Dictionary:

interest

  (ĭn'trĭst, -tər-ĭst, -trĕst')

1. 1. A state of curiosity or concern about or attention to something: an interest in sports.
   2. Something, such as a quality, subject, or activity, that evokes this mental state: counts the theater among his interests.
2. Regard for one's own benefit or advantage; self-interest. Often used in the plural: It is in your best interest to cooperate. She kept her own interests in mind.
3. 1. A right, claim, or legal share: an interest in the new company.
   2. Something in which such a right, claim, or share is held: has interests overseas.
   3. A person or group of persons holding such a right, claim, or share: a petroleum interest.
4. Involvement with or participation in something: She has an interest in the quality of her education.
5. 1. A charge for a loan, usually a percentage of the amount loaned.
   2. An excess or bonus beyond what is expected or due.
6. 1. An interest group.
   2. The particular cause supported by an interest group.

1. To arouse the curiosity or hold the attention of: Your opinions interest me.
2. To cause to become involved or concerned with: tried to interest her in taking a walk.
3. Obsolete. To concern or affect.

in the interest (or interests) of

1. To the advantage of; for the sake of: thinking in the interest of the whole family; ate breakfast on the train in the interest of time.

[Middle English, from Old French, from Latin, it is of importance, third person sing. present tense of interesse, to be between, take part in : inter-, inter- + esse, to be.]

1. The charge for the privilege of borrowing money, typically expressed as an annual percentage rate.

2. The amount of ownership a stockholder has in a company, usually expressed as a percentage.

Investopedia Says:
1. Lenders make money from interest, borrowers pay it.

2. Someone who holds more than 5-10% of the stock in a company is said to hold significant interest.

Related Links:
Whether you're buying lunch, a home or a stock, you're influenced by interest rates. How Interest Rates Affect The Stock Market
We go over the impact it can have on your spending money AND your investment returns! Understanding Credit Card Interest
If you're a homeowner, this is one item you want to understand and use on your return. The Mortgage Interest Tax Deduction
Understand the various factors that influence them so you can learn to anticipate their movements for profit. Trying To Predict Interest Rates

Phrase used in quoting bond prices to indicate that, in addition to the price quoted, the seller will receive Accrued Interest.

Money paid for the use of money, expressed as a percentage rate for the period of time in use, generally an annual rate. Bank interest is both an amount paid to attract deposit funds, and a finance charge for money loaned to borrowers. Prior to the federal Truth in Lending Act of 1968, lenders used widely differing methods of calculating loan interest. Since then, interest due on consumer loans must be computed in terms of an Annual Percentage Rate (APR) utilizing interest rate tables from the Federal Reserve Board or from financial publishers, and the total cost of borrowing disclosed when a loan is made. Federal regulation of credit was intended to make it easier for consumers to shop for credit. Loan interest paid over the term of a loan may in fact be less than the total Finance Charge cost of borrowing if the lender charges a commitment fee or discount points payable in advance. Interest on loans may also include late payment fees, annual fees, and over-limit charges.

See also Add-on Interest; Compound Interest; Daily Interest; Discount; Exact Interest; Legal Rate of Interest; Precomputed Interest; Prime Rate; Rule of the 78s; Simple Interest; Usury.

1. cost of the use of money.
Example: Lenders require payment of interest at a specified rate, to compensate for risk, deferment of benefits, inflation, and administrative burdens.

2. The type and extent of ownership.
Example: One may hold either a partial or Fee Simple interest in a property. That interest entitles one to specific ownership rights.

noun

1. Mental acquisitiveness: curiosity, curiousness, inquisitiveness. Idioms: thirst for knowledge. See investigate.
2. Curiosity about or attention to someone or something: concern, concernment, interestedness, regard. See concern/unconcern.
3. Something that contributes to or increases one's well-being. advantage, benefit, good, profit. See help/harm/harmless.
4. A right or legal share in something: claim, portion, stake, title. See part/whole.

verb

To arouse the interest and attention of: attract, intrigue. Slang turn on. See excite/bore/interest.

Definition: advantage
Antonyms: disadvantage

n

Definition: attraction, curiosity
Antonyms: apathy, boredom, disinterest, indifference

v

Definition: hold the attention of
Antonyms: bore, bother, disenchant, disinterest

For more information on interest, visit Britannica.com.

Interests, or "vested interests," was an expression popularly used around the opening of the twentieth century to designate the colossal business corporations that dominated the American scene. Among these interests were the so-called money trust, sugar trust, tobacco trust, oil trust, beef trust, and steel trust, all of which became subjects for strong attacks by muckraking reformers, especially during the presidency of Theodore Roosevelt. These attacks, published in books, magazines, and newspapers and delivered from the political platform, inaugurated an era of reform at the local, state, and national levels that lasted until the United States entered World War I.

Bibliography

Hofstadter, Richard. The Age of Reform, from Bryan to F. D. R. New York: Vintage Books, 1955.

Usury laws, inspired both by Scripture and by a misunderstanding of monetary economics, have probably never prevented lenders from charging interest. Throughout early modern Europe, not only states, businesses, and private individuals, but even religious institutions from mosques to monasteries commonly lent and borrowed with interest. Nonetheless, usury laws have shaped the history of credit by forcing contracting parties to disguise interest payments as something else. No one, of course, is fooled by the subterfuge, but it has often determined the nature of monetary institutions and severely limited the survival of documentation through which historians might study the movement of the interest rate. By the eighteenth century, as religious objections weakened, the debate over usury laws became utilitarian rather than doctrinal. At the same time, a new debate over the determination of the interest rate became central to the economic theory of the Enlightenment, and to the rejection of earlier mercantilist policies.

Usury Legislation

"Lend without expecting any return," counsels Jesus in the Sermon on the Mount (Luke 6:34–35), and though the context would suggest that one should not even expect repayment of the principal, the medieval church read his statement as a prohibition on interest. The lesson was reinforced by certain passages of the Old Testament that denounce "usury" without clearly defining the word (Exodus 22:25; Deuteronomy 23:19–20; Psalms 15:5), as well as Aristotle's doctrine that money is sterile (Politics 1:10; Ethics 5:5). Jews were often permitted to lend to Christians at interest since they fell outside the spiritual authority of the church, thus demonstrating that the original purpose of usury legislation was to protect the lender from sin, not to protect the borrower from exploitation. The reputation of Jews as moneylenders was greatly exaggerated, however, and they never played more than a minor role in credit markets before the rise of the Rothschild Bank in the nineteenth century.

A papal bull of 1425 permitted Catholics to buy and sell perpetual annuities, at least when mortgaged against real property (a distinction that was eventually ignored). The Orthodox Church also relaxed usury laws by the sixteenth century. Though the Koran also denounces usury (2:275, 3:130, 4:161, 30:39), in the early fifteenth century the Ottomans came to allow a form of perpetual annuity known as the cash waqf. Originally created to fund charitable institutions such as schools and mosques, it became a common form of private investment by the sixteenth century.

In western Europe in the sixteenth century, Protestant reformers began to chip away at the remaining religious prohibitions on interest, which they associated with Scholasticism. Luther, Calvin, and Zwingli variously argued that interest is not usurious so long as the rate charged is moderate and the contract is in accordance with the Golden Rule ("Do unto others as you would have them do unto you"). Luther, moreover, insisted that one should submit to the laws of the state and not invoke biblical usury prohibitions as an excuse for default. In Catholic Europe, the Jesuits played a similar role in promoting the toleration of interest. The effect of such teachings was not so much to extinguish as to secularize discussions of usury law, so that by the eighteenth century the debate had become almost entirely utilitarian rather than exegetical.

Some Enlightenment writers, including John Locke and Jeremy Bentham, insisted on the complete deregulation of interest. Adam Smith believed that a legal ceiling on interest rates was justified to prevent consumption loans to spendthrifts, since lenders would consider them a bad risk at the legal rate. He agreed, however, that if the ceiling were set below the market rate for commercial loans, it would be counterproductive since merchants would be forced to borrow outside the law. Without the security provided by the law courts, lenders would charge a risk premium, thus actually raising, not lowering, interest rates. Anne-Robert-Jacques Turgot made much the same point when he described an incident in Angoulême in 1769, in which a group of insolvent debtors brought financial panic, and thus extraordinarily high interest rates, on the entire city by attempting to prosecute their creditors for usury.

Long-Term Interest

Long-term bonds in early modern Europe usually took the form of perpetual annuities. The purchaser of the annuity (that is, the lender) paid a lump sum, in return for which the seller (or borrower) promised to pay a fixed coupon once a year forever. On the Continent the contract of sale had to pass before a notary (thus incurring notarial fees), as did any resale to a third party. The lender could not require the borrower to repay the principal, though the borrower could do so voluntarily at any time, and thus extinguish the loan. Throughout Europe, permissible coupon rates tended to fall from 10 percent or more in the sixteenth century to 5 percent or less in the eighteenth century. In any given period, coupon rates recorded in notarized contracts were usually simply the maximum allowed by law, and thus seemed to represent a legal fiction. That is, contracting parties presumably varied the yield rate of the bond simply by agreeing to a sales price somewhat higher or lower than that stated in the contract. For historians, the fluctuation of long-term interest rates on private bonds is thus largely unrecoverable.

European states also borrowed primarily through perpetual annuities, the most famous being the Consols with which Britain consolidated its national debt after the Glorious Revolution (1688–1689). By the eighteenth century state bonds were actively traded on national stock exchanges, and yield rates can often be inferred from the quotations printed in commercial newspapers. In Britain and the Netherlands, where representative assemblies managed the national debt to the advantage of their wealthy constituents, the risk on state bonds was essentially zero, and yield rates fell as low as 3 percent. In France, on the contrary, the monarchy issued partial defaults on its debt every few decades and could only continue to borrow by offering exceptionally high interest rates (which, of course, rendered future defaults more likely). The need for cheap credit to finance increasingly costly wars thus seems to have worked to the advantage of representative regimes, a fact that goes a long way toward explaining the widespread movement for constitutional reform in the second half of the century.

Short-Term Interest

Starting in northern Italy at the end of the thirteenth century, merchants developed a variety of new forms of short-term credit that bore hidden interest. By far the most important were the promissory note and the bill of exchange. A promissory note is little more than an IOU by which the debtor (who in most cases is purchasing merchandise on credit rather than actually borrowing cash) promises to pay to the creditor, "or his order," a given sum on a given date. Typically written at term of two to six months, rarely more than a year, such notes make no mention of interest, but the interest is in fact included in the face value. At any given moment the market value of a promissory note is thus its face value minus the "discount," or interest over the remaining term. If, for instance, the discount rate is currently 8 percent per year (0.08), then a promissory note with a face value of 100 ducats payable in six months (0.50 year) is worth:

The discount rate thus expresses interest not as a percentage of the principal borrowed, but as a percentage of the final payment (interest plus principal). If r is the interest rate as conventionally calculated, d is the discount rate and t is the term, then:

At short term, however, the difference between r and d is negligible.

Through the bill of exchange, a merchant sells the right to collect a sum of money from his correspondent in a different city. Rather than an IOU, it is thus a sort of "he-owes-you" used to transfer funds between two geographically distant locations, either within the same country (inland bills) or in different countries (foreign bills). The value of the bill of exchange depends on the going exchange rate, expressed as a percentage premium or loss for inland bills, and as a rate of exchange between two national currencies in the case of foreign bills. As with the promissory note, the bill of exchange nowhere mentions interest, but merchants openly charged less for bills written at longer term. Even sight bills (technically payable one day after acceptance by the party on whom they were drawn) included a small amount of hidden interest, since it would take them several weeks to reach their destination through the mail. Bills payable one, two, or more months after acceptance sold at correspondingly more advantageous exchange rates. One of the curious results is that the going rate of exchange at any city A on another city B was consistently different from the rate of exchange at B on A. If a merchant purchased a bill of exchange at A on B, sent it to B, instructed his correspondent to use the funds to purchase another bill at B on A, and finally cashed the latter in A, he would end up with more than he started with, the difference corresponding to the interest on his initial outlay.

Bills of exchange and promissory notes did not require notarization. By the seventeenth century (and probably earlier) they were negotiable throughout Europe by simple endorsement. Issued by businesses large and small, they circulated widely. Unlike cash, commercial paper, with its hidden interest, constantly gained value until it came due. The portfolio of credits outstanding thus came to replace cash as the largest reserve of liquid wealth, not only for wholesale merchants but even for humble artisans and shopkeepers. The movement of the interest rate therefore directly concerned all business people.

The Movement of Interest Rates

The economic history of Europe has been written largely on the basis of grain prices. The movement of interest rates, though equally important, is less well known, largely because the habit of disguising interest makes the rates so difficult to recover. Eighteenth-century economists asserted that interest rates had fallen steadily from about 10 percent in the sixteenth century, to 6 to 8 percent in the seventeenth century, and to 5 percent or less in the eighteenth century. This long-run movement has been substantiated by the research of Sidney Homer and Richard Sylla.

The short-run movement of the discount rate at Paris and Amsterdam came to light suddenly in the eighteenth century, thanks to exchange rate quotations in The Course of the Exchange. Beginning in 1723, this British commercial newspaper printed two exchange rates at London on Amsterdam, one for sight bills and one for two-month bills. The percentage difference between the rates corresponds to the discount rate in Amsterdam, at least as it was known to London exchange agents. The newspaper similarly printed twin rates on Paris from 1740. For the period through 1789, discount rates in Paris averaged 5 percent and tended to peak in the autumn months as grain merchants borrowed heavily to finance the purchase of the harvest. Discount rates at Amsterdam averaged 4.5 percent and were not clearly tied to the agricultural cycle. Discount rates at Paris correlated poorly with those at Amsterdam, demonstrating that the two markets were not highly integrated. The most pronounced feature of each series was the sharp rise of interest rates during financial panics that tended to occur two or three times a decade.

Several studies have demonstrated that the London and Amsterdam capital markets were highly integrated with each other in the eighteenth century, and that one of the principal mechanisms of integration was interest rate arbitrage. That is, speculators frequently used the exchange market to move funds between these two cities in order to take advantage of the higher rate of return. London and Amsterdam were probably the exception, however. Interest rate arbitrage appears to have been far less significant at Paris, and the same was probably true in other financial centers.

The Eighteenth-Century Debate

The economists of the Enlightenment shared with their mercantilist predecessors the conviction that high interest rates are a disincentive to invest, since any investment earning less than the interest rate will be unprofitable. Early modern economic policy was thus largely a set of strategies for reducing the interest rate. Enlightenment writers came to differ sharply from the mercantilists, however, in their theory of the determination of the interest rate, and thus in the specific strategies that they considered advisable.

Mercantilist writings of the seventeenth and early eighteenth centuries, including those of John Locke, are marked by a belief that the rate of interest is an inverse function of the money supply. Though often poorly articulated, this quantity theory of interest, suggestive of John Maynard Keynes's "liquidity curve," was clearly central to monetary thought and went largely unchallenged until the mid-eighteenth century. Like many late mercantilists, Montesquieu, in his Spirit of the Laws (1748), saw proof of the quantity theory of interest in the decline of interest rates from roughly 10 percent to 5 percent since the discovery of the Americas, which he thought was due to the resulting influx of silver. Thus, to encourage investment, mercantilists sought to draw bullion into the country by means of a favorable balance of trade. At times they also proposed more creative devices for increasing the money supply, such as John Law's 1705 scheme to issue a paper currency based on the value of land.

Inspired in part by the early eighteenth-century writings of Richard Cantillon and Pierre de Boisguilbert, the Enlightenment subjected the quantity theory of interest to systematic critique. Boisguilbert had pointed out that most of the money supply was quasi-money in the form of commercial paper, and that its quantity was not dependent on stocks of coin. Cantillon argued effectively that an increase in the money supply would raise prices and thus leave the real money supply unaltered, with no long-run effect on interest rates. Adam Smith, David Hume, and the French Physiocrats repeated and developed these arguments. As Hume pithily remarked in 1752, "Silver is more common than gold; and therefore you receive a greater quantity of it for the same commodities. But do you pay less interest for it?"

Enlightenment writers came thus to argue that the rate of interest is an inverse function not of the supply of money, but of the supply of productive capital. The new theory, like the old one, offered a plausible explanation of the gradual decline of interest rates since the sixteenth century. Since the supply of capital was thought also to determine the rate of profit, the hope was now that at equilibrium the interest rate would fall below the profit rate, rendering all regulation of the interest rate unnecessary. Smith asserted that in England the profit rate was currently about 10 percent, and the interest rate about 5 percent. Though he acknowledged that the relationship was not strictly linear, he believed that the interest rate would rise or fall with the profit rate in such a way as to leave investors with a reasonable net profit. Still, the Physiocrats feared that excessive government borrowing might crowd out private investment by artificially bidding up the interest rate, and consequently sought to persuade the French monarchy to reduce budget deficits.

Bibliography

Primary Sources

Hume, David. "Of Interest." In Essays Moral, Political and Literary. Revised ed. Edited by Eugene F. Miller. Indianapolis, 1987.

Smith, Adam. An Inquiry into the Nature and Causes of the Wealth of Nations. Edited by Edwin Cannan. New York, 1937.

Turgot, Anne-Robert-Jacques. Ecrits économiques. Edited by Bernard Cazes. Paris, 1970.

Secondary Sources

De Roover, Raymond. "What Is Dry Exchange? A Contribution to the Study of English Mercantilism." Journal of Political Economy 52 (1944): 250–266.

Eagly, Robert V., and V. Kerry Smith. "Domestic and International Integration of the London Money Market, 1731–1789." Journal of Economic History 36 (1976): 198–212.

Ferguson, Niall. The Cash Nexus: Money and Power in the Modern World, 1700–2000. New York, 2001.

Heckscher, Eli F. Mercantilism. 2nd ed. 2 vols. Translated by Mendel Shapiro. New York, 1955.

Hoffman, Philip T., Gilles Postel-Vinay, and Jean-Laurent Rosenthal. Priceless Markets: The Political Economy of Credit in Paris, 1660–1870. Chicago, 2000.

Homer, Sidney, and Richard Sylla. A History of Interest Rates. 3rd ed. New Brunswick, N.J., 1991.

Mandaville, Jon E. "Usurious Piety: The Cash Waqf Controversy in the Ottoman Empire." International Journal of Middle Eastern Studies 10 (1979): 289–308.

Neal, Larry. The Rise of Financial Capitalism: International Capital Markets in the Age of Reason. Cambridge, U.K., 1990.

Rist, Charles. History of Monetary and Credit Theory from John Law to the Present Day. Translated by Jane Degras. New York, 1940.

Taeusch, Carl F. "The Concept of 'Usury': The History of an Idea." Journal of the History of Ideas 3 (1942): 291–318.

—THOMAS M. LUCKETT

A comprehensive term to describe any right, claim, or privilege that an individual has toward real or personal property. Compensation for the use of borrowed money.

There are two basic types of interest: legal and conventional. Legal interest is prescribed by the applicable state statute as the highest that may be legally contracted for, or charged. Conventional interest is interest at a rate that has been set and agreed upon by the parties themselves without outside intervention. It must be within the legally prescribed interest rate to avoid the criminal prosecution of the lender for violation of usury laws.

The charge for borrowing money or the return for lending it.

Quotes:

"The virtues and vices are all put in motion by interest." - Francois De La Rochefoucauld

"I don't believe in principle, but I do in interest." - James Russell Lowell

"Only free peoples can hold their purpose and their honor steady to a common end and prefer the interest of mankind to any narrow interest of their own." - Woodrow T. Wilson

"Interest makes some people blind, and others quick-sighted." - Francis Beaumont

"There are no uninteresting things, there are only uninterested people." - Gilbert K. Chesterton

"A man's interest in the world is only an overflow from his interest in himself." - George Bernard Shaw

See more famous quotes about Interest

It has been suggested that Interest expense be merged into this article or section. (Discuss)

It has been suggested that Compound interest be merged into this article or section. (Discuss)

For other senses of this word, see interest (disambiguation).

Interest is a fee paid on borrowed assets. By far the most common form these assets are lent in is money, but other assets may be lent to the borrower, such as shares, consumer goods through hire purchase, major assets such as aircraft, and even entire factories in finance lease arrangements. In each case the interest is calculated upon the value of the assets in the same manner as upon money.

The fee is compensation to the lender for foregoing other useful investments that could have been made with the loaned money. Instead of the lender using the assets directly, they are advanced to the borrower. The borrower then enjoys the benefit of the use of the assets ahead of the effort required to obtain them, while the lender enjoys the benefit of the fee paid by the borrower for the privilege. The amount lent, or the value of the assets lent, is called the principal. This principal value is held by the borrower on credit. Interest is therefore the price of credit, not the price of money as is commonly - and mistakenly - believed. The percentage of the principal which is paid as fee (the interest), over a certain period of time, is called the interest rate.

History of interest

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The charge of interest dates back to 1500 B.C. among the Sumerian and Egyptian cultures. References to the concept can be found in the religious text of the Abrahamic religions such as the counsel against excessive interest.

Interest is the earning of capital, particularly the price paid for the use of savings over a given period of time. In medieval times, time was considered to be property of God. Therefore, to charge interest was considered to commerce with God's property. Also, 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. The church regarded this as a sin of usury, nevertheless, this rule was never strictly obeyed and eroded gradually until it disappeared during the industrial revolution. Some scholars think that banking started among Jewish families because of the restrictions of the church.

... financial oppression of Jews tended to occur in areas where they were most disliked, and if Jews reacted by concentrating on moneylending to gentiles, 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 practised it were excommunicated. But the Christians also imposed the harshest financial burdens on the Jews. The Jews reacted by engaging in the one business where Christian laws actually discriminated in their favour, and so became identified with the hated trade of moneylending.^[1]

Usury has always been viewed negatively by the Roman Catholic Church. The Second Lateran Council condemned any repayment of a debt with more money than was originally loaned; the Council of Vienna explicitly prohibited usury and declared any legislation tolerant of usury to be heretical; the first scholastics reproved the charging of interest. 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.

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, it could not be viewed in the same manner. The School of Salamanca elaborated various reasons that justified the charging of interest. The person who received a loan benefited; 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 utilizing the loaned money. Finally, and perhaps most originally, was the consideration of money itself as a 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 understood as the price of credit and, therefore, subject to the laws of supply and demand. The first attempt to control interest rates through money printing was made by the French central Bank until 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. In the early 20th cetury, 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. Among academics, the more modern views of John Maynard Keynes and Milton Friedman are widely accepted.

Today, some argue that Islamic banking ought to be interest-free by law.

References

• Colish, Marcia, "Medieval Foundations of the Western Intellectual Tradtion 400-1400"; Yale University Press, New Haven, 1997. (Specifically p.333-334 are relevant to this article)
• Denzinger, Henry, "The Sources of Catholic Dogma", B. Herder Book Co. St. Louis, 1955
• "Catechism of the Catholic Church", Liberia Editrice Vaticana, 1994
• Plucknett, K "A Concise History of the Common Law", Little, Brown, 1956

Types of interest

Simple interest

Simple Interest is calculated only on the principal, or on that portion of the principal which remains unpaid.

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

where A is the amount of interest, P the principal, r the interest rate as a percentage, and n the number of time periods elapsed since the loan was taken.

For example, imagine Jim borrows $23,000 to buy a car, and simple interest is charged at a rate of 5.5% per annum. After five years, and assuming none of the loan has been paid off, Jim owes:

At this point, Jim owes a total of $29,325 (principal plus interest).

To calculate the simple interest rate r, add together all interest paid, or payable, in a period. Divide the result by the principal at the beginning of the period. The result is the simple interest rate. For example, given a $100 principal:

• Credit card debt where $1/day is charged: 1/100 = 1%/day.
• 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 three problems with simple interest.

1. The time periods used for measurement can be different, making comparisons wrong. One cannot claim that 1%/day of credit card interest is 'equal' to a 365%/year GIC.
2. The time value of money means that $3 paid every six months costs more than $6 paid only at year end. So the 6% bond cannot be 'equated' to the 6% GIC.
3. When interest is due, but not paid, the consequences are unclear. For example, does it remain 'interest payable', like the bond's $3 payment after six months? Alternatively, will it be added to the original principal, as would typically be the case in the 1%/day borrowed via the credit card? In the latter case, it is no longer simple interest, but compound interest.

Compound interest

Main article: Compound interest

In the short run, compound Interest is very similar to Simple Interest, however, as time continues the difference becomes considerably larger. The conceptual difference is that the principal changes with every time period, as any interest incurred over the period is added to the principal. Put another way, the lender is charging interest on the interest.

Assuming that no part of the principal or subsequent interest has been paid, the amount of compound interest incurred is calculated by the following formula:

where A, P, r and n have the same meanings as before.

For example, if the 5.5% interest on Jim's car were calculated as compound interest, he would end up owing, in addition to the $23,000 principal, the following interest:

Failed to parse (unknown function\begin): \begin{align} A & = 23000 \cdot \left( \left( 1 + \frac{5.5}{100} \right) ^ 5 - 1 \right) \\ & = 23000 \cdot \left( 1.055^5 - 1 \right) \\ & = 7060 \\ \end{align}

In this case, then, Jim would owe principal of $23,000 and interest of $7,060, for a total of $30,060.

A problem with compound interest is that the resulting obligation can be difficult to interpret. To simplify this problem, a common convention in economics is to disclose the interest rate as though the term were one year, with annual compounding, yielding the effective interest rate. However, interest rates in lending are often quoted as nominal interest rates, i.e., compounding interest uncorrected for the frequency of compounding. The discussion at compound interest shows how to convert to and from the different measures of interest.

Loans often include various non-interest charges and fees. One example are points on a mortgage loan in the United States. When such fees are present, lenders are regularly required to provide information on the 'true' cost of finance, often expressed as an annual percentage rate (APR). The APR attempts to express the total cost of a loan as an interest rate after including the additional fees and expenses, although details may vary by jurisdiction.

In economics, continuous compounding is often used due to its particular mathematical properties.

Fixed and floating rates

Commercial loans generally use compound interest, but they may not always have a single interest rate over the life of the loan. Loans for which the interest rate does not change are referred to as fixed rate loans. Loans may also have a changeable rate over the life of the loan based on some reference rate (such as LIBOR and EURIBOR), usually plus (or minus) a fixed margin. These are known as floating rate, variable rate or adjustable rate loans.

Combinations of fixed-rate and floating-rate loans are possible and frequently used. Less frequently, loans may have different interest rates applied over the life of the loan, where the changes to the interest rate are governed by specific criteria other than an underlying interest rate. An example would be a loan that uses specific periods of time to dictate specific changes in the rate, such as a rate of 5% in the first year, 6% in the second, and 7% in the third.

Theoretical composition of interest rates

In economics, interest is considered the price of money, 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 by the real interest rate plus inflation, among other factors. A simple formula for the nominal interest is:

i = r + π

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

This formula attempts to measure the value of the interest in units of stable purchasing power. However, if this statement was true, it would imply at least two misconceptions. First, that all interest rates within an area that shares the same inflation (i.e: the same country) should be the same. Second, that the lender knows the inflation for the period of time that he/she is 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, the US 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 US government.

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

i_t = r_{t + 1} + π_{t + 1} + σ

Where 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, π_{t + 1} is the inflation expected over the period of the loan and σ is the representative value for the risk engaged in the operation.

Cumulative interest or return

Cumulative interest/return: This calculation 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. Since the difference in rates gets magnified by time, so the speaker's point is more clearly made.

Other conventions and uses

Other exceptions:

• US and Canadian T-Bills (short term Government debt) have a different convention. 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)
• 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).

Rule of 78s: Some consumer loans calculate interest by 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. Approximately 3/4 of all interest due on a one year loan 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. [1]

In 1992, the United States outlawed the use of "Rule of 78s" interest in connection with mortgage refinancings and other consumer loans over five years in term.^[2] Certain other jurisdictions have outlawed application of the Rule of 78s in certain types of loans, particularly consumer loans. [2]

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

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

Opportunity cost: This 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.

Inflation: Since the lender is deferring his consumption, he will at a bare minimum, want to recover enough to pay the increased cost of goods due to inflation. Because future inflation is unknown, there are three tactics.

• Charge X% interest 'plus inflation'. Many governments issue 'real-return' or 'inflation indexed' bonds. The principal amount and the interest payments are continually increased by the rate of inflations. See the discussion at real interest rate.
• Decide on the 'expected' inflation rate. This still leaves both parties 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.

Default: 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.

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.

Deferred consumption: Charging interest equal only to inflation will leave the lender with the same purchasing power, but he would prefer his own consumption NOW rather than later. There will be an interest premium of the delay. See the discussion at time value of money. He may not want to consume, but instead would invest in another product. The possible return he could realize in competing investments will determine what interest he charges.

Length of time: Time has two effects.

• Shorter terms have less risk of default and inflation because the near future is easier to predict. Broadly speaking, if interest rates increase, then investment decreases due to the higher cost of borrowing (all else being equal).

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 used as the main tool of monetary policy. The central bank offers to buy or sell money at the desired rate and, due to their control of certain tools (such as, in many countries, the ability to print money) they are able to influence overall market interest rates.

Investment can change rapidly to changes in interest rates, affecting national income, and, through Okun's Law, changes in output affect unemployment.

Open market operations in the United States

The effective federal funds rate charted over fifty years

The Federal Reserve (often referred to as 'The 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, which 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 which 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, bonds, and shares have some of the characteristics of money and are included in the broad money supply.

By setting i*_n, the government institution can affect the markets to alter the total of loans, bonds and shares 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.

Interest in mathematics

Jacob Bernoulli discovered the mathematical constant e by studying a question about compound interest.

He realized that if an account that starts with $1.00 and pays 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 this sequence can be modeled as follows:

Failed to parse (unknown function\dfrac): \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.

See also

• Rate of return on investment
• Cash accumulation equation
• Credit rating agency
• Credit card interest
• Debt-based monetary system
• Discount
• Fisher equation
• Hire purchase
• Leasing
• Monetary policy
• Mortgage loan
• Risk-free interest rate
• Yield curve
• Time value of money
• Usury

References

1. ^ Johnson, Paul: A History of the Jews (New York: HarperCollins Publishers, 1987) ISBN 0-06-091533-1. p.174
2. ^ 15 U.S.C. § 1615

• Duffie, Darrell and Kenneth J. Singleton (2003). Credit Risk: Pricing, Measurement, and Management. Princeton University Press. ISBN13 978-0691090467. 
• Lando, David (2004). Credit Risk Modeling: Theory and Applications. Princeton University Press. ISBN13 978-0691089294. 
• van Deventer, Donald R. and Kenji Imai (2003). Credit Risk Models and the Basel Accords. John Wiley & Sons. ISBN13 978-0470820919. 

External links

• Simple Interest Calculator
• Compound Interest Calculator
• Compound interest calculator, taking periodic savings, taxes and inflation into account.

This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)

Common misspelling(s) of interest

• intrest

Dansk (Danish)
n. - interesse, tiltrækning, hobby, fordel, rente, andel
v. tr. - interessere

idioms:

• in the interest of    af hensyn til, til fordel for
• interest rate    rente
• with interest    med renter

Nederlands (Dutch)
belangstelling, rente, belang, invloed, interesseren

Français (French)
n. - intérêt, (Fin) intérêt, (Fin, Comm) intérêts, participation
v. tr. - intéresser, concerner, (Comm) attirer l'attention

idioms:

• at interest    à intérêt
• in the interest of    dans l'intérêt de
• interest rate    (Fin) taux d'intérêt
• of interest    d'intérêt
• with interest    avec intérêt

Deutsch (German)
v. - interessieren
n. - Zins, Interesse, Anteil, Bedeutung

idioms:

• at interest    gegen od. auf Zinsen
• in the interest of    im Interesse von
• interest rate    Zinssatz
• of interest    interessant od. von Interesse sein (für)
• with interest    verzinst, interessiert, übermäßig

Ελληνική (Greek)
v. - ενδιαφέρω, προσελκύω, κινώ το ενδιαφέρον
n. - ενδιαφέρον, συμφέρον, κέρδος, συμμετοχή, μερίδιο, (οικον.) τόκος, όμιλος οικονομικών συμφερόντων

idioms:

• in the interest of    προς χάριν, επ' ονόματι
• interest rate    επιτόκιο
• with interest    με τόκο, (μτφ.) με το παραπάνω

Italiano (Italian)
interessare, interesse

idioms:

• in the interest of    nell'interesse di
• interest rate    tasso di interesse
• with interest    con interesse

Português (Portuguese)
v. - interessar
n. - interesse (m), juros (m pl)

idioms:

• in the interest of    com a intenção de
• interest rate    taxa (f) de juros (Fin.)
• with interest    com mais força

Русский (Russian)
интересовать, интерес, преимущество, доля, процентный доход

idioms:

• in the interest of    в интересах
• interest rate    процентная ставка
• with interest    с процентами

Español (Spanish)
n. - interés, provecho, beneficio, dividendo, participación, rédito
v. tr. - interesarse, participar en o de

idioms:

• at interest    a interés
• in the interest of    en beneficio de
• interest rate    tipo de interés
• of interest    de interés
• with interest    con interés

Svenska (Swedish)
v. - intressera, göra intresserad, angå
n. - intresse, egen fördel, engagemang, andel, insats, ränta (äv. bildl.)

中文（简体） (Chinese (Simplified))
兴趣, 利息, 嗜好, 使感兴趣, 与...有关系

idioms:

• in the interest of    为了, 为了...的利益
• interest rate    利率
• with interest    有兴趣地, 带利息, 通过某种关系

中文（繁體） (Chinese (Traditional))
n. - 興趣, 利息, 嗜好
v. tr. - 使感興趣, 與...有關係

idioms:

• in the interest of    為了, 為了...的利益
• interest rate    利率
• with interest    有興趣地, 帶利息, 通過某種關係

한국어 (Korean)
n. - 관심, 중요성, 이해관계, 이자
v. tr. - ~에 흥미를 일으키게 하다, 관계 시키다

idioms:

• in the interest of    (진리, 나라 등을) 위하여
• with interest    흥미를 가지고, 이자를 붙여서

日本語 (Japanese)
n. - 興味, 関心, 関心事, 利益, 興味をそそる力, 利子, 利息, 利害関係, 権利, 感興, 趣味, 権益, 勢力, 信用
v. - 興味を起こさせる, 関心を持たせる, 関係させる, 勧める

idioms:

• controlling interest    支配的利権
• in the interest of    のために, 用で
• interest rate    利子率, 利率
• vested interest    既得権, 支配者層
• with interest    興味を持って, 利息を付けて

العربيه (Arabic)
‏(فعل) يثير انتباه, يرغب (الاسم) منفعه, فائدة, اهتمام‏

עברית (Hebrew)
n. - ‮התעניינות, טובה, אינטרס, תועלת, תחביב, עניין, ריבית, השקעה, חלק בעסק, רווח, יתרון‬
v. tr. - ‮עורר עניין‬

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