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

Interest is the price of credit, or of credit to the extent it has been drawn down.

The interest due may consist of a stand-alone fee or may be lumped in with the return of some or all of the resources that are the subject of the credit arrangement. Yet other arrangements are possible for the payment of interest in equivalent value, but they are not common.

The resources advanced on credit and the interest due upon that credit are predominantly in money, though the use of money is not strictly necessary for either. The terminology used may change when the resources, payments, or arrangement types take certain forms. Interest is the broad term that covers most of them and describes the economic substance of the fees required in each case.

Meanings

Related terms

Credit is the making available or provision of resources (such as setting a credit limit or granting a loan) by one party to another party where that second party does not immediately pay the first party for the resources in full, and instead either arranges to pay for or to return those resources or equivalent value at a later date. This act generates a debt. The first party is called a creditor, also known as a lender. The second party is called a debtor, also known as a borrower.

The value of the resources provided is called the principal, and the proportion thereof due in interest is called the interest rate. Interest rates are expressed as percentages of the principal value per unit of time. Most commonly that time unit is one year, but other periods, such as half-years and quarters, are also in use. When the time unit is one year an interest rate is then cited as some figure % pa, such as 6%pa, where “pa” is an acronym standing for the Latin term per annum meaning per year.

From the creditor’s perspective, interest is the compensation required for being restricted for the duration of the credit agreement in the possible uses (including sale or other disposal) to which the resources may be put. From the debtor’s perspective, interest is the cost incurred in obtaining useful resources while not having to pay for or otherwise generate equivalent value of the resources at or before the time of use. These two perspectives lead to the market forces of supply and demand, respectively, whose interplay sets market rates of interest.

Controversy over definition of interest

It is commonly held that interest is the price of money. Since by far the resource that is most commonly advanced on credit is money (and that interest payments are even more likely to be in money) this mistake is understandable, and is made even by many well-educated financial and economics professionals. Nevertheless it is still mistaken, for a few reasons.

First, even though the bulk of principal and interest are in monetary form, the use of money is not strictly necessary in any part of an interest-generating arrangement. Other resources may be used instead for both principal and interest due upon that principal.

Second, and more importantly, the reason for want of credit is to obtain resources at a point in time earlier than would be the case if the party in want of the resources had to make the whole effort to generate either them or their equivalent value. Instead of the full production effort required they are borrowed from a creditor, thereby saving time and effort. When the resource borrowed is money, this means the borrower is obtaining the advantage of the use of money without providing equal value for it in the form of goods or services to the lender. The interest payable is then a compensation to the lender for foregoing other investments or consumption possibilities that could have been pursued with the resources so lent during that time period. The borrower then enjoys the benefit of the use of the resources ahead of due time and effort, while the lender enjoys the benefit of the interest paid by the borrower for the privilege.

It is this ability to obtain resources earlier in time than would otherwise be the case (if they could be obtained at all) that is the defining characteristic of borrowing. It is this ability that must be paid for by interest payments to the party whose lending of those resources makes this possible. That is, interest is the price of credit and not the price of money or other particular resource so lent. The resources themselves have their own prices, these being whatever the actual productive efforts are required to generate them or their equivalent value in full. The price of money, for instance, is the effort needed to provide that money’s worth in labour (whether physical or mental) or goods to another who will pay that money in return.

Alternative theories of interest

Time preference theory

See main article – time preference theory of capital returns

The time preference theory of interest, originated by Carl Mengerand Eugen von Böhm-Bawerk, asserts that interest can be explained in terms of a core rate corresponding to the point of indifference between using resources now and using them with a premium in the future. Added to this are additional premiums for risk and inflation.

Critics assert that this theory cannot account for the daily movements in interest rates. In response, followers of Menger and Böhm-Bawerk now say that interest rates are the result of opportunity costs and other influences being daily fluctuations that bounce around the long run trend set by time preference and the additional premiums.

Productivity theory

See main article – productivity theory of capital returns

The productivity theory of interest asserts that interest is a part of the return that arises from ordinary productivity, whether through biological growth or human manufacture. The total amount out is greater than the total amount in, and the difference is composed of interest and profit, divided among debt and equity providers respectively.

Investment opportunity

See main article – investment opportunity theory of capital returns

The opportunity cost theory asserts that interest rates are just kinds of opportunity costs that arise in comparison with alternative investments that could be made with the funds.

Exploitation

See main article – exploitation theory of capital returns

Critics of interest (and other types of passive income), such as Marxists, assert that interest is one form in which value is appropriated from the true producers of that value.

Economic substance

Capital and interest

In economics, the nature of interest was a controversy that is part of a broader controversy over what constituted capital. The word capital comes from the Latin "capita", meaning head and was used in connection with interest as the principal being "the head of the debt". However, the controversy over capital was that capital was also referred to as the physical goods used to produce other goods. Interest, in this view, is the value of the goods produced net of operating costs.

Capital generally is now divided into a number of types, including real capital and financial capital. In reference to physical goods, and other components of real capital, in older economic writings we may find the term “originary interest.”. Today, the term originary interest is an anachronism replaced by normal profit. Interest today is now used to refer to returns upon loans.

Relationships with other factor incomes

Factor incomes are the returns to the providers of resources used in production generally. They are all interrelated and influence each other, as well as each having their own external forces influencing them. A change in any one factor will cause the equilibrium levels for all factors to change, which can echo back around and around.

In any instance, which factor takes priority in determining which others depends on the external forces at work. The interconnection of the factors then sees them all responding in their own way, directly and indirectly. This makes it hard to separate various influences from each other - see the article ceteris paribus.

Interest and profits

Profit is the factor income from business capital. Profits can then either be added to the business’s resources (retained profits), paid to creditors (interest on debt finance), or paid to owners (dividends, drawings, distributions, and similar terms).

Interest on short-term debt is, economically, ultimately expensed when what it originally helped pay for (inputs bought on credit that are then turned into finished merchandise) are sold. Interest on working capital debt (accounts payable and so forth) are therefore operating expenses therefore a deduction against business capital. In turn, interest on short term debt is clearly a deduction against profits.

What funds the business capital is the financial capital, consisting of debt and equity. Interest on debt finance is therefore one of the two factor incomes payable to the providers of financial capital. The providers of equity capital are the ultimate owners of the business capital, and all the profits are theirs either to be taken as dividends or retained within the business. Debt capital funds an addition to the original business capital, and takes legal priority over equity for the payment of interest and principal. Therefore, as far as either the business itself or the equity providers are concerned, interest on debt capital is a deduction against profits. An increase in interest payable is then interpretable as a reduction of profits, which means a reduction of the maximum possible dividends/drawings/distributions that may be taken. The owners are compensated by the fact that the cost of debt is generally lower than the equity returns they normally expect, and so the use of debt can increase their rates of return.

With the formal separation of ownership and management, the managers of the business must pay heed to their cost of capital generally. This is embodied in the concept of the Weighted average cost of capital. Interest rates are one of the two classes of components of the WACC. The other component is the normal rate of profit (formerly known as originary interest) that equity investors expect to be matched or exceeded by actual returns upon their equity investments. One of the aims of the finance department of a corporation is to shop around for the best deals on interest rates so as to keep that corporation’s WACC as low as possible.

When profits increase for reasons other than cuts in interest expenses a corporation tends to increase its demand for all types of capital. This increased demand for capital includes increased demands for credit, both of a short-term and long-term nature. This is then an upward influence on interest rates. However, an increase in profits, or improvements in the predictability of profits, also lower the perceived riskiness of the firm and hence lowers the minimum rate of interest that suppliers require upon credit. This in turn leads to an increase in supply of credit, thereby making actual interest rates fall until they match the required minimum. In aggregate, interest rates can go up or down depending on the relative strengths of these influences, plus outside influences.

Interest and rent

Just as there is a confusion over interest in economics, there is a confusion over the related term of rent. The markets for rental and interest evolved separately, and only later did the connection between them explicitly form.

There is rent as ordinarily understood and economic rent.

Ordinary rent is properly understood as a particular application of interest under certain conditions. Rent is then the interest fee payable when the assets taken on credit are not money and where the ownership of the assets do not pass to the borrower upon the maturation of the rental contract. If ownership does pass at the end of a contract then the arrangement is called hire purchase instead of rental, and the payments involved are only part interest with the other part being principal so as to pay off the goods over time. Ordinary rents are a subset of interest because the advancing of the goods in question is a form of credit.

Economic rents arise from scarcity of the goods themselves separate from the scarcity of the labour that makes them. The market price paid for something that garners economic rent is consistently above the combination of the market prices of all the factors that can be employed to make the good. Economic rents arise when there are restrictions of some kind (natural or human-made) that prevent competition from driving down the price to match the cost of the factor inputs. Economic rents are separate from interest nearly entirely.

The particular conditions that lead to the use of the term rent may include those that arise from economic rent as well as ordinary rent. Under these conditions, the total payment made is part ordinary rent and part economic rent, where only the ordinary part is related to interest rates..

Despite the shift in terminology the economic substance of the connection between interest and ordinary rent is real. The relationship between interest and rent is not often appreciated, especially on the part of those who rent real property or goods. Nevertheless the relationship is there, and the mathematics remains the same. The structure of payments under hire-purchase, for instance, is identical to that of an amortizing loan. The same also often applies to many finance leases. See the discussion on business practice. In this vein a lender of money is also referred to as a type of rentier by Marxists, Keynesians, and other similar thinkers.

An increase in interest rates will lead to an increase in rents. This is most direct when interest rates are directly used as references for commercial rental and hire-purchase agreements. It is also indirect through the connection of borrowing money to buy goods that are then lent out. An increase in interest rates reduces the supply of goods (such as housing or other consumer goods, or commercial property, etc) because less credit will be taken so as to pay for them. The lowering of this supply reduces the level of competition for their rental, allowing their rental rates to be increased.

An increase in rents other than resulting from interest rate increases will lead to an increase in interest rates. When rental incomes increase, there is increased ability to service debts undertaken to purchase the goods lent out. This increases the demand for credit, and hence the price of credit, ie interest rates.

Interest and wages

Interest and interest rates have little direct relationship with wages, but indirect relationships between the two do exist.

The provision of financial capital generally influences the demand for labour. When the financial capital is converted to business capital, more capital means more funding for payrolls, which means more labour is demanded. As financial capital includes credit, matters that increase the supply of credit will perforce increase the demand for labour. The extra capital will be supplied because the minimum rate of return required upon one of more parts of it has reduced. Therefore, ceteris paribus, a reduction in the minimum rates of interest that creditors require will lead to an increase in wages.

In the opposite direction of demand for credit, a person’s wages level (along with spending history and similar matters) is included in that information that a lender requires for determination of how much consumer credit to advance to that person and what interest rate to change for that credit. An increase in wages, particularly of disposable income, leads to increased ability to service debt. In the same manner as for rent, this in turn increases the maximum rate of interest that people are willing to pay. Again, this increased ability to service debt then leads to an increased demand for debt. When this demand is taken to credit markets, the price of credit increases, meaning that actual rates of interest increase.

Market rates

Market rates of interest arise from the interplay of the conditions of the supply of credit and of the demand for credit, just as for any other marketable item. Those conditions may be the long-term at equilibrium or the clearing of markets moment by moment.

Supply

A supplier of credit – a creditor - is someone who will lend when the actual rate of return achievable for a given risk level exceeds the minimum required rate of return at that risk level.

A professional lender is also open to consider - and will often insist upon - the implementation of specific risk-reduction measures. The implementation of these will lower the amount of risk, and hence the required interest. If these measures are not present, either the required minimum rate is higher or the credit may not be forthcoming at all. Alternatively, a professional lender may elect not to require measures that are industry standard so that the credit can be supplied where it otherwise would not, and compensating this increased risk with a premium that is correspondingly above the industry standard level.

Demand

A demander of credit - a debtor - is someone who will borrow when the actual rate of interest achievable for a given set of risk-mitigation factors falls below the maximum acceptable rate of interest.

The borrower can also negotiate for lower interest rates by offering risk-reduction measures. Alternatively, the borrower can propose higher interest rates in return for relaxations of normally-expected risk-reduction measures.

The demand for credit is divided into consumer demand and producer demand.

Consumer demand is the want of credit to purchase goods and services ahead of the time at which they could be purchased if they had to be saved up for and paid in cash. Interest is the price paid for this ability.

Business demand is the want of various kinds of capital (working or financial) in credit form, so as to conduct business activities. Business demand for credit may be short-term or mid- to long-term, corresponding loosely to requirements for working capital (part of business capital) or debt financing (part of financial capital). Credit for working capital demand is dependent on the state of trade for that business at any time. Credit as part of financial capital. Debt financing is part of the more general demand for capital funding to purchase longer term business capital assets, and is dealt with as a component along with equity under project assessment using the Weighted average cost of capital. In both cases, interest is the price paid for the ability of the owners of the business to expand the totality of assets they can use without supplying as much equity funding as would otherwise be needed.

Equilibrium rates

The requirement for interest in return for the advancement of resources is a subset of the need for a return on all resources provided as capital generally. Aside from legalities, debt differs from equity by being at the low to middle ranges of the risk-return spectrum, with the exception of high-yield debt. Nevertheless, the credit market still competes with other possible investments and so is fully subject to opportunity cost accordingly.

The existence of alternative investments includes other classes of debt at different risk levels. There is not just one interest rate but a slew of interest rates applicable to these different classes. Supply and demand operate at the level of these classes as well as opportunity cost among them keeping them interlinked.

Simply put as with all equilibrium prices, the equilibrium interest rate for a given risk level is where the amount willing to be supplied matches the amount that is demanded. The supply conditions are visually represented in the standard way by an upward sloping curve - the more credit that may be supplied, the higher the interest rate required to supply it. Similarly, the demand conditions are also visually represented in the standard way by a downward sloping curve - the more credit that may be supplied, the higher the interest rate required to supply it. The market clearing rate for the period over which the two curves are valid is where they cross. There will be a particular market interest rate for that type of risk level and a total amount of debt that will be kept outstanding as long as those conditions last via constant re-lending of principal upon maturation.

Opinion is divided on whether there exists a so-called natural rate of interest. The rate of interest at equilibrium may be zero (meaning there is no more debt outstanding when equilibrium is reached), or may be a positive number (meaning that there will be debt that is outstanding in equilibrium and recycled indefinitely at the same interest rate). See the varying discussions on the theories of capital returns.

Short term rates

In the short-run very few investments are where they “should” be on the risk-return spectrum. Instead, an interest rate for a given risk level may frequently be above or below it instead. That is, a credit investment may be dominant or dominated by other investments, whether of different risk levels within the same broad investment class or by other investment classes entirely. This departure from the spectrum means there are gains to be had in shifting to the investment with the higher return per unit of risk, which action itself will eventually bring all returns back into line (figuratively and literally). Accordingly, the momentary existence of opportunity costs is a major influence upon interest rates, at least in the short-run.

A second cause of movement in short-term rates is shifts in the fundamentals as identified by whichever theory of interest is correct. Changes in these fundamentals then alters the amount of capital that people may devote to lending or amount they will try to borrow. These then influence market rates in turn when these people take their preferences to the debt market and allocate capital to or away from it. This further increases the scope of opportunity costs.

The amount of capital borrowed or provided may also change for reasons wholly unrelated to investment opportunities or the underlying fundamentals of interest rates. For instance, a creditor may find him or herself in need of funds immediately, and so may call in or liquidate loans and withdraw resources from the debt market even though their fundamentals setting minimum required rates are unchanged. Alternatively, an owner of resources may have absolutely no present use for them and so supply them on credit to a debtor (such as a deposit account in a bank) without any reference to a minimum rate of return.

Finally, there are also the influences of government activity to consider. When the government intervenes, the market clearing rate is not the natural rate as the market rate is not being set exclusively by the interplay of free market forces. See below in the discussion on government intervention.

Interest and macroeconomics

Interest is included in the cost of living

The price of credit of various kinds is included in some baskets of prices used to calculate inflation. When interest rates increase, this increased cost of servicing existing debt is included as an increase in the cost of living because of people having mortgages over their homes.

Credit expansion and inflation

In credit expansion, central banks temporarily increase the supply of credit by expanding the money supply and directing these funds to the credit markets through Open Market Operations. However, the expansion of the money supply also leads to price-inflation, which in time causes the existing suppliers of credit to increase their required. Unless central banks expand the money supply even further, interest rates will swing up higher to where they were before to compensate for the inflation until the effects of the monetary expansion wear off.

The combination of monetary expansion causing a swing in interest rates, which itself adds a component to inflation measurement, leads to headaches for economists and financial professionals alike.

Yield curve

See main article - yield curve

The market for producer debt is generally divided into the so-called money market and the bond market, matching the difference between discount instruments and coupon instruments. Interest rates in money-market instruments is usually lower than interest rates in bond market instruments, even from the same issuer. Despite that division, it is possible to make a plot of interest rates on negotiable instruments against their maturity, which is called the yield curve. As a general rule, the longer into the future that the maturation date is, the higher the interest rate is. This type of curve is called normal. On some occasions this general rule can fail to hold. The yield curve is said to be inverted when there are interest rates for longer maturities that are lower than for shorter maturities. What this circumstance portends for the economy is a matter of debate.

Interest 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.

Government activity and intervention

Government activity can alter interest rates indirectly through influencing the underlying components or can alter the daily rates directly.

Indirect influences

Government activity can influence interest rates up or down by altering the fundamentals of whichever theory of interest is correct, or by various ways of influencing the opportunity costs of investing in debt.

Alteration of factors in the time-preference theory

Government policy and programs can exert considerable influences upon people’s time preferences and the additional factors that go into minimum and maximum acceptable rates of interest. For example, the existence of the welfare state can increase people’s time preference through reduction of motives to save for retirement or “rainy day” expense, and also reduction of motives to undertake private insurance which then reduces the amount of capital that insurers have to invest with. The government can also act to change risk premiums up and down for particular businesses, broad industries and sectors, and entire national economies. Finally, governments are by far the most responsible for inflation, and what central banks do strongly influences expectations about inflation and hence required inflation premiums.

The nature of government spending can also alter the nature of time-preference factors in aggregate even without changing any preferences of any individual. A shift in resources from a set of parties with a low time preference to a set of parties with a high time preference will change the aggregate time preference from low to high, occasioning a shift from saving and investment to consumption. It is a central tenet of Keynesian economics that governments do precisely that, through redistributive income tax policies, for the express purpose of reducing saving and increasing consumption.

Alteration of opportunity cost

Government activities need neither be general nor even aimed at debt markets for there to be an influence upon interest rates. All that needs to happen for there to be an influence on interest rates is something that alters the opportunity cost faced by those who have or are contemplating investing in debt. For example, a change in policy that just makes returns on equity more or less expensive than present will increase or decrease the amount of capital supplied to debt markets. Conversely, these changes can also influence the demand for debt. The possibilities are endless.

Direct influences

Direct influence is where governments, or central banks, take a direct role in achieving particular goals for market interest rates.

Floors and ceilings

Governments are fully capable of mandating interest rate floors and ceilings. For example, commercial banks in the US were once prohibited from offering any interest at all upon cheque accounts. In response to this, the cash interest was replaced by interest paid in kind, such as free consumer goods for opening accounts.

The use of floors and ceilings to control interest rates has fallen out of favour in western countries along with the use of floors and ceilings for general price controlling.

Credit expansion and contraction

Today, most intervention in interest rates is done through the creation and destruction of money and credit.

A practice no longer used was alteration of the reserve fractions required to be held. An increase in the required reserve fractions would reduce the money supply, which for a short time would reduce the credit supply and so drive up the price of credit, and conversely when required reserve fractions were reduced.

The direct generation of money to be sent to debt markets has also fallen out of favour, at least among western governments and central banks.

What is done by most central banks today is the targeting of particular interest rates, especially overnight rates upon borrowings from the central bank or upon accounts held by private banks at central banks, by adding and withdrawing credit through Open Market Operations.

Actual government intervention today (2007)

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.

Criticism of government intervention in interest rates

Critics of government intervention claim that all that is achieved is the distortion of pricing signals that businesses need to formulate valid plans for the future.

This is a central element of some theories about the business cycle. The forcing of interest rates down to stimulate growth, it is claimed, leads to a boom and malinvestment, which must be followed first by inflation as the monetary expansion that forces the interest rates down takes hold, then bust as interest rates are raised back again in order to fight that inflation and unemployment result when the malinvestments are liquidated.

Different schools of economic thought have different ideas on the importance of this belief. The Rational Expectations school, for example, believes that investors are rational and foresighted enough to act in such a way that central bank activity effectively has no influence. The Keynesians, on the other hand, deny the ability to be so rational and foresighted, claiming instead that people are driven by animal passions rather than reason and so central banks are able to fool people.

Mathematics in interest

See main article – mathematics of interest.

Simple interest

Simple interest is calculated only on the principal, or on that portion of the principal which remains unpaid. It is simple because there is no interest payable on previous interest that has been calculated but not paid.

The interest owed at the end of each period is always equal to the original principal multiplied by the nominal annual interest rate, r, divided by the number of periods per year:

${\mbox{Interest}}={\mbox{principal}}\cdot {\frac {r}{n\cdot 100}}$

When simple interest accumulates, the formula for the total amount owed after m periods is

${\mbox{Total owed}}={\mbox{principal}}\cdot {\frac {r\cdot m}{n\cdot 100}}$

The simple interest method is used in bonds, for example. An amount of simple interest is calculated for each coupon that is then paid at regular intervals to the bondholder.

If the bondholder reinvests the coupon receipts at the same interest rate, then that bondholder creates a compound interest situation.

Compound interest

See main article – compound interest

Compound interest is when interest is added to the outstanding principle and then future interest calculated upon that larger outstanding amount. It is compound because interest is then payable upon previous interest as well as the original principle. This leads to interest and outstanding principal growing exponentially.

$P_{m}=P_{0}\cdot (1+{\frac {r}{n\cdot 100}})^{m}$

Continuous interest

See main article - continuous compounding

As one compounds more and more frequently, the higher that the annualised rate of interest becomes. There is a limit to how far this is taken. When the periods are theoretically infinitely short and there are an inversely infinite number per year, one then has continuous compounding. The compounding formula then becomes identical to that for the natural exponent.

$PV=OV\cdot e^{(t\cdot i)}$

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

Amortization

See main article – amortization.

Amortization in lending is where the principal is paid back in pieces at the same time as the interest is paid. At each payment period, the total payment is composed of an interest component and a principal component. The bulk of the first payment tends to be interest. As time passes, the proportions change in favour of payments against principal because the outstanding principle upon which the interest is calculated is successively being reduced by the principal components. Finally, the bulk of the last payment tends to be principal, which settles the outstanding balance of principal owed. This phenomenon is called the amortization schedule, and individual payments can be analyzed using an amortization calculator.

Nominal and effective rates

See main articles – Annual Percentage Yield and effective interest rate

When interest payments must be made several times per year there often arises a distinction between the effective interest rate actually paid for the whole year and the stated nominal rate “per annum”. This is achieved by working out the interest rate per period and then compounding that interest per period up to the length of a whole year.

For example, if a loan is marketed as having a headline rate of 8% nominal rate and payable quarterly, it means that interest is payable at 2% per quarter. The effective interest rate actually payable per year is found when that 2% is compounded over the four quarters. This gives a figure that is slightly higher than the stated headline rate, in this case 8.24%pa.

${\begin{alignedat}{2}ER&=((1+{\dfrac {2}{100}})^{4})-1)\cdot 100\\&=(1.08243216-1)\cdot 100\\&=8.24\%\\\end{alignedat}}$

Additional fees and charges

Loans often include various non-interest charges and fees. One example are points on a mortgage loan in the United States. A customer may be pleased to find a lender with a lower interest rate, but then find that there are higher fees charged for the establishment of the loan.

For example, on a principal of $50,000 borrowed for 10 years at 8%pa payable once per year, the official interest cost will be $4,000 per year. If there is also an up-front establishment fee of say $600 this is the same as paying $4,000 per year on a principal of $49,400, which is a true interest rate of 8.097%pa.

Since the purpose of the fee is to cover administration costs that are independent of the size of the principal, the smaller the principal then the higher that fees are as a proportion of the total cost of borrowing. When such fees are present, lenders are regularly required to provide information on the 'true' cost of finance after including the additional fees and expenses, although details may vary by jurisdiction.

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), 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.

Interest in business practice

Lending can take place at the retail level or the corporate level.

Retail means front counter service to natural people and small businesses run by owner-operators.

Banking at the corporate level means the regular financing needs of corporations, and also governments. Here the lending focus is often upon the use of negotiable instruments issued by the corporation or government.

Retail lending

The determination of interest for retail lending is simple because it the loans are generally fixed as being between a specific borrower and a specific lender.

The retail loan may be either short-term or long-term. Short term loans are fixed rate, while longer term loans may be either fixed or variable rate.

Discount instruments

Interest on short-term debts, such as Bills of exchange and promissory notes, is received through discounting. In a discount instrument, the payment and receipt of interest is bound up with the purchase and sale of the whole instrument. A given instrument will have a value stated on its face (hence, face-value) as receivable by the holder on a certain date. Prior to that date the instrument has an actual present value less than that face value. The interest is earned by the lender by way of purchasing that instrument at this lesser value and holding it either until maturation or sale to another. As time passes the face value climbs higher, and upon sale or maturation the net gain is the interest component of the whole receipts. Similarly, for the borrower the interest expense comes from receiving at the outset only a value discounted from the face value while paying that full face value upon maturation.

Coupon-bearing instruments

Interest on longer term debts, such as bonds, is usually physically separate from that of the principal. The term coupon comes from the time when lenders who bought bonds physically had to detach paper coupons from the bond document and then mail them to the issuer. The issuer would mail back a cheque for the amount on that coupon. Today this is done electronically.

The nominal interest rate on a bond is the ratio of the coupons to the principal value. For example, on a $100,000 bond paying a nominal 6% pa on two coupons per year, each coupon would pay each $300, which is 3% of the principal . This 3% rate is the coupon rate, and is fixed for the life of the bond.

This rate differs from the fluctuating market rate of interest that is actually used to value the bond as a whole. As the relative and absolute financial situation of the issuing body changes, the market rate of interest that is applicable to the issuer’s instruments of a given type also varies. When the market rate happens to match the coupon rate, then the bond will be valued at par. That is, its actual value in the market will be equal to the face value that will be paid back on maturity. However, if the market rate falls below the coupon rate then that bond is paying more than the market requires the issuer to pay on a bond of that type. This causes the value of the existing bonds to rise, which are then said to sell at a premium to face value. Similarly, if the market rate required rises above the actual coupon rate then the bond is seen to be worth less than the face value and is said to be trading at a discount.

As the interest is paid separately from the repayment of the principal, each is also valued separately. Each future payment (both coupon and principal) is individually discounted using whatever interest rate the valuer deems appropriate. The value of the bond is the sum of all those discounted values. If the rate used is the same as the coupon rate then the bond value will be equal to the face value. If the rate used is above the coupon rate then the bond value will be below the face value, and the bond is said to trade at discount. If on the other hand the rate used is below the coupon rate then the present value will be above the face value, and the bond is said to trade at a premium.

Hybrid instruments

Hybrid securities are those that have features of both debt and equity instruments. For example, perpetual bonds are debt instruments that share with equity the feature of never maturing, while preference shares are equity instruments that share with debt the feature of paying fixed interest. Both of these have values calculated in the same basic way.

Non-monetary lending

Although far and away the most common asset lent by value is cash, there is also a substantial number of lending transactions where the resources lent are not money. Nevertheless, since they are still advanced by a lender and taken by a borrower on credit, the interest payable on the assigned value as principal is the same.

On the retail level, a common example most people will be familiar with is hire purchase agreements with the stores who sell and hire out consumer goods. The sale price of the consumer good in question, plus any facility establishment costs and the like, become part of the principal. An interest rate is set, and the hirer-purchaser pays regular amounts to the lender-seller that are composed of part interest and part principal in identical mathematical fashion to an amortising loan. Agreements may also include complications that change the effective interest payable on the principal.

There are a few different types of securities lending. One of the more controversial, and the most common reason for securities lending, is the practice of short-selling shares. In this case, a broker lends shares to a client, who then sells them. The client must pay interest to the broker on the value of the shares at the initiation of the entire procedure, and must return the same number of shares back on an agreed date irrespective of their value at that date.

A finance lease or capital lease is a type of lease - the other being an operating lease. The lessee must pay the lessor interest upon the agreed principal value of the leased resources, with these payments being admixed with payment of principal.

A change in terminology often results when resources other than money are involved. For example, when the resource lent is real estate or commercial property, the fee is called rent instead. See the discussion on the relationships of interest and rent. In some instances rental rates are explicitly synonymous with interest rates, and the terms rent and interest are used together in the same contract, such as in hire-purchase agreements.

All of the above involved the payment of the interest, whether by that name or another, in the form of money, but the interest need not be payable in money for it still to be interest. For example, the largest of the major banks - who have special relationships with central banks - can and do still engage in direct gold lending. As well as the gold principal being returned at a future point, the periodic interest is also payable in gold. The interest rates on gold loans are very low, being of the order of 1-2%, because there is no need for an inflation premium.

Accounting and taxation treatment of interest

Interest on short-term debt is part of business operating revenue for the creditor, built into the revenues of sales of what was sold on credit. On the other side, interest for the debtor is properly capitalised as an asset rather than an expense, just as payments for inventory and wages should be, because what it paid for (inputs on credit) still exists as an identifiable and recognisable asset of the business (inventory, recorded at total historical cost). That interest is not recognised as an expense until the assets generated are sold. Then the interest is an expense, as a component of Cost Of Goods Sold (COGS).

Interest is an actual expense, recognised as soon as it is accrued or paid as appropriate for the accounting basis used.

What type of an expense it is recognised as depends on the actual nature of the credit that gave rise to the expense. The distinction follows that between non-capital and capital borrowings.

Interest expense non-capital borrowings will be included in operating expenditure because it is part of operating methods and the inventory cycle.

By contrast, interest on capital is treated as an expense entirely separate to operations. However, it is not for that reason a capital expenditure because it is still an actual expense - capital expenditures are generally booked as assets rather than expenses.

As a general rule, business may deduct interest and interest-like payments from taxable income as expenses, so long as they are incurred in the process of generating taxable income. Nevertheless, there are different taxation treatments for interest for different circumstances, and change for different jurisdictions. For example, interest on a loan to purchase one’s own home is (in 2007) deductible against personal income under US income tax rules, but not under Australian personal income tax rules.

Interest in history

Ancient

The charging of interest dates back to 1500 B.C. among the Sumerian and Egyptian cultures.

Medieval

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.

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.

Renaissance

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 money 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.

Arguments over interest held today

Arguments against

Moral

Some argue that Islamic banking ought to be interest-free by law.

See also

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

References

Economics:

• Menger, C (2004) Principles of Economics, Ludwig von Mises Institute electronic version of Libertarian Books Edition. Full book is available online.
• Reisman, G, (1998) Capitalism: A treatise on economics, Jameson Books, Ottawa. ISBN 0-915463-73-3. Full book is available online.
• von Mises, L, (1981) The theory of money and credit, Liberty Classics, Indianapolis,. Ind. ISBN 0-913966-70-3. Hardcover. (Softcover ISBN 0-913966-71-1).
• Böhm-Bawerk, E (1959) Capitalism and interest, Libertarian Books Edition. The three volumes – History & Critique, Positive Theory, and Further Essays - are in a single bound set.

Supplier pricing:

• 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.

History:

• Colish, Marcia, "Medieval Foundations of the Western Intellectual Tradition 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

External links

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