premium of the delay. They may not want to consume, but instead would invest in another product. The possible return they could realize in competing investments will determine what interest they charge.

Length of time

Shorter terms often have less risk of default and exposure to inflation because the near future is easier to predict. In these circumstances, short term interest rates are lower than longer term interest rates (an upward sloping yield curve).

Government intervention

Interest rates are generally determined by the market, but government intervention – usually by a central bank – may strongly influence short-term interest rates, and is one of the main tools of monetary policy. The central bank offers to borrow (or lend) large quantities of money at a rate which they determine (sometimes this is money that they have created ex nihilo, i.e. printed) which has a major influence on supply and demand and hence on market interest rates.

Open market operations in the United States

The effective federal funds rate charted over more than fifty years.[citation needed]

The Federal Reserve (Fed) implements monetary policy largely by targeting the federal funds rate. This is the rate that banks charge each other for overnight loans of federal funds. Federal funds are the reserves held by banks at the Fed.

Open market operations are one tool within monetary policy implemented by the Federal Reserve to steer short-term interest rates. Using the power to buy and sell treasury securities, the Open Market Desk at the Federal Reserve Bank of New York can supply the market with dollars by purchasing T-notes, hence increasing the nation’s money supply. By increasing the money supply or Aggregate Supply of Funding (ASF), interest rates will fall due to the excess of dollars banks will end up with in their reserves. Excess reserves may be lent in the Fed funds market to other banks, thus driving down rates.

Interest rates and credit risk

It is increasingly recognized that the business cycle, interest rates and credit risk are tightly interrelated. The Jarrow-Turnbull model was the first model of credit risk that explicitly had random interest rates at its core. Lando (2004), Darrell Duffie and Singleton (2003), and van Deventer and Imai (2003) discuss interest rates when the issuer of the interest-bearing instrument can default.

Money and inflation

Loans and bonds have some of the characteristics of money and are included in the broad money supply.

National governments (provided, of course, that the country has retained its own currency) can influence interest rates and thus the supply and demand for such loans, thus altering the total of loans and bonds issued. Generally speaking, a higher real interest rate reduces the broad money supply.

Through the quantity theory of money, increases in the money supply lead to inflation. This means that interest rates can affect inflation in the future.[citation needed]

Interest in mathematics

It is thought that Jacob Bernoulli discovered the mathematical constant e by studying a question about compound interest.[10] He realized that if an account that starts with $1.00 and pays say 100% interest per year, at the end of the year, the value is $2.00; but if the interest is computed and added twice in the year, the $1 is multiplied by 1.5 twice, yielding $1.00×1.5² = $2.25. Compounding quarterly yields $1.00×1.254 = $2.4414…, and so on.

Bernoulli noticed that if the frequency of compounding is increased without limit, this sequence can be modeled as follows:

\lim_{n \rightarrow \infty} \left( 1 + \dfrac{1}{n} \right) ^n = e,

where n is the number of times the interest is to be compounded in a year.


The balance of a loan with regular monthly payments is augmented by the monthly interest charge and decreased by the payment so

B_{k + 1} = \big( 1 + r \big) B_{k} - p,


i = loan rate/100 = annual rate in decimal form (e.g. 10% = 0.10 The loan rate is the rate used to compute payments and balances.)
r = period rate = i/12 for monthly payments (customary usage for convenience)[1]
B0 = initial balance (loan principal)
Bk = balance after k payments
k = balance index
p = period (monthly) payment

By repeated substitution one obtains expressions for Bk, which are linearly proportional to B0 and p and use of the formula for the partial sum of a geometric series results in

B_{k} = (1 + r)^k B_{0} - \frac{(1+r)^k - 1}{r} p

A solution of this expression for p in terms of B0 and Bn reduces to

p = r \Bigg[ \frac{(1+r)^{n} B_{0}-B_{n}}{(1+r)^{n}-1} \Bigg]

To find the payment if the loan is to be paid off in n payments one sets Bn = 0.

The PMT function found in spreadsheet programs can be used to calculate the monthly payment of a loan:

p=PMT(rate,num,PV,FV,) = PMT(r,n,-B_0,B_n,)\;

An interest-only payment on the current balance would be

p_{I}= r B.

The total interest, IT, paid on the loan is

I_{T} = np - B_{0}.

The formulas for a regular savings program are similar but the payments are added to the balances instead of being subtracted and the formula for the payment is the negative of the one above. These formulas are only approximate since actual loan balances are affected by rounding. To avoid an underpayment at the end of the loan, the payment must be rounded up to the next cent. The final payment would then be (1+r)Bn-1.

Consider a similar loan but with a new period equal to k periods of the problem above. If rk and pk are the new rate and payment, we now have

B_{k} = B'_{0} = (1 + r_{k})B_{0} - p_{k}.

Comparing this with the expression for Bk above we note that

r_{k} = (1 + r)^{k}-1


p_{k} = \frac{p}{r} r_{k}.

The last equation allows us to define a constant that is the same for both problems,

B^{*} = \frac{p}{r} = \frac{p_{k}}{r_{k}}

and Bk can be written as

B_{k} = (1 + r_{k}) B_{0} - r_{k} B^*.

Solving for rk we find a formula for rk involving known quantities and Bk, the balance after k periods,

r_{k} = \frac{B_{0} - B_{k}}{B^{*} - B_{0}}

Since B0 could be any balance in the loan, the formula works for any two balances separate by k periods and can be used to compute a value for the annual interest rate.

B* is a scale invariant since it does not change with changes in the length of the period.

Rearranging the equation for B* one gets a transformation coefficient (scale factor),

\lambda_{k} = \frac{p_{k}}{p} = \frac{r_{k}}{r} = \frac{(1 + r)^{k} - 1}{r} = k[1 + \frac{(k - 1)r}{2} + \cdots] (see binomial theorem)

and we see that r and p transform in the same manner,

r_k=\lambda_k r\;
p_k=\lambda_k p\;

The change in the balance transforms likewise,

\Delta B_k=B'-B=(\lambda_k rB-\lambda_k p)=\lambda_k \Delta B \;

which gives an insight into the meaning of some of the coefficients found in the formulas above. The annual rate, r12, assumes only one payment per year and is not an “effective” rate for monthly payments. With monthly payments the monthly interest is paid out of each payment and so should not be compounded and an annual rate of 12·r would make more sense. If one just made interest-only payments the amount paid for the year would be 12·r·B0.

Substituting pk = rk B* into the equation for the Bk we get,


Since Bn = 0 we can solve for B*,

B^{*} = B_{0} \bigg(\frac{1}{r_{n}} + 1 \bigg).

Substituting back into the formula for the Bk shows that they are a linear function of the rk and therefore the λk,


This is the easiest way of estimating the balances if the λk are known. Substituting into the first formula for Bk above and solving for λk+1 we get,


λ0 and λn can be found using the formula for λk above or computing the λk recursively from λ0 = 0 to λn.

Since p=rB* the formula for the payment reduces to,


and the average interest rate over the period of the loan is

r_{loan} = \frac{I_{T}}{nB_{0}} = r + \frac{1}{\lambda_{n}} - \frac{1}{n},

which is less than r if n>1.

See also

Look up interest in Wiktionary, the free dictionary.



This article includes a list of references, but its sources remain unclear because it has insufficient inline citations. Please help to improve this article by introducing more precise citations. (January 2009)

Specific references

  1. ^ Sullivan, arthur; Steven M. Sheffrin (2003). Economics: Principles in action. Upper Saddle River, New Jersey 07458: Pearson Prentice Hall. pp. 261. ISBN 0-13-063085-3.
  2. ^ Sullivan, arthur; Steven M. Sheffrin (2003). Economics: Principles in action. Upper Saddle River, New Jersey 07458: Pearson Prentice Hall. pp. 506. ISBN 0-13-063085-3.
  3. ^ Johnson, Paul: A History of the Jews (New York: HarperCollins Publishers, 1987) ISBN 0-06-091533-1, pp. 172–73.
  4. ^ Temin, Peter: Financial Intermediation in the Early Roman Empire, The Journal of Economic History, Cambridge University Press, 2004, vol. 64, issue 03, p. 15.
  5. ^ a b Moehlman, 1934, p. 6.
  6. ^ Noonan, John T., Jr. 1993. “Development of Moral Doctrine.” 54 Theological Stud. 662.
  7. ^ No. 2547: Charging Interest
  8. ^ a b Rule of 78 – Watch out for this auto loan trick
  9. ^ 15 U.S.C. § 1615
  10. ^ O’Connor, J J; Robertson, E F. “The number e. MacTutor History of Mathematics.

General references

  • Duffie, Darrell and Kenneth J. Singleton (2003). Credit Risk: Pricing, Measurement, and Management. Princeton University Press. ISBN 978-0-691-09046-7.
  • Kellison, Stephen G. (1970). The Theory of Interest. Richard D. Irwin, Inc.. Library of Congress Catalog Card No. 79-98251.
  • Lando, David (2004). Credit Risk Modeling: Theory and Applications. Princeton University Press. ISBN 978-0-691-08929-4.
  • van Deventer, Donald R. and Kenji Imai (2003). Credit Risk Models and the Basel Accords. John Wiley & Sons. ISBN 978-0-470-82091-9.

Deepak Tiwari(Rizvi college)BBI student

External links


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