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An interest rate is the amount of
interest In and , interest is payment from a or deposit-taking financial institution to a or depositor of an amount above repayment of the (that is, the amount borrowed), at a particular rate. It is distinct from a which the borrower may pay the len ...

interest
due per period, as a proportion of the amount lent, deposited, or borrowed (called the
principal sum Debt is an obligation that requires one party, the debtor A debtor or debitor is a legal entity (legal person) that owes a debt Debt is an obligation that requires one party, the debtor, to pay money or other agreed-upon value to ...
). The total interest on an amount lent or borrowed depends on the principal sum, the interest rate, the compounding frequency, and the length of time over which it is lent, deposited, or borrowed. The interest rate is defined as the proportion of an amount loaned which a lender charges as interest to the borrower, normally expressed as an annual percentage. It is the rate a bank or other lender charges to borrow its money, or the rate a bank pays its savers for keeping money in an account. The annual interest rate is the rate over a period of one year. Other interest rates apply over different periods, such as a month or a day, but they are usually annualized. The interest rate has been characterized as "an index of the preference . . . for a dollar of present ncomeover a dollar of future income." The borrower wants, or needs, to have money sooner rather than later, and is willing to pay a fee—the interest rate—for that privilege.


Influencing factors

Interest rates vary according to: * the government's directives to the central bank to accomplish the government's goals * the currency of the principal sum lent or borrowed * the term to maturity of the investment * the perceived default probability of the borrower * supply and demand in the market * the amount of collateral * special features like call provisions * reserve requirements * compensating balance as well as other factors.


Example

A company borrows
capital Capital most commonly refers to: * Capital letter Letter case (or just case) is the distinction between the letters that are in larger uppercase or capitals (or more formally ''majuscule'') and smaller lowercase (or more formally ''minusc ...
from a bank to buy assets for its business. In return, the bank charges the company interest. (The lender might also require rights over the new assets as
collateral Collateral may refer to: Business and finance * Collateral (finance) In loan agreement, lending agreements, collateral is a Borrower, borrower's pledge (law), pledge of specific property to a lender, to Secured loan, secure repayment of a loan. ...
.) A bank will use the capital deposited by individuals to make loans to their clients. In return, the bank should pay individuals who have deposited their capital interest. The amount of interest payment depends on the interest rate and the amount of capital they deposited.


Related terms

''Base rate'' usually refers to the annualized rate offered on overnight deposits by the central bank or other monetary authority. The ''Annual percentage rate'' (APR) may refer either to a nominal APR or an effective APR (EAPR). The difference between the two is that the EAPR accounts for fees and compounding, while the nominal APR does not. The ''annual equivalent rate'' (AER), also called the effective annual rate, is used to help consumers compare products with different compounding frequencies on a common basis, but does not account for fees. A ''discount rate'' is applied to calculate
present value In economics Economics () is a social science Social science is the Branches of science, branch of science devoted to the study of society, societies and the Social relation, relationships among individuals within those societies. ...
. For an interest-bearing security, ''
coupon rate In marketing, a coupon is a ticket or document that can be redeemed for a financial discount or rebate when purchasing a product. Customarily, coupons are issued by manufacturers of consumer packaged goods or by retailers, to be used in r ...
'' is the ratio of the annual coupon amount (the coupon paid per year) per unit of par value, whereas ''
current yield The current yield, interest yield, income yield, flat yield, market yield, mark to market yield or running yield is a financial Finance is a term for the management, creation, and study of money and investments. Pamela Drake and Frank Fabozz ...
'' is the ratio of the annual coupon divided by its current market price. ''
Yield to maturity The yield to maturity (YTM), book yield or redemption yield of a bond Bond or bonds may refer to: Common meanings * Bond (finance) In finance Finance is the study of financial institutions, financial markets and how they operate within ...
'' is a bond's expected
internal rate of return Internal rate of return (IRR) is a method of calculating an investment To invest is to allocate money Image:National-Debt-Gillray.jpeg, In a 1786 James Gillray caricature, the plentiful money bags handed to King George III are contrasted wi ...
, assuming it will be held to maturity, that is, the discount rate which equates all remaining cash flows to the investor (all remaining coupons and repayment of the par value at maturity) with the current market price. Based on the banking business, there are deposit interest rate and loan interest rate. Based on the relationship between supply and demand of market interest rate, there are fixed interest rate and floating interest rate.


Monetary policy

''Interest rate targets'' are a vital tool of
monetary policy Monetary policy is the policy adopted by the monetary authority In finance and economics, a monetary authority is the entity that manages a country’s currency and money supply, often with the objective of controlling inflation targeting, infla ...

monetary policy
and are taken into account when dealing with variables like
investment Investment is the dedication of an asset to attain an increase in value over a period of time. Investment requires a sacrifice of some present asset, such as time, money, or effort. In finance Finance is the study of financial institution ...

investment
,
inflation In economics, inflation refers to a general progressive increase in prices of goods and services in an economy. When the general price level rises, each unit of currency buys fewer goods and services; consequently, inflation corresponds to a r ...

inflation
, and
unemployment Unemployment, according to the OECD The Organisation for Economic Co-operation and Development (OECD; french: Organisation de Coopération et de Développement Économiques, OCDE) is an intergovernmental economic organisation with 38&nbs ...
. The
central bank A central bank, reserve bank, or monetary authority is an institution that manages the and of a or formal monetary union, and oversees their . In contrast to a , a central bank possesses a on increasing the . Most central banks also have ...

central bank
s of countries generally tend to reduce interest rates when they wish to increase investment and consumption in the country's economy. However, a low interest rate as a macro-economic policy can be
risky
risky
and may lead to the creation of an
economic bubble An economic bubble is a situation in which asset prices are much higher than the underlying fundamentals can reasonably justify. Bubbles are sometimes caused by unlikely and overly optimistic projections about the future. It could also be describ ...
, in which large amounts of investments are poured into the real-estate market and stock market. In developed economies, interest-rate adjustments are thus made to keep inflation within a target range for the health of
economic activities Economics () is the social science that studies how people interact with value; in particular, the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. ...
or cap the interest rate concurrently with
economic growth Economic growth can be defined as the increase or improvement in the inflation-adjusted market value of the goods and services produced by an economics, economy over time. Statisticians conventionally measure such growth as the percent rate of i ...

economic growth
to safeguard economic
momentum In Newtonian mechanics, linear momentum, translational momentum, or simply momentum is the product of the mass Mass is the quantity Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinui ...

momentum
.


History

In the past two centuries, interest rates have been variously set either by national governments or central banks. For example, the Federal Reserve federal funds rate in the United States has varied between about 0.25% and 19% from 1954 to 2008, while the
Bank of England The Bank of England is the central bank of the United Kingdom and the model on which most modern central banks have been based. Established in 1694 to act as the Kingdom of England, English Government's banker, and still one of the bankers for t ...

Bank of England
base rate varied between 0.5% and 15% from 1989 to 2009, and Germany experienced rates close to 90% in the 1920s down to about 2% in the 2000s. During an attempt to tackle spiraling hyperinflation in 2007, the Central Bank of Zimbabwe increased interest rates for borrowing to 800%. The interest rates on prime credits in the late 1970s and early 1980s were far higher than had been recorded – higher than previous US peaks since 1800, than British peaks since 1700, or than Dutch peaks since 1600; "since modern capital markets came into existence, there have never been such high long-term rates" as in this period. Possibly before modern capital markets, there have been some accounts that savings deposits could achieve an annual return of at least 25% and up to as high as 50%. (William Ellis and Richard Dawes, "Lessons on the Phenomenon of Industrial Life... ", 1857, p III–IV)


Reasons for changes

* Political short-term gain: Lowering interest rates can give the economy a short-run boost. Under normal conditions, most economists think a cut in interest rates will only give a short term gain in economic activity that will soon be offset by inflation. The quick boost can influence elections. Most economists advocate independent central banks to limit the influence of politics on interest rates. * Deferred consumption: When money is loaned the lender delays spending the money on
consumption Consumption may refer to: *Resource consumption *Tuberculosis, an infectious disease, historically in biology: * Consumption (ecology), receipt of energy by consuming other organisms in social sciences: * Consumption (economics), the purchasing of ...
goods. Since according to
time preference In economics, time preference (or time discounting, delay discounting, temporal discounting, long-term orientation) is the current relative valuation placed on receiving a good or some cash In economics Economics () is the social sci ...
theory people prefer goods now to goods later, in a free market there will be a positive interest rate. * Inflationary expectations: Most economies generally exhibit
inflation In economics, inflation refers to a general progressive increase in prices of goods and services in an economy. When the general price level rises, each unit of currency buys fewer goods and services; consequently, inflation corresponds to a r ...

inflation
, meaning a given amount of money buys fewer goods in the future than it will now. The borrower needs to compensate the lender for this. * Alternative investments: The lender has a choice between using his money in different investments. If he chooses one, he forgoes the returns from all the others. Different investments effectively compete for funds. * Risks of investment: There is always a risk that the borrower will go
bankrupt Bankruptcy is a legal process through which people or other entities who cannot repay debts to creditors may seek relief from some or all of their debts. In most jurisdictions, bankruptcy is imposed by a court order, often initiated by the debtor. ...

bankrupt
, abscond, die, or otherwise
default Default may refer to: Law * Default (law), the failure to do something required by law ** Default (finance) In finance Finance is the study of financial institutions, financial markets and how they operate within the financial system. It ...
on the loan. This means that a lender generally charges a
risk premium Overview A risk premium is a measure of excess return that is required by an individual to compensate them for being subjected to an increased level of risk. It is used widely in finance and economics with the general definition being the expect ...
to ensure that, across his investments, he is compensated for those that fail. * Liquidity preference: People prefer to have their resources available in a form that can immediately be exchanged, rather than a form that takes time to realize. * Taxes: Because some of the gains from interest may be subject to taxes, the lender may insist on a higher rate to make up for this loss. * Banks: Banks can tend to change the interest rate to either slow down or speed up economy growth. This involves either raising interest rates to slow the economy down, or lowering interest rates to promote economic growth. * Economy: Interest rates can fluctuate according to the status of the economy. It will generally be found that if the economy is strong then the interest rates will be high, if the economy is weak the interest rates will be low.


Non-market-based theories

Some economists like
Karl Marx Karl Heinrich Marx (; 5 May 1818 – 14 March 1883) was a German philosopher A philosopher is someone who practices philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about reason, M ...

Karl Marx
argue that interest rates are not actually set purely by market competition. Rather they argue that interest rates are ultimately set in line with social customs and legal institutions.
Karl Marx Karl Heinrich Marx (; 5 May 1818 – 14 March 1883) was a German philosopher A philosopher is someone who practices philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about reason, M ...

Karl Marx
writes:
"Customs, juristic tradition, etc., have as much to do with determining the average rate of interest as competition itself, in so far as it exists not merely as an average, but rather as actual magnitude. In many law disputes, where interest has to be calculated, an average rate of interest has to be assumed as the legal rate. If we inquire further as to why the limits of a mean rate of interest cannot be deduced from general laws, we find the answer lies simply in the nature of interest."


Real vs nominal

The
nominal interest rateIn finance and economics, the nominal interest rate or nominal rate of interest is either of two distinct things: # the rate of interest In finance Finance is the study of financial institutions, financial markets and how they operate within ...
is the rate of interest with no adjustment for
inflation In economics, inflation refers to a general progressive increase in prices of goods and services in an economy. When the general price level rises, each unit of currency buys fewer goods and services; consequently, inflation corresponds to a r ...

inflation
. For example, suppose someone deposits $100 with a bank for 1 year, and they receive interest of $10 (before tax), so at the end of the year, their balance is $110 (before tax). In this case, regardless of the rate of inflation, the
nominal interest rateIn finance and economics, the nominal interest rate or nominal rate of interest is either of two distinct things: # the rate of interest In finance Finance is the study of financial institutions, financial markets and how they operate within ...
is 10% ''per annum'' (before tax). The
real interest rate The real interest rate is the rate of interest an investor, saver or lender receives (or expects to receive) after allowing for inflation. It can be described more formally by the Fisher equation In financial mathematicsMathematical finance, also ...
measures the growth in real value of the loan plus interest, taking
inflation In economics, inflation refers to a general progressive increase in prices of goods and services in an economy. When the general price level rises, each unit of currency buys fewer goods and services; consequently, inflation corresponds to a r ...

inflation
into account. The repayment of principal plus interest is measured in real terms compared against the
buying power Bargaining power is the relative power of parties in a situation to exert influence over each other. If both parties are on an equal footing in a debate, then they will have equal bargaining power, such as in a perfectly competitive market In eco ...
of the amount at the time it was borrowed, lent, deposited or invested. If inflation is 10%, then the $110 in the account at the end of the year has the same purchasing power (that is, buys the same amount) as the $100 had a year ago. The
real interest rate The real interest rate is the rate of interest an investor, saver or lender receives (or expects to receive) after allowing for inflation. It can be described more formally by the Fisher equation In financial mathematicsMathematical finance, also ...
is zero in this case. The real interest rate is given by the
Fisher equation In financial mathematicsMathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets. Generally, mathematical finance will derive a ...
: : r = \frac-1\,\! where ''p'' is the inflation rate. For low rates and short periods, the
linear approximation In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It ...
applies: : r \approx i-p\,\! The Fisher equation applies both ''
ex ante The term ''ex-ante'' (sometimes written ''ex ante'' or ''exante'') is a phrase meaning "before the event". Ex-ante or notional demand refers to the desire for goods and services which is not backed by the ability to pay for those goods and services. ...
'' and ''
ex post Notes and references Notes References Sources * * * Further reading * * {{Latin phrases E ...
''. ''Ex ante'', the rates are projected rates, whereas ''ex post'', the rates are historical.


Market rates

There is a
market Market may refer to: *Market (economics) *Market economy *Marketplace, a physical marketplace or public market Geography *Märket, an island shared by Finland and Sweden Art, entertainment, and media Films *Market (1965 film), ''Market'' (1965 ...
for investments, including the
money market The money market is a component of the economy which provides short-term funds. The money market deals in short-term loans, generally for a period of a year or less. As short-term securities became a commodity In economics Economic ...
,
bond market The bond market (also debt market or credit market) is a financial market A financial market is a market Market may refer to: *Market (economics) *Market economy *Marketplace, a physical marketplace or public market Geography *Märket, an i ...
,
stock market A stock market, equity market, or share market is the aggregation of buyers and sellers of stock In finance, stock (also capital stock) consists of all of the shares In financial markets A financial market is a market in whic ...

stock market
, and
currency market The foreign exchange market (Forex, FX, or currency market) is a global decentralization, decentralized or Over-the-counter (finance), over-the-counter (OTC) market for the trading of currency, currencies. This market determines Exchange rate ...
as well as retail
bank A bank is a financial institution Financial institutions, otherwise known as banking institutions, are corporation A corporation is an organization—usually a group of people or a company—authorized by the State (polity), stat ...

bank
ing. Interest rates reflect: * The risk-free cost of capital * Expected
inflation In economics, inflation refers to a general progressive increase in prices of goods and services in an economy. When the general price level rises, each unit of currency buys fewer goods and services; consequently, inflation corresponds to a r ...

inflation
*
Risk premium Overview A risk premium is a measure of excess return that is required by an individual to compensate them for being subjected to an increased level of risk. It is used widely in finance and economics with the general definition being the expect ...
*
Transaction cost In economics and related disciplines, a transaction cost is a cost in making any economic trade when participating in a Market (economics), market. Oliver E. Williamson defines transaction costs as the costs of running an economic system of companie ...
s


Inflationary expectations

According to the theory of
rational expectations In economics, "rational expectations" are model-consistent expectations, in that agent (economics), agents inside the model (economics), model are assumed to "know the model" and on average take the model's predictions as valid. Rational expectat ...
, borrowers and lenders form an expectation of
inflation In economics, inflation refers to a general progressive increase in prices of goods and services in an economy. When the general price level rises, each unit of currency buys fewer goods and services; consequently, inflation corresponds to a r ...

inflation
in the future. The acceptable nominal interest rate at which they are willing and able to borrow or lend includes the
real interest rate The real interest rate is the rate of interest an investor, saver or lender receives (or expects to receive) after allowing for inflation. It can be described more formally by the Fisher equation In financial mathematicsMathematical finance, also ...
they require to receive, or are willing and able to pay, plus the rate of
inflation In economics, inflation refers to a general progressive increase in prices of goods and services in an economy. When the general price level rises, each unit of currency buys fewer goods and services; consequently, inflation corresponds to a r ...

inflation
they expect.


Risk

The level of
risk In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty Uncertainty refers to Epistemology, epistemic situations involving imperfect or unknown information. It applies to predictions of future events, to ...

risk
in investments is taken into consideration. Riskier investments such as
shares In financial markets A financial market is a market in which people trade financial securities and derivatives at low transaction costs. Some of the securities include stocks and bonds, raw materials and precious metals, which are known ...
and
junk bond In finance Finance is the study of financial institutions, financial markets and how they operate within the financial system. It is concerned with the creation and management of money and investments. Savers and investors have money availab ...
s are normally expected to deliver higher returns than safer ones like
government bond A government bond or sovereign bond is an debt obligation issued by a national government to support government spending. It generally includes a commitment to pay periodic interest, called ''coupon payments,'' and to repay the face value on t ...
s. The additional return above the risk-free nominal interest rate which is expected from a risky investment is the
risk premium Overview A risk premium is a measure of excess return that is required by an individual to compensate them for being subjected to an increased level of risk. It is used widely in finance and economics with the general definition being the expect ...
. The risk premium an investor requires on an investment depends on the risk preferences of the investor. Evidence suggests that most lenders are risk-averse. A maturity risk premium applied to a longer-term investment reflects a higher perceived risk of default. There are four kinds of risk: * repricing risk * basis risk * yield curve risk * optionality


Liquidity preference

Most investors prefer their money to be in
cash In economics Economics () is a social science Social science is the Branches of science, branch of science devoted to the study of society, societies and the Social relation, relationships among individuals within those societie ...
rather than in less
fungible In economics Economics () is the social science that studies how people interact with value; in particular, the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of good ...
investments. Cash is on hand to be spent immediately if the need arises, but some investments require time or effort to transfer into spendable form. The preference for cash is known as
liquidity preference__NOTOC__ In macroeconomic theory, liquidity preference is the demand for money In monetary economics Monetary economics is the branch of economics that studies the different competing theories of money: it provides a framework for analyzing ...
. A 1-year loan, for instance, is very liquid compared to a 10-year loan. A 10-year US
Treasury bond United States Treasury securities are government debt In public finance, government debt, also known as public interest, public debt, national debt and sovereign debt, is the total amount of debt owed at a point in time by a government or s ...
, however, is still relatively liquid because it can easily be sold on the market.


A market model

A basic interest rate pricing model for an asset is : i_n = i_r + p_e + r_p + l_p\,\! where : ''in'' is the nominal interest rate on a given investment :''ir'' is the risk-free return to capital : ''i*n'' is the nominal interest rate on a short-term risk-free liquid bond (such as U.S. Treasury bills). : ''rp'' is a risk premium reflecting the length of the investment and the likelihood the borrower will default : ''lp'' is a liquidity premium (reflecting the perceived difficulty of converting the asset into money and thus into goods). : ''pe'' is the expected inflation rate. Assuming perfect information, ''pe'' is the same for all participants in the market, and the interest rate model simplifies to : i_n = i^*_n + r_p + l_p\,\!


Spread

The ''spread'' of interest rates is the lending rate minus the deposit rate. This spread covers operating costs for banks providing loans and deposits. A ''negative spread'' is where a deposit rate is higher than the lending rate.


In macroeconomics


Output and unemployment

Higher interest rates increase the cost of borrowing which can reduce
physical investment Investment is the amount of Good (economics), goods purchased or accumulated per unit time which are not consumed at the present time. The types of investment are residential investment in housing that will provide a flow of housing services over a ...
and output and increase unemployment. Higher rates encourage more saving and reduce inflation.


Open market operations in the United States

The Federal Reserve (often referred to as 'the Fed') implements
monetary policy Monetary policy is the policy adopted by the monetary authority In finance and economics, a monetary authority is the entity that manages a country’s currency and money supply, often with the objective of controlling inflation targeting, infla ...

monetary policy
largely by targeting the federal funds rate. This is the rate that banks charge each other for overnight loans of
federal funds In the United States The United States of America (USA), commonly known as the United States (U.S. or US), or America, is a country Contiguous United States, primarily located in North America. It consists of 50 U.S. state, states, a Wa ...
, which are the reserves held by banks at the Fed.
Open market operation An open market operation (OMO) is an activity by a central bank A central bank, reserve bank, or monetary authority is an institution that manages the currency and monetary policy of a State (polity), state or formal monetary union, and over ...
s 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 A security is a tradable financial asset A financial asset is a non-physical asset In financial accounting Financial accounting is the field of accounting Accounting or Accountancy is the measurement, processing, and communication o ...
.


Money and inflation

Loans, bonds, and shares have some of the characteristics of money and are included in the
broad money In economics Economics () is the social science that studies how people interact with value; in particular, the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods an ...
supply. By setting i*n, the government institution can affect the markets to alter the total of loans, bonds and shares issued. Generally speaking, a higher real interest rate reduces the broad money supply. Through the
quantity theory of money#REDIRECT Quantity theory of money In monetary economics, the quantity theory of money (QTM) states that the general price level of goods and services is directly proportional to the amount of money in circulation, or money supply In macroeco ...
, increases in the money supply lead to inflation.


Impact on savings and pensions

Financial economist Financial economics is the branch of economics Economics () is the social science that studies how people interact with value; in particular, the Production (economics), production, distribution (economics), distribution, and Consumption ( ...
s such as World Pensions Council (WPC) researchers have argued that durably low interest rates in most G20 countries will have an adverse impact on the
funding Funding is the act of providing resources A resource is a source or supply from which a benefit is produced and that has some utility. Resources can broadly be classified upon their availability — they are classified into renewable and non-re ...

funding
positions of pension funds as "without returns that outstrip inflation, pension investors face the real value of their savings declining rather than ratcheting up over the next few years". Current interest rates in savings accounts often fail to keep up with the pace of inflation. From 1982 until 2012, most Western economies experienced a period of low inflation combined with relatively high returns on investments across all
asset class In finance, an asset class is a group of financial instrument Finance is the study of financial institutions, financial markets and how they operate within the financial system. It is concerned with the creation and management of money I ...
es including government bonds. This brought a certain sense of complacency amongst some pension
actuarial Actuarial science is the discipline that applies mathematics, mathematical and statistics, statistical methods to Risk assessment, assess risk in insurance, finance, and other industries and professions. More generally, actuaries apply rigorous m ...
consultants and
regulators Regulator may refer to: Technology * Regulator (automatic control), a device that maintains a designated characteristic, as in: ** Battery regulator ** Pressure regulator ** Diving regulator ** Voltage regulator * Regulator (sewer), a control devic ...
, making it seem reasonable to use optimistic economic assumptions to calculate the
present value In economics Economics () is a social science Social science is the Branches of science, branch of science devoted to the study of society, societies and the Social relation, relationships among individuals within those societies. ...
of future pension liabilities.


Mathematical note

Because interest and inflation are generally given as percentage increases, the formulae above are (linear) approximations. For instance, : i_n = i_r + p_e\,\! is only approximate. In reality, the relationship is : (1 + i_n) = (1 + i_r)(1 + p_e)\,\! so : i_r = \frac - 1\,\! The two approximations, eliminating higher order terms, are: :\begin (1+x)(1+y) &= 1+x+y+xy &&\approx 1+x+y\\ \frac &= 1-x+x^2-x^3+\cdots &&\approx 1-x \end The formulae in this article are exact if
logarithmic unit A logarithmic scale (or log scale) is a way of displaying numerical data over a very wide range of values in a compact way—typically the largest numbers in the data are hundreds or even thousands of times larger than the smallest numbers. Such a s ...
s are used for relative changes, or equivalently if
logarithm In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained (), and quantities and their changes ( and ). There is no ...

logarithm
s of indices are used in place of rates, and hold even for large relative changes.


Zero rate policy

A so-called "zero interest-rate policy" (ZIRP) is a very low—near-zero—central bank target interest rate. At this
zero lower boundThe Zero Lower Bound (''ZLB'') or Zero Nominal Lower Bound (''ZNLB'') is a macroeconomic problem that occurs when the short-term nominal interest rate is at or near zero, causing a liquidity trap and limiting the central bank's capacity to stimulate ...
the central bank faces difficulties with conventional monetary policy, because it is generally believed that market interest rates cannot realistically be pushed down into negative territory.


Negative nominal or real rates

''Nominal'' interest rates are normally positive, but not always. In contrast, ''real'' interest rates can be negative, when nominal interest rates are below inflation. When this is done via government policy (for example, via reserve requirements), this is deemed
financial repression Financial repression comprises "policies that result in savers earning returns below the rate of inflation" in order to allow banks to "provide cheap loans to companies and governments, reducing the burden of repayments". It can be particularly eff ...
, and was practiced by countries such as the United States and United Kingdom following World War II (from 1945) until the late 1970s or early 1980s (during and following the
Post–World War II economic expansion The post–World War II economic expansion, also known as the postwar economic boom or the Golden Age of Capitalism, was a broad period of worldwide economic expansion An economic expansion is an increase in the level of economic activity ...
). In the late 1970s, United States Treasury securities with negative real interest rates were deemed ''certificates of confiscation''.


On central bank reserves

A so-called "negative interest rate policy" (NIRP) is a negative (below zero) central bank target interest rate.


Theory

Given the alternative of holding cash, and thus earning 0%, rather than lending it out, profit-seeking lenders will not lend below 0%, as that will guarantee a loss, and a bank offering a negative deposit rate will find few takers, as savers will instead hold cash. Negative interest rates have been proposed in the past, notably in the late 19th century by
Silvio Gesell Johann Silvio Gesell (; 17 March 1862 – 11 March 1930) was a German-Argentine merchant A merchant is a person who trades in commodities produced by other people, especially one who trades with foreign countries. Historically, a merchant is ...
. A negative interest rate can be described (as by Gesell) as a "tax on holding money"; he proposed it as the ''
Freigeld As part of the theory of Freiwirtschaft, Freigeld ('free money', ) is a monetary In a 1786 James Gillray caricature, the plentiful money bags handed to King George III are contrasted with the beggar whose legs and arms were amputated, in ...
'' (free money) component of his ''
Freiwirtschaft ( German for "free economy") is an economic idea In philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about reason, Metaphysics, existence, Epistemology, knowledge, Ethics, values, Philosop ...
'' (free economy) system. To prevent people from holding cash (and thus earning 0%), Gesell suggested issuing money for a limited duration, after which it must be exchanged for new bills; attempts to hold money thus result in it expiring and becoming worthless. Along similar lines,
John Maynard Keynes John Maynard Keynes, 1st Baron Keynes, ( ; 5 June 1883 – 21 April 1946) was an English economist An economist is a professional and practitioner in the social science Social science is the branch The branches and leaves of a ...

John Maynard Keynes
approvingly cited the idea of a carrying tax on money, (1936, ''
The General Theory of Employment, Interest and Money ''The General Theory of Employment, Interest and Money'' of 1936 is a book by English economist John Maynard Keynes John Maynard Keynes, 1st Baron Keynes, ( ; 5 June 1883 – 21 April 1946) was an English economist, whose ideas fundamenta ...
'') but dismissed it due to administrative difficulties. More recently, a carry tax on currency was proposed by a
Federal Reserve The Federal Reserve System (also known as the Federal Reserve or simply the Fed) is the central banking system of the United States of America. It was created on December 23, 1913, with the enactment of the Federal Reserve Act, after a series ...

Federal Reserve
employee (Marvin Goodfriend) in 1999, to be implemented via magnetic strips on bills, deducting the carry tax upon deposit, the tax being based on how long the bill had been held. It has been proposed that a negative interest rate can in principle be levied on existing paper currency via a
serial number A serial number is a unique identifier A unique identifier (UID) is an identifier An identifier is a name that identifies (that is, labels the identity of) either a unique object or a unique ''class'' of objects, where the "object" or class ...

serial number
lottery, such as randomly choosing a number 0 through 9 and declaring that notes whose serial number end in that digit are worthless, yielding an average 10% loss of paper cash holdings to hoarders; a drawn two-digit number could match the last two digits on the note for a 1% loss. This was proposed by an anonymous student of
Greg Mankiw Nicholas Gregory Mankiw (; born February 3, 1958) is an American macroeconomist who is currently the Robert M. Beren Professor of Economics at Harvard University. Mankiw is best known in academia for his work on New Keynesian economics. Mankiw h ...
, though more as a thought experiment than a genuine proposal.


Practice

Both the
European Central Bank The European Central Bank (ECB) is the prime component of the Eurosystem The Eurosystem is the monetary authority In finance Finance is the study of financial institutions, financial markets and how they operate within the financia ...

European Central Bank
starting in 2014 and the
Bank of Japan A bank is a financial institution Financial institutions, otherwise known as banking institutions, are corporations that provide services as intermediaries of financial markets. Broadly speaking, there are three major types of financial in ...

Bank of Japan
starting in early 2016 pursued the policy on top of their earlier and continuing
quantitative easing Quantitative easing (QE) is a monetary policy whereby a central bank purchases predetermined amounts of government bonds or other financial assets (e.g., municipal bonds, corporate bonds, stocks, etc.) in order to inject money into the economy to ...
policies. The latter's policy was said at its inception to be trying to 'change Japan's “deflationary mindset.”' In 2016 Sweden, Denmark and Switzerland—not directly participants in the
Euro The euro (currency symbol, symbol: euro sign, €; ISO 4217, code: EUR) is the official currency of 19 of the Member state of the European Union, member states of the European Union. This group of states is known as the eurozone or euro area ...

Euro
currency zone—also had NIRPs in place. Countries such as Sweden and Denmark have set negative interest on reserves—that is to say, they have charged interest on reserves. In July 2009, Sweden's central bank, the Riksbank, set its policy repo rate, the interest rate on its one-week deposit facility, at 0.25%, at the same time as setting its overnight deposit rate at −0.25%. The existence of the negative overnight deposit rate was a technical consequence of the fact that overnight deposit rates are generally set at 0.5% below or 0.75% below the policy rate. The Riksbank studied the impact of these changes and stated in a commentary report that they led to no disruptions in Swedish financial markets.


On government bond yields

During the
European debt crisis The European debt crisis, often also referred to as the eurozone crisis or the European sovereign debt crisis, is a multi-year debt crisis Debt crisis is a situation in which a government (nation, state/province, county, or city etc.) loses the ...
, government bonds of some countries (Switzerland, Denmark, Germany, Finland, the Netherlands and Austria) have been sold at negative yields. Suggested explanations include desire for safety and protection against the eurozone breaking up (in which case some eurozone countries might redenominate their debt into a stronger currency).


On corporate bond yields

For practical purposes, investors and academics typically view the yields on government or quasi-government bonds guaranteed by a small number of the most creditworthy governments (UK, USA, Switzerland, EU, Japan) to effectively have negligible default risk. As financial theory would predict, investors and academics typically do not view non-government guaranteed corporate bonds in the same way. Most credit analysts value them at a spread to similar government bonds with similar duration, geographic exposure, and currency exposure. Through 2018 there have only been a few of these corporate bonds that have traded at negative nominal interest rates. The most notable example of this was Nestle, some of whose AAA-rated bonds traded at negative nominal interest rate in 2015. However, some academics and investors believe this may have been influenced by volatility in the currency market during this period.


See also

*
Forward rate The forward rate is the future yield on a bond. It is calculated using the yield curve. For example, the yield on a three-month Treasury bill six months from now is a ''forward rate''.. Forward rate calculation To extract the forward rate, we n ...
* List of countries by central bank interest rates * Macroeconomics * Rate of return * Short-rate model * Spot contract#Bonds and swaps, Spot rate


Notes


References

* {{DEFAULTSORT:Interest Rate Interest rates, Mathematical finance Monetary policy