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For more information on interest, visit Britannica.com.

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.

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

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.

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.

Interest is commonly calculated using one of two methods: simple interest calculation, or compound interest calculation.

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.

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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

• Banking and Financial Services - interest: fee charged for use of capital or extension of credit; sum paid as percentage of money on deposit
• Mortgages and Financing - interest: charge made at set rate on money borrowed to purchase property, added to principal amount borrowed

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]}

Contents 1 History of interest 2 Types of interest 2.1 Simple interest 2.2 Composition of interest rates 2.3 Cumulative interest or return 2.4 Other conventions and uses 3 Market interest rates 3.1 Opportunity cost 3.2 Inflation 3.3 Default 3.4 Default Interest 3.5 Deferred consumption 3.6 Length of time 3.7 Government intervention 3.8 Open market operations in the United States 3.9 Interest rates and credit risk 3.10 Money and inflation 4 Interest in mathematics 5 Formulae 6 See also 7 References 7.1 Specific references 7.2 General references 8 External links

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:

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,

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,

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:

Where i is the nominal interest, r is the real interest and 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:

Here, is the nominal interest at the time of the loan, is the real interest expected over the period of the loan, is the inflation expected over the period of the loan and is the representative value for the risk engaged in the operation.

Cumulative interest or return

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

Exceptions:

• 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

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.

Inflation

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.

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 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:

,

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

Formulae

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

,

where

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)

B_k = balance after k payments

k = balance index

p = period (monthly) payment

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

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

To find the payment if the loan is to be finished in n payments one sets B_n = 0.

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

An interest-only payment on the current balance would be

.

The total interest, I_T, paid on the loan is

.

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)B_n-1.

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

.

Comparing this with the expression for B_k above we note that

and

.

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

and B_k can be written as

.

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

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),

(see binomial theorem)

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

The change in the balance transforms likewise,

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 p_k = r_k B* into the equation for the B_k we get,

Since B_n = 0 we can solve for B*,

.

Substituting back into the formula for the B_k shows that they are a linear function of the r_k and therefore the λ_k,

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

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

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

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

,

which is less than r if n>1.

See also

Look up interest in Wiktionary, the free dictionary.

• Actuarial notation
• Promissory note
• Rate of return
• Cash accumulation equation
• Compound interest
• Credit rating agency
• Credit card interest
• Discount
• Fisher equation
• Hire purchase
• Interest expense
• Interest rate
• Leasing
• Monetary policy
• Mortgage loan
• Risk-free interest rate
• Yield curve
• Time value of money
• Simple Interest

Religion:

• Usury
• Riba

References

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. http://www.pearsonschool.com/index.cfm?locator=PSZ3R9&PMDbSiteId=2781&PMDbSolutionId=6724&PMDbCategoryId=&PMDbProgramId=12881&level=4. 
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. http://www.pearsonschool.com/index.cfm?locator=PSZ3R9&PMDbSiteId=2781&PMDbSolutionId=6724&PMDbCategoryId=&PMDbProgramId=12881&level=4. 
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. http://www.gap-system.org/~history/PrintHT/e.html. 

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

• White Paper: More than Math, The Lost Art of Interest calculation
• Mortgages made clear Financial Services Authority (UK)
• OECD interest rate statistics
• Calculate Your Interest

• You can see a list of current interest rates at these sites:
  • World Interest Rates
  • Forex Motion
  • "Which way to pay"

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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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