interest rate

TheInfoList

OR:

An interest rate is the amount of
interest In finance and economics, interest is payment from a debtor, borrower or deposit-taking financial institution to a lender or depositor of an amount above repayment of the principal sum (that is, the amount borrowed), at a particular rate. It is ...
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 entity (legal person) that owes a debt to another entity. The entity may be an individual, a firm, a government, a company or other le ...
). 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 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 may refer to: Common uses * Capital city, a municipality of primary status ** List of national capitals, List of national capital cities * Capital letter, an upper-case letter Economics and social sciences * Capital (economics), the dura ...
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.) 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
effective interest rate The effective interest rate (EIR), effective annual interest rate, annual equivalent rate (AER) or simply effective rate is the percentage of interest rate, interest on a loan or financial product if compound interest accumulates over a year duri ...
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 and finance, present value (PV), also known as present discounted value, is the value of an expected income stream determined as of the date of valuation. The present value is usually less than the future value because money has inte ...
. 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 ...
'' is the ratio of the annual coupon amount (the coupon paid per year) per unit of par value, whereas '' current yield'' 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 (finance), bond or other security (finance), fixed-interest security, such as Gilt-edged securities, gilts, is an estimate of the total rate of return anticipated to be earned ...
'' is a bond's expected
internal rate of return Internal rate of return (IRR) is a method of calculating an investment’s rate of return. The term ''internal'' refers to the fact that the calculation excludes external factors, such as the risk-free rate, inflation, the cost of capital, or fin ...
, 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 of a nation to control either the interest rate payable for federal funds, very short-term borrowing (borrowing by banks from each other to meet their short-term needs) or the money s ...
and are taken into account when dealing with variables like
investment Investment is the dedication of money to purchase 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, the purpose of investing is ...
,
inflation In economics, inflation is an increase in the general price level 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 reductio ...
, and
unemployment Unemployment, according to the OECD (Organisation for Economic Co-operation and Development), is people above a specified age (usually 15) not being in paid employment or self-employment but currently available for Work (human activity), w ...
. The
central bank A central bank, reserve bank, or monetary authority is an institution that manages the currency and monetary policy of a country or monetary union, and oversees their commercial bank, commercial banking system. In contrast to a commercial ba ...
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 and may lead to the creation of an
economic bubble An economic bubble (also called a speculative bubble or a financial bubble) is a period when current asset prices greatly exceed their Intrinsic theory of value, intrinsic valuation, being the valuation that the underlying long-term fundamentals ...
, 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 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 in a financial year. Statisticians conventionally measure such growth as the perce ...
to safeguard economic
momentum In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the Multiplication, product of the mass and velocity of an object. It is a Euclidean vector, vector quantity, possessing a magnitude and a dire ...
.

# 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, the federal funds rate is the interest rate at which depository institutions (banks and credit unions) lend reserve balances to other depository institutions overnight on an collateral (finance), uncollateralized basis ...
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 fo ...
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 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 Production (economics), good or some cash at an earlier date compared with ...
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 is an increase in the general price level 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 reductio ...
, 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 ...
, abscond, die, or otherwise
default Default may refer to: Law * Default (law), the failure to do something required by law ** Default (finance), failure to satisfy the terms of a loan obligation or failure to pay back a loan ** Default judgment, a binding judgment in favor of eit ...
on the loan. This means that a lender generally charges a
risk premium A risk premium is a measure of excess return that is required by an individual to compensate being subjected to an increased level of risk. It is used widely in finance and economics, the general definition being the expected risky Rate of retur ...
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.

# Real versus nominal

The
nominal interest rate In finance and economics, the nominal interest rate or nominal rate of interest is the rate of interest stated on a loan or investment, without any adjustments or fees. Examples of adjustments or fees # An adjustment for inflation(in contrast with ...
is the rate of interest with no adjustment for
inflation In economics, inflation is an increase in the general price level 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 reductio ...
. For example, suppose someone deposits $100 with a bank for one 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 rate In finance and economics, the nominal interest rate or nominal rate of interest is the rate of interest stated on a loan or investment, without any adjustments or fees. Examples of adjustments or fees # An adjustment for inflation(in contrast with ... 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, which states that the real interest rate is approxi ... measures the growth in real value of the loan plus interest, taking inflation In economics, inflation is an increase in the general price level 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 reductio ... into account. The repayment of principal plus interest is measured in real terms compared against the buying power 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, which states that the real interest rate is approxi ...
is zero in this case. The real interest rate is given by the Fisher equation: : $r = \frac-1\,\!$ where ''p'' is the inflation rate. For low rates and short periods, the linear approximation applies: : $r \approx i-p\,\!$ The Fisher equation applies both '' ex ante'' and ''
ex post References Notes References Further reading

* * {{Latin phrases Lists of Latin phrases, E ...
''. ''Ex ante'', the rates are projected rates, whereas ''ex post'', the rates are historical.

# Market rates

There is a market for investments, including the
money market The money market is a component of the economy that provides short-term funds. The money market deals in short-term loans, generally for a period of a year or less. As Security (finance)#Debt, short-term securities became a commodity, the mone ...
,
bond market The bond market (also debt market or credit market) is a financial market where participants can issue new debt, known as the primary market, or buy and sell debt security (finance), securities, known as the secondary market. This is usually in th ...
,
stock market A stock market, equity market, or share market is the aggregation of buyers and sellers of stocks (also called shares), which represent ownership claims on businesses; these may include ''securities'' listed on a public stock exchange, as ...
, 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 (economics), market for the trading of currency, currencies. This market d ...
as well as retail
bank A bank is a financial institution that accepts deposits from the public and creates a demand deposit while simultaneously making loans. Lending activities can be directly performed by the bank or indirectly through capital markets. Beca ...
ing. Interest rates reflect: * The risk-free cost of capital * Expected
inflation In economics, inflation is an increase in the general price level 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 reductio ...
*
Risk premium A risk premium is a measure of excess return that is required by an individual to compensate being subjected to an increased level of risk. It is used widely in finance and economics, the general definition being the expected risky Rate of retur ...
*
Transaction cost In economics Economics () is the social science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behavi ...
s

## Inflationary expectations

According to the theory of
rational expectations In economics Economics () is the social science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the be ...
, borrowers and lenders form an expectation of
inflation In economics, inflation is an increase in the general price level 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 reductio ...
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, which states that the real interest rate is approxi ...
they require to receive, or are willing and able to pay, plus the rate of
inflation In economics, inflation is an increase in the general price level 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 reductio ...
they expect.

## Risk

The level of
risk In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty about the effects/implications of an activity with respect to something that humans value (such as health, well-being, wealth, property or the environme ...
in investments is taken into consideration. Riskier investments such as
shares In finance, financial markets, a share is a unit of Equity (finance), equity ownership in the capital stock of a corporation, and can refer to units of mutual funds, limited partnerships, and real estate investment trusts. Share capital refers t ...
and
junk bond In finance Finance is the study and discipline of money, currency and capital assets. It is related to, but not synonymous with economics, the study of Production (economics), production, Distribution (economics), distribution, and Consump ...
s are normally expected to deliver higher returns than safer ones like
government bond A government bond or sovereign bond is a form of bond issued by a government A government is the system or group of people governing an organized community, generally a state. In the case of its broad associative definition, go ...
s. The additional return above the risk-free nominal interest rate which is expected from a risky investment is the
risk premium A risk premium is a measure of excess return that is required by an individual to compensate being subjected to an increased level of risk. It is used widely in finance and economics, the general definition being the expected risky Rate of retur ...
. 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, cash is money in the physical form of currency, such as banknotes and coins. In bookkeeping and financial accounting, cash is current assets comprising currency or currency equivalents that can be accessed immediately or near-immed ...
rather than in less
fungible In economics, fungibility is the property of a goods, good or a commodity whose individual units are essentially interchangeable, and each of whose parts is indistinguishable from any other part. Fungible tokens can be exchanged or replaced; f ...
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, considered as liquidity Liquidity is a concept in economics involving the convertibility of assets and obligations. It can include: * Market liquidity, the ea ...
. 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, also called Treasuries or Treasurys, are government bond, government debt instruments issued by the United States Department of the Treasury to finance government spending as an alternative to taxation. Sin ...
, 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 : $i_n = i^*_n + r_p + l_p\,\!$

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 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 of a nation to control either the interest rate payable for federal funds, very short-term borrowing (borrowing by banks from each other to meet their short-term needs) or the money s ...
largely by targeting the
federal funds rate In the United States, the federal funds rate is the interest rate at which depository institutions (banks and credit unions) lend reserve balances to other depository institutions overnight on an collateral (finance), uncollateralized basis ...
. This is the rate that banks charge each other for overnight loans of
federal funds In the United States, federal funds are overnight borrowings between banks and other entities to maintain their bank reserves at the Federal Reserve. Banks keep reserves at Federal Reserve Banks to meet their reserve requirements and to clear ...
, which are the reserves held by banks at the Fed.
Open market operation In macroeconomics, an open market operation (OMO) is an activity by a central bank to give (or take) liquidity in its currency to (or from) a bank or a group of banks. The central bank can either buy or sell government bonds (or other financial as ...
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. The term commonly refers to any form of financial instrument, but its legal definition varies by jurisdiction. In some countries and languages people commonly use the term "security" to refer to any for ...
.

## Money and inflation

Loans, bonds, and shares have some of the characteristics of money and are included in the
broad money In economics, broad money is a measure of the amount of money, or money supply, in a national economy including both highly liquid "narrow money" and less liquid forms. The European Central Bank, the OECD and the Bank of England all have their own ...
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 In monetary economics, the quantity theory of money (often abbreviated QTM) is one of the directions of Western economic thought that emerged in the 16th-17th centuries. The QTM states that the general price level of goods and services is directly ...
, increases in the money supply lead to inflation.

# Impact on savings and pensions

Financial economist Financial economics, also known as finance, is the branch of economics Economics () is the social science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consump ...
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 to finance a need, program, or project. While this is usually in the form of money, it can also take the form of effort or time from an organization or company. Generally, this word is used when a firm uses ...
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 classes including government bonds. This brought a certain sense of complacency amongst some pension actuarial consultants and regulators, making it seem reasonable to use optimistic economic assumptions to calculate the
present value In economics and finance, present value (PV), also known as present discounted value, is the value of an expected income stream determined as of the date of valuation. The present value is usually less than the future value because money has inte ...
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 : $\left(1 + i_n\right) = \left(1 + i_r\right)\left(1 + p_e\right)\,\!$ so : $i_r = \frac - 1\,\!$ The two approximations, eliminating higher order terms, are: :$\begin \left(1+x\right)\left(1+y\right) &= 1+x+y+xy &&\approx 1+x+y\\ \frac &= 1-x+x^2-x^3+\cdots &&\approx 1-x \end$ 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 are used for relative changes, or equivalently if
logarithm In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number  to the base  is the exponent to which must be raised, to produce . For example, since , the ''logarithm base'' 10 of ...
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 bound 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" to allow banks to "provide cheap loans to companies and governments, reducing the burden of repayments." It can be particularly effective a ...
, 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 beginning after World War II and ending with the 1973–1975 recession. The Un ...
). 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. A negative interest rate can be described (as by Gesell) as a "tax on holding money"; he proposed it as the '' Freigeld'' (free money) component of his '' Freiwirtschaft'' (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 whose ideas fundamentally changed the theory and practice of macroeconomics and the economic policies of governments. Originally trained in m ...
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'' is a book by English economist John Maynard Keynes published in February 1936. It caused a profound shift in economic thought, giving macroeconomics a central place in economic theory and ...
'') but dismissed it due to administrative difficulties. More recently, a carry tax on currency was proposed by a
Federal Reserve The Federal Reserve System (often shortened to 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 ...
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 assigned incrementally or sequentially to an item, to ''uniquely'' identify it. Serial numbers need not be strictly numerical. They may contain letters and other typographical symbols, or may consist enti ...
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 monetary Eurosystem and the European System of Central Banks (ESCB) as well as one of seven institutions of the European Union. It is one of the world's Big Four (banking)#Intern ...
starting in 2014 and the
Bank of Japan The is the central bank of Japan.Louis Frédéric, Nussbaum, Louis Frédéric. (2005). "Nihon Ginkō" in The bank is often called for short. It has its headquarters in Chūō, Tokyo, Chūō, Tokyo. History Like most modern Japanese instituti ...
starting in early 2016 pursued the policy on top of their earlier and continuing
quantitative easing Quantitative easing (QE) is a monetary policy action whereby a central bank purchases predetermined amounts of government bonds or other financial assets in order to stimulate economic activity. Quantitative easing is a novel form of monetary pol ...
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 out of the Member state of the European Union, member states of the European Union (EU). This group of states is known as the eurozone o ...
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 that took place in the European Union (EU) from 2009 until the mid to late 2010s. Several eurozone membe ...
, 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.

*
Forward rate The forward rate is the future yield on a bond (finance), 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 for ...
* List of countries by central bank interest rates *
Macroeconomics Macroeconomics (from the Greek prefix ''makro-'' meaning "large" + ''economics'') is a branch of economics dealing with performance, structure, behavior, and decision-making of an economy as a whole. For example, using interest rates, taxes, and ...
*
Rate of return In finance, return is a Profit (accounting), profit on an investment. It comprises any change in value of the investment, and/or cash flows (or securities, or other investments) which the investor receives from that investment, such as interest pa ...
*
Short-rate model A short-rate model, in the context of interest rate derivatives, is a mathematical model that describes the future evolution of interest rates by describing the future evolution of the short rate, usually written r_t \,. The short rate Under a sho ...
*
Spot rate In finance Finance is the study and discipline of money, currency and capital assets. It is related to, but not synonymous with economics, the study of Production (economics), production, Distribution (economics), distribution, and Consump ...

# References

* {{DEFAULTSORT:Interest Rate Mathematical finance Monetary policy