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Aninterest rate is the amount ofinterest due per period, as a proportion of the amount lent,deposited, or borrowed. Interest rate periods are ordinarily a year and are oftenannualized when not. Alongside interest rates, three other variables determine total interest:principal sum,compounding frequency, and length of time.
Interest rates reflect a borrower's willingness to pay for money now over money in the future.[1] Indebt financing, companies borrowcapital from a bank, in the expectation that the borrowed capital may be used to generate areturn on investment greater than the interest rates. Failure of a borrower to continue paying interest is an example ofdefault, which may be followed bybankruptcy proceedings.Collateral is sometimes given in the event of default.
Inmonetary policy andmacroeconomics, the term "interest rate" is often used as shorthand for a central bank's policy rate, such as theUnited States Federal Reserve'sfederal funds rate. "Interest rate" is also sometimes used synonymously withovernight rate,bank rate, base rate,discount rate,coupon rate,repo rate,prime rate,yield to maturity, andinternal rate of return.
Thenominal interest rate is the interest rate without adjusting forinflation, whereas thereal interest rate takes inflation into account. Real interest rates measure the interest accumulated and repayment of principal inreal terms by comparing the sum against thebuying power of the amount at the time it was borrowed, lent, deposited or invested. Where inflation is the same as nominal interest rate, the real interest rate is zero.
The real interest rate is given by theFisher equation:
wherep is the inflation rate.
For low rates and short periods, thelinear approximation applies:
The Fisher equation applies bothex ante andex post.Ex ante, the rates are projected rates, whereasex post, the rates are historical.
The term "interest rate" is also often used as shorthand for a number of specific rates, most commonly theovernight rate,bank rate, or other interest rate set by acentral bank.[citation needed] In this regard, theUnited States Federal Reserve'sFederal Funds Rate is often simply known as the "interest rate" or "rate",[2] due to its global macroeconomic and financial significance.[citation needed] InUnited Kingdom contexts,Official Bank Rate of theBank of England is also known as "the interest rate".[3] "Interest rate" is also sometimes used synonymously with base rate,discount rate,coupon rate,repo rate,prime rate,yield to maturity,internal rate of return,spot rate,forward rate, and benchmark rates such asLibor andSONIA.[citation needed]
Base rate usually refers to the annualizedeffective interest rate offered on overnight deposits by the central bank or other monetary authority.[citation needed]
Theannual 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.[citation needed]
Theannual equivalent rate (AER), also called the effective annual rate, factors into account compounding frequencies of products, but does not account for fees.[citation needed]
Discount rate can both refer to thediscount window of central banks and more generally as the annual rate used todiscount future values intopresent value.[4]
For an interest-bearing security,coupon rate is the ratio of the annualcoupon amount (the coupon paid per year) per unit ofpar value, whereascurrent yield is the ratio of the annual coupon divided by its current market price.[citation needed]
Yield to maturity is a bond's expectedinternal rate of return, 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.[citation needed]
Based on the relationship between supply and demand of market interest rate, there arefixed interest rate andfloating interest rate.[citation needed]
Interest rate targets are a vital tool ofmonetary policy and are taken into account when dealing with variables likeinvestment,inflation, andunemployment. Thecentral banks of countries generally tend to reduce interest rates when they wish to increase investment and consumption in the country'seconomy. However, a low interest rate as a macro-economic policy can berisky and may lead to the creation of aneconomic bubble, in which large amounts of investments are poured into the real-estate market and stock market. Indeveloped economies, interest-rate adjustments are thus made to keep inflation within a target range for the health ofeconomic activities or cap the interest rate concurrently witheconomic growth to safeguard economic momentum.[5][6][7][8][9]
In the past two centuries, interest rates have been variously set either by national governments or central banks. For example, the Federal Reservefederal funds rate in the United States has varied between about 0.25% and 19% from 1954 to 2008, while theBank of England base rate varied between 0.5% and 15% from 1989 to 2009,[10][11] and Germany experienced rates close to 90% in the 1920s down to about 2% in the 2000s.[12][13] During an attempt to tackle spiralinghyperinflation in 2007, the Central Bank ofZimbabwe increased interest rates for borrowing to 800%.[14]
Theinterest 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.[15]
Before modern capital markets, there have been accounts that savings deposits could achieve an annual return of at least 25% and up to as high as 50%.[16]
A so-called "zero interest-rate policy" (ZIRP) is a very low—near-zero—central bank target interest rate. At thiszero 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.
In the United States, the policy was used in 2008-2015, following the2008 financial crisis, and 2020-2022, during theCOVID-19 pandemic.[18]
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 known asfinancial repression, which was practiced by countries such as the United States and United Kingdomfollowing World War II until the late 1970s or early 1980s, during and following thePost–World War II economic expansion.[19][20] In the late 1970s,United States Treasury securities with negative real interest rates were deemedcertificates of confiscation.[21]
A so-called "negative interest rate policy" (NIRP) is a negative central bank target interest rate.
In theory, profit-seeking lenders will not lend below 0% if given the alternative of holding cash, as that will guarantee a loss. Likewise, a bank offering a negative deposit rate will find few takers, as savers will instead hold cash.[22]
Negative interest rates have been proposed in the past, notably in the late 19th century bySilvio Gesell.[23] A negative interest rate can be described as a "tax on holding money"; Gesell proposed it as theFreigeld (free money) component of hisFreiwirtschaft (free economy) system. To prevent people from holding cash, 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 approvingly cited the idea of a carrying tax on money,[23][24] but dismissed it due to administrative difficulties.[25] In 1999, a carry tax on currency was proposed byFederal Reserve employee Marvin Goodfriend, 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.[25]
It has also been proposed that a negative interest rate can in principle be levied on existing paper currency via aserial 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 ofGreg Mankiw,[23] though more as a thought experiment than a genuine proposal.[26]
Both theEuropean Central Bank starting in 2014 and theBank of Japan starting in early 2016 pursued the policy on top of their earlier and continuingquantitative easing policies. The latter's policy was said at its inception to be trying to "change Japan's 'deflationary mindset.'" In 2016Sweden, Denmark and Switzerland—not directly participants in theEuro currency zone—also had NIRPs in place.[27]
Countries such as Sweden and Denmark have set negative interest on reserves—that is to say, they have charged interest on reserves.[28][29][30][31]
In July 2009, Sweden's central bank, theRiksbank, 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%.[32] 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.[32][33] The Riksbank studied the impact of these changes and stated in a commentary report[34] that they led to no disruptions in Swedish financial markets.
During theEuropean debt crisis, 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).[36]
Interest rates affect economic activity broadly, which is the reason why they are normally the main instrument of themonetary policies conducted bycentral banks.[37] Changes in interest rates will affect firms'investment behaviour, either raising or lowering theopportunity cost of investing. Interest rate changes also affectasset prices likestock prices andhouse prices, which again influence households'consumption decisions through awealth effect. Additionally, international interest rate differentials affect exchange rates and consequentlyexports andimports. These various channels are collectively known as themonetary transmission mechanism. Consumption, investment and net exports are all important components ofaggregate demand. Consequently, by influencing the general interest rate level, monetary policy can affect overall demand for goods and services in the economy and henceoutput andemployment.[38] Changes in employment will over time affectwage setting, which again affectspricing and consequently ultimately inflation. The relation between employment (or unemployment) and inflation is known as thePhillips curve.[37]
For economies maintaining afixed exchange rate system, determining the interest rate is also an important instrument of monetary policy as internationalcapital flows are in part determined by interest rate differentials between countries.[39]
The Federal Reserve (often referred to as 'the Fed') implementsmonetary policy largely by targeting thefederal funds rate (FFR). This is the rate that banks charge each other for overnight loans offederal funds, which are the reserves held by banks at the Fed. Until the2008 financial crisis, the Fed relied onopen market operations, i.e. selling and buying securities in the open market to adjust the supply of reserve balances so as to keep the FFR close to the Fed's target.[40] However, since 2008 the actual conduct of monetary policy implementation has changed considerably, the Fed using instead various administered interest rates (i.e., interest rates that are set directly by the Fed rather than being determined by the market forces of supply and demand) as the primary tools to steer short-term market interest rates towards the Fed's policy target.[41]
Financial economists such asWorld Pensions Council (WPC) researchers have argued that durably low interest rates in most G20 countries will have an adverse impact on thefunding 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".[42] Current interest rates insavings accounts often fail to keep up with the pace of inflation.[43]
From 1982 until 2012, most Western economies experienced a period of low inflation combined with relatively high returns on investments across allasset classes including government bonds. This brought a certain sense of complacency[citation needed] amongst some pensionactuarial consultants andregulators, making it seem reasonable to use optimistic economic assumptions to calculate thepresent value of future pension liabilities.
Aninterest-free economy or interest free economy is aneconomy that does not have pure interest rates.An interest free economy may use eitherbarter,debt,credit, ormoney as itsmedium of exchange.Historically, there has been a taboo againstusury and charging interest rates across many cultures and religions.In some contexts, "interest-free economy" may refer to azero interest-rate policy, a macroeconomic concept for describing an economy that is characterized by a low nominal interest rate.
The total interest rate typically consists of four components:pure (risk-free) interest, arisk premium, expected inflation or deflation, and administrative costs.In an interest-free economy, the pure interest rate component of the total interest rate would not exist, by definition.Depending on how the economy is structured, the other three components of interest of the total interest may or may not remain, so an interest-free economy does not necessarily have to be free of all types of interest.
Banks could still profit from loaning money in an interest-free economy, if they are paid by the administrative costs component of the total interest rate.[44]There is amarket for investments, including themoney market,bond market,stock market, andcurrency market as well as retailbanking.
Interest rates reflect:
According to the theory ofrational expectations, borrowers and lenders form an expectation ofinflation in the future. The acceptable nominal interest rate at which they are willing and able to borrow or lend includes thereal interest rate they require to receive, or are willing to pay, plus the rate ofinflation they expect. Under behavioral expectations, the formation of expectations deviates from rational expectations due to cognitive limitations and information processing costs. Agents may exhibit myopia (limited attention) to certain economic variables, form expectations based on simplified heuristics, or update their beliefs more gradually than under full rationality. These behavioral frictions can affect monetary policy transmission and optimal policy design.[45]
The level ofrisk in investments is taken into consideration.Riskier investments such asshares andjunk bonds are normally expected to deliver higher returns than safer ones likegovernment bonds.
The additional return above the risk-free nominal interest rate which is expected from a risky investment is therisk premium. The risk premium an investor requires on an investment depends on therisk preferences of the investor. Evidence suggests that most lenders are risk-averse.[46]
Amaturity risk premium applied to a longer-term investment reflects a higher perceived risk of default.
There are four kinds of risk:
Most economic agents exhibit aliquidity preference, defined as the propensity to holdcash or highly liquid assets over lessfungible investments, reflecting both precautionary and transactional motives. Liquidity preference manifests in the yield differential between assets of varying maturities and convertibility costs, where cash provides immediate transaction capability with zero conversion costs. This preference creates a term structure of required returns, exemplified by the higher yields typically demanded for longer-duration assets. For instance, while a 1-year loan offers relatively rapid convertibility to cash, a 10-year loan commands a greater liquidity premium. However, the existence of deep secondary markets can partially mitigate illiquidity costs, as evidenced by USTreasury bonds, which maintain significant liquidity despite longer maturities due to their unique status as a safe asset and the associated financial sector stability benefits.[47][48]
A basic interest rate pricing model for an asset is
where
Assuming perfect information,pe is the same for all participants in the market, and the interest rate model simplifies to
Because interest and inflation are generally given as percentage increases, the formulae above are(linear) approximations.
For instance,
is only approximate. In reality, the relationship is
so
The two approximations, eliminatinghigher order terms, are:
The formulae in this article are exact iflogarithmic units are used for relative changes, or equivalently iflogarithms ofindices are used in place of rates, and hold even for large relative changes.
Thespread of interest rates is the lending rate minus the deposit rate.[49] This spread covers operating costs for banks providing loans and deposits. Anegative spread is where a deposit rate is higher than the lending rate.[50]
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Interest rates vary according to:
as well as other factors.[51]
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