# Interest rate

An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited or borrowed (called the principal sum). 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.

It is defined as the proportion of an amount loaned which a lender charges as interest to the borrower, normally expressed as an annual percentage.[1] 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.[2]

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 annualised.

## 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

as well as other factors.

## Example

A company borrows capital 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 rate offered on overnight deposits by the central bank or other monetary authority.

Annual percentage rate (APR) and effective annual rate or annual equivalent rate (AER) are used to help consumers compare products with different payment structures on a common basis.

A discount rate is applied to calculate present value.

For an interest-bearing security, coupon rate 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 is a bond's expected internal 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.

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.

Based on the changes between different interest rates, there are base interest rate and cash interest rate.

## Monetary policy

Interest rate targets are a vital tool of monetary policy and are taken into account when dealing with variables like investment, inflation, and unemployment. The central banks 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, 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 to safeguard economic momentum.[3][4][5][6][7]

## History

Germany experienced deposit interest rates from 14% in 1969 down to almost 2% in 2003

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 base rate varied between 0.5% and 15% from 1989 to 2009,[8][9] and Germany experienced rates close to 90% in the 1920s down to about 2% in the 2000s.[10][11] During an attempt to tackle spiraling hyperinflation in 2007, the Central Bank of Zimbabwe increased interest rates for borrowing to 800%.[12]

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.[13]

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 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, 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, abscond, die, or otherwise default on the loan. This means that a lender generally charges a risk premium 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.[14]
• 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 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 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."[15]

## Real vs nominal

The nominal interest rate is the rate of interest with no adjustment for 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 rate is 10% per annum (before tax). The real interest rate measures the growth in real value of the loan plus interest, taking inflation 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 is zero in this case. The real interest rate is given by the Fisher equation: ${\displaystyle r={\frac {1+i}{1+p}}-1\,\!}$ where p is the inflation rate. For low rates and short periods, the linear approximation applies: ${\displaystyle r\approx i-p\,\!}$ The Fisher equation applies both ex ante and ex post. 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, bond market, stock market, and currency market as well as retail banking. Interest rates reflect: ### Inflationary expectations According to the theory of rational expectations, borrowers and lenders form an expectation of 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 they require to receive, or are willing and able to pay, plus the rate of inflation they expect. ### Risk The level of risk in investments is taken into consideration. Riskier investments such as shares and junk bonds are normally expected to deliver higher returns than safer ones like government bonds. The additional return above the risk-free nominal interest rate which is expected from a risky investment is the risk premium. 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.[16] 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 rather than in less fungible 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. A 1-year loan, for instance, is very liquid compared to a 10-year loan. A 10-year US Treasury bond, 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 ${\displaystyle i_{n}=i_{r}+p_{e}+r_{p}+l_{p}\,\!}$ 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 ${\displaystyle i_{n}=i_{n}^{*}+r_{p}+l_{p}\,\!}$ ### Spread The spread of interest rates is the lending rate minus the deposit rate.[17] 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.[18] ## 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 effective federal funds rate in the US charted over more than half a century The Federal Reserve (often referred to as 'the Fed') implements monetary policy largely by targeting the federal funds rate. This is the rate that banks charge each other for overnight loans of federal funds, which are the reserves held by banks at the Fed. Open market operations are one tool within monetary policy implemented by the Federal Reserve to steer short-term interest rates using the power to buy and sell treasury securities. ### Money and inflation Loans, bonds, and shares have some of the characteristics of money and are included in the broad money 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, increases in the money supply lead to inflation. ## Impact on savings and pensions Financial economists 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 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” [19] 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 of future pension liabilities. ## Mathematical note Because interest and inflation are generally given as percentage increases, the formulae above are (linear) approximations. For instance, ${\displaystyle i_{n}=i_{r}+p_{e}\,\!}$ is only approximate. In reality, the relationship is ${\displaystyle (1+i_{n})=(1+i_{r})(1+p_{e})\,\!}$ so ${\displaystyle i_{r}={\frac {1+i_{n}}{1+p_{e}}}-1\,\!}$ The two approximations, eliminating higher order terms, are: {\displaystyle {\begin{aligned}(1+x)(1+y)&=1+x+y+xy&&\approx 1+x+y\\{\frac {1}{1+x}}&=1-x+x^{2}-x^{3}+\cdots &&\approx 1-x\end{aligned}}} The formulae in this article are exact if logarithmic units are used for relative changes, or equivalently if logarithms 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, 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).[20][21] In the late 1970s, United States Treasury securities with negative real interest rates were deemed certificates of confiscation.[22] ### 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.[23] Negative interest rates have been proposed in the past, notably in the late 19th century by Silvio Gesell.[24] 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 approvingly cited the idea of a carrying tax on money,[24] (1936, The General Theory of Employment, Interest and Money) but dismissed it due to administrative difficulties.[25] More recently, a carry tax on currency was proposed by a 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.[25] It has been proposed that a negative interest rate can in principle be levied on existing paper currency via a 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,[24] though more as a thought experiment than a genuine proposal.[26] A much simpler method to achieve negative real interest rates and provide a disincentive to holding cash, is for governments to encourage mildly inflationary monetary policy; indeed, this is what Keynes recommended back in 1936. #### Practice Both the European Central Bank starting in 2014 and the Bank of Japan starting in early 2016 pursued the policy on top of their earlier and continuing quantitative easing 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 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, 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%.[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. The US Federal Reserve called an end to quantitative easing in September 2017 and subsequently raised its benchmark short-term interest rate by a quarter percentage point.[35] ### On government bond yields During the European 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] ### 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 ## Notes 1. ^ "interest rate - Definition of interest rate in English by Oxford Dictionaries". Oxford Dictionaries - English. Retrieved 8 January 2018. 2. ^ "interest rate Meaning in the Cambridge English Dictionary". Dictionary.cambridge.org. Retrieved 8 January 2018. 3. ^ "INSIGHT-Mild inflation, low interest rates could help economy". Reuters. 2 August 2011. 4. ^ Sepehri, Ardeshir; Moshiri, Saeed (2004). "Inflation‐Growth Profiles Across Countries: Evidence from Developing and Developed Countries". International Review of Applied Economics. 18 (2): 191–207. doi:10.1080/0269217042000186679. 5. ^ "Inflation : Finding the right balance" (PDF). Imf.org. Retrieved 8 January 2018. 6. ^ "Finance & Development, June 2003 - Contents". Finance and Development – F&D. 7. ^ "Finance & Development, March 2010 – Back to Basics". Finance and Development – F&D. 8. ^ moneyextra.com Interest Rate History Archived 2008-10-16 at the Wayback Machine. Retrieved 2008-10-27 9. ^ "UK interest rates lowered to 0.5%". BBC News. 5 March 2009. 10. ^ (Homer, Sylla & Sylla 1996, p. 509) 11. ^ Bundesbank. BBK – Statistics – Time series database Archived 2009-02-12 at the Wayback Machine. Retrieved 2008-10-27 12. ^ worldeconomies.co.uk Zimbabwe currency revised to help inflation Archived 2009-02-11 at the Wayback Machine 13. ^ (Homer, Sylla & Sylla 1996, p. 1) 14. ^ Commonwealth Bank Why do Interest Rates Change? Archived 2014-02-26 at the Wayback Machine 15. ^ Marx, Karl. https://www.marxists.org/archive/marx/works/1894-c3/ch22.htm. Missing or empty |title= (help) 16. ^ Benchimol, J., 2014. Risk aversion in the Eurozone, Research in Economics, vol. 68, issue 1, pp. 39–56. 17. ^ 18. ^ Negative Spread Law & Legal Definition, retrieved January 2013 19. ^ M. Nicolas J. Firzli quoted in Sinead Cruise (4 August 2012). "'Zero Return World Squeezes Retirement Plans'". Reuters with CNBC. . Retrieved 5 Aug 2012. 20. ^ William H. Gross. "The Caine Mutiny Part 2 – PIMCO". Pacific Investment Management Company LLC. 21. ^ "Financial Repression Redux (Reinhart, Kirkegaard, Sbrancia June 2011)" (PDF). Imf.org. Retrieved 8 January 2018. 22. ^ Norris, Floyd (28 October 2010). "U.S. Bonds That Could Return Less Than Their Price". The New York Times. 23. ^ 24. ^ a b c Mankiw, N. Gregory (18 April 2009). "It May Be Time for the Fed to Go Negative". The New York Times. 25. ^ a b McCullagh, Declan (27 October 1999). "Cash and the 'Carry Tax'". WIRED. Retrieved 2011-12-21. 26. ^ See follow-up blog posts for discussion: "Observations on Negative Interest Rates", 19 April 2009; "More on Negative Interest Rates", 22 April 2009; "More on Negative Interest Rates", 7 May 2009, all in Greg Mankiw's Blog: Random Observations for Students of Economics 27. ^ Nakamichi, Takashi, Megumi Fujikawa and Eleanor Warnock, "Bank of Japan Introduces Negative Interest Rates" (possibly subscription-only), Wall Street Journal, January 29, 2016. Retrieved 2016-01-29. 28. ^ Goodhart, C.A.E. (January 2013). "The Potential Instruments of Monetary Policy" (PDF). Financial Markets Group Paper (Special Paper 219). London School of Economics. 9–10. ISSN 1359-9151. Retrieved 13 April 2013. 29. ^ Blinder, Alan S. (February 2012). "Revisiting Monetary Policy in a Low-Inflation and Low-Utilization Environment". Journal of Money, Credit and Banking. 44 (Supplement s1): 141–146. doi:10.1111/j.1538-4616.2011.00481.x. 30. ^ Thoma, Mark (August 27, 2012). "Would Lowering the Interest Rate on Excess Reserves Stimulate the Economy?". Economist's View. Retrieved 13 April 2013. 31. ^ Parameswaran, Ashwin (2013-01-07). "On The Folly of Inflation Targeting In A World Of Interest Bearing Money". Macroeconomic Resilience. Retrieved 13 April 2013. 32. ^ a b "Repo rate table". Sveriges Riksbank. Retrieved 21 August 2013. 33. ^ Ward, Andrew; Oakley, David (27 August 2009). "Bankers watch as Sweden goes negative". Financial Times. London. 34. ^ Beechey, Meredith; Elmér, Heidi (30 September 2009). "The lower limit of the Riksbank's repo rate" (PDF). Sveriges Riksbank. Retrieved 21 August 2013. 35. ^ "Global debt bomb ticking: GCC on the brink of a economic meltdown". ameinfo.com. 2018-06-28. Retrieved 2018-06-28. 36. ^ Wigglesworth, Robin (18 July 2012). "Schatz yields turn negative for first time". Financial Times. London. ## References Certificate of deposit A certificate of deposit (CD) is a time deposit, a financial product commonly sold by banks, thrift institutions, and credit unions. CDs are similar to savings accounts in that they are insured "money in the bank" and thus virtually risk free. In the USA, CDs are insured by the Federal Deposit Insurance Corporation (FDIC) for banks and by the National Credit Union Administration (NCUA) for credit unions. They differ from savings accounts in that the CD has a specific, fixed term (often one, three, or six months, or one to five years) and usually, a fixed interest rate. The bank intends that the customer hold the CD until maturity, at which time they can withdraw the money and accrued interest. In exchange for the customer depositing the money for an agreed term, institutions usually grant higher interest rates than they do on accounts that customers can withdraw from on demand—though this may not be the case in an inverted yield curve situation. Fixed rates are common, but some institutions offer CDs with various forms of variable rates. For example, in mid-2004, interest rates were expected to rise—and many banks and credit unions began to offer CDs with a "bump-up" feature. These allow for a single readjustment of the interest rate, at a time of the consumer's choosing, during the term of the CD. Sometimes, financial institutions introduce CDs indexed to the stock market, bond market, or other indices. Some features of CDs are: A larger principal should/may receive a higher interest rate. A longer term usually earns a higher interest rate, except in the case of an inverted yield curve (e.g., preceding a recession). Smaller institutions tend to offer higher interest rates than larger ones. Personal CD accounts generally receive higher interest rates than business CD accounts. Banks and credit unions that are not insured by the FDIC or NCUA generally offer higher interest rates.CDs typically require a minimum deposit, and may offer higher rates for larger deposits. The best rates are generally offered on "Jumbo CDs" with minimum deposits of100,000.

The consumer who opens a CD may receive a paper certificate, but it is now common for a CD to consist simply of a book entry and an item shown in the consumer's periodic bank statements. That is, there is often no "certificate" as such. Consumers who want a hard copy that verifies their CD purchase may request a paper statement from the bank, or print out their own from the financial institution's online banking service.

Compound interest

Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest. Compound interest is standard in finance and economics.

Compound interest is contrasted with simple interest, where previously accumulated interest is not added to the principal amount of the current period, so there is no compounding. The simple annual interest rate is the interest amount per period, multiplied by the number of periods per year. The simple annual interest rate is also known as the nominal interest rate (not to be confused with the interest rate not adjusted for inflation, which goes by the same name).

Compound Interest = P (1+(r/n))^nt

Effective interest rate

The effective interest rate (EIR), effective annual interest rate, annual equivalent rate (AER) or simply effective rate is the interest rate on a loan or financial product restated from the nominal interest rate as an interest rate with annual compound interest payable in arrears.

It is used to compare the annual interest between loans with different compounding periods like week, month, year, etc. The effective interest rate differs in one important respect from the annual percentage rate (APR): the APR method converts this weekly or monthly interest rate into what would be called an annual rate that doesn’t take into account the effect of compounding.

By contrast, in the EIR, the periodic rate is annualized using compounding. It is the standard in the European Union and a large number of countries around the world.

The EIR is more precise in financial terms, taking into consideration the effects of compounding, i.e. the fact that for each period, interest is not calculated on the principal, but on the amount of the previous period, including capital and interest. This reasoning is easily understandable when looking at savings: interest is capitalized every month, and every month the saver earns interest on the interest from the previous period. As an effect of compounding, the interest earned over a year represent 26.82% of the initial amount, instead of 24%, the monthly 2% interest rate simply multiplied by 12. If we consider borrowings instead of savings, the compounded interest rate reflects the opportunity cost for the borrower not to be able to invest the interest he pays to the lender into an asset generating the same percentage of return. The term nominal EIR or nominal APR can be used to refer to an annualized rate that does not take into account front-fees and other costs can be included.

Annual percentage yield or effective annual yield is the analogous concept used for savings or investment products, such as a certificate of deposit. Since any loan is an investment product for the lender, the terms may be used to apply to the same transaction, depending on the point of view.

Effective annual interest or yield may be calculated or applied differently depending on the circumstances, and the definition should be studied carefully. For example, a bank may refer to the yield on a loan portfolio after expected losses as its effective yield and include income from other fees, meaning that the interest paid by each borrower may differ substantially from the bank's effective yield.

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 uncollateralized basis. Reserve balances are amounts held at the Federal Reserve to maintain depository institutions' reserve requirements. Institutions with surplus balances in their accounts lend those balances to institutions in need of larger balances. The federal funds rate is an important benchmark in financial markets.The interest rate that the borrowing bank pays to the lending bank to borrow the funds is negotiated between the two banks, and the weighted average of this rate across all such transactions is the federal funds effective rate.

The federal funds target rate is determined by a meeting of the members of the Federal Open Market Committee which normally occurs eight times a year about seven weeks apart. The committee may also hold additional meetings and implement target rate changes outside of its normal schedule.

The Federal Reserve uses open market operations to make the federal funds effective rate follow the federal funds target rate. The target rate is chosen in part to influence the money supply in the U.S. economy

Forward rate agreement

In finance, a forward rate agreement (FRA) is an interest rate derivative (IRD). In particular it is a linear IRD with strong associations with interest rate swaps (IRSs).

Government bond

A government bond or sovereign bond is a bond issued by a national government, generally with a promise to pay periodic interest payments called coupon payments and to repay the face value on the maturity date. The aim of a government bond is to support government spending. Government bonds are usually denominated in the country's own currency, in which case the government cannot be forced to default, although it may choose to do so. If a government is close to default on its debt the media often refer to this as a sovereign debt crisis.The terms on which a government can sell bonds depend on how creditworthy the market considers it to be. International credit rating agencies will provide ratings for the bonds, but market participants will make up their own minds about this.

For example, a bondholder invests $20,000 (called face value) into a 10-year government bond with a 10% annual coupon; the government would pay the bondholder 10% of the$20,000 each year. At the maturity date the government would give back the original $20,000. IS–LM model The IS–LM model, or Hicks–Hansen model, is a macroeconomic tool that shows the relationship between interest rates (ordinate) and assets market (also known as real output in goods and services market plus money market, as abscissa). The intersection of the "investment–saving" (IS) and "liquidity preference–money supply" (LM) curves models "general equilibrium" where supposed simultaneous equilibria occur in both the goods and the asset markets. Yet two equivalent interpretations are possible: first, the IS–LM model explains changes in national income when price level is fixed short-run; second, the IS–LM model shows why an aggregate demand curve can shift. Hence, this tool is sometimes used not only to analyse economic fluctuations but also to suggest potential levels for appropriate stabilisation policies.The model was developed by John Hicks in 1937, and later extended by Alvin Hansen, as a mathematical representation of Keynesian macroeconomic theory. Between the 1940s and mid-1970s, it was the leading framework of macroeconomic analysis. While it has been largely absent from macroeconomic research ever since, it is still a backbone conceptual introductory tool in many macroeconomics textbooks. By itself, the IS–LM model is used to study the short run when prices are fixed or sticky and no inflation is taken into consideration. But in practice the main role of the model is as a path to explain the AD–AS model. Interest Interest, in finance and economics, is payment from a 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 distinct from a fee which the borrower may pay the lender or some third party. It is also distinct from dividend which is paid by a company to its shareholders (owners) from its profit or reserve, but not at a particular rate decided beforehand, rather on a pro rata basis as a share in the reward gained by risk taking entrepreneurs when the revenue earned exceeds the total costs.For example, a customer would usually pay interest to borrow from a bank, so they pay the bank an amount which is more than the amount they borrowed; or a customer may earn interest on their savings, and so they may withdraw more than they originally deposited. In the case of savings, the customer is the lender, and the bank plays the role of the borrower. Interest differs from profit, in that interest is received by a lender, whereas profit is received by the owner of an asset, investment or enterprise. (Interest may be part or the whole of the profit on an investment, but the two concepts are distinct from each other from an accounting perspective.) The rate of interest is equal to the interest amount paid or received over a particular period divided by the principal sum borrowed or lent (usually expressed as a percentage). Compound interest means that interest is earned on prior interest in addition to the principal. Due to compounding, the total amount of debt grows exponentially, and its mathematical study led to the discovery of the number e. In practice, interest is most often calculated on a daily, monthly, or yearly basis, and its impact is influenced greatly by its compounding rate. Interest rate derivative In finance, an interest rate derivative (IRD) is a derivative whose payments are determined through calculation techniques where the underlying benchmark product is an interest rate, or set of different interest rates. There are a multitude of different interest rate indices that can be used in this definition. IRDs are popular with all financial market participants given the need for almost any area of finance to either hedge or speculate on the movement of interest rates. Interest rate future An interest rate future is a financial derivative (a futures contract) with an interest-bearing instrument as the underlying asset. It is a particular type of interest rate derivative. Examples include Treasury-bill futures, Treasury-bond futures and Eurodollar futures. The global market for exchange-traded interest rate futures is notionally valued by the Bank for International Settlements at$5,794,200 million in 2005.

Interest rate option

An Interest rate option is a specific financial derivative contract whose value is based on interest rates. Its value is tied to an underlying interest rate, such as the yield on 10 year treasury notes.

Similar to equity options, there are two types of contracts: calls and puts. A call gives the bearer the right, but not the obligation, to benefit off a rise in interest rates. A put gives the bearer the right, but not the obligation, to profit from a decrease in interest rates.

The exchange of these interest rate derivatives are monitored and facilitated by a central exchange such as those operated by CME Group.

Interest rate swap

In finance, an interest rate swap (IRS) is an interest rate derivative (IRD). It involves exchange of interest rates between two parties. In particular it is a linear IRD and one of the most liquid, benchmark products. It has associations with forward rate agreements (FRAs), and with zero coupon swaps (ZCSs).

Monetary policy

Monetary policy is the process by which the monetary authority of a country, typically the central bank or currency board, controls either the cost of very short-term borrowing or the money supply, often targeting inflation or the interest rate to ensure price stability and general trust in the currency.Further goals of a monetary policy are usually to contribute to the stability of gross domestic product, to achieve and maintain low unemployment, and to maintain predictable exchange rates with other currencies.

Monetary economics provides insight into how to craft an optimal monetary policy. In developed countries, monetary policy has been generally formed separately from fiscal policy, which refers to taxation, government spending, and associated borrowing.Monetary policy is referred to as being either expansionary or contractionary. Expansionary policy occurs when a monetary authority uses its tools to stimulate the economy. An expansionary policy maintains short-term interest rates at a lower than usual rate or increases the total supply of money in the economy more rapidly than usual. It is traditionally used to try to combat unemployment in a recession by lowering interest rates in the hope that less expensive credit will entice businesses into expanding. This increases aggregate demand (the overall demand for all goods and services in an economy), which boosts short-term growth as measured by gross domestic product (GDP) growth. Expansionary monetary policy usually diminishes the value of the currency relative to other currencies (the exchange rate).The opposite of expansionary monetary policy is contractionary monetary policy, which maintains short-term interest rates higher than usual or which slows the rate of growth in the money supply or even shrinks it. This slows short-term economic growth and lessens inflation. Contractionary monetary policy can lead to increased unemployment and depressed borrowing and spending by consumers and businesses, which can eventually result in an economic recession if implemented too vigorously.

Outline of finance

The following outline is provided as an overview of and topical guide to finance:

Finance – addresses the ways in which individuals and organizations raise and allocate monetary resources over time, taking into account the risks entailed in their projects.

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 always less than or equal to the future value because money has interest-earning potential, a characteristic referred to as the time value of money, except during times of negative interest rates, when the present value will be more than the future value. Time value can be described with the simplified phrase, "A dollar today is worth more than a dollar tomorrow". Here, 'worth more' means that its value is greater. A dollar today is worth more than a dollar tomorrow because the dollar can be invested and earn a day's worth of interest, making the total accumulate to a value more than a dollar by tomorrow. Interest can be compared to rent. Just as rent is paid to a landlord by a tenant without the ownership of the asset being transferred, interest is paid to a lender by a borrower who gains access to the money for a time before paying it back. By letting the borrower have access to the money, the lender has sacrificed the exchange value of this money, and is compensated for it in the form of interest. The initial amount of the borrowed funds (the present value) is less than the total amount of money paid to the lender.

Present value calculations, and similarly future value calculations, are used to value loans, mortgages, annuities, sinking funds, perpetuities, bonds, and more. These calculations are used to make comparisons between cash flows that don’t occur at simultaneous times, since time dates must be consistent in order to make comparisons between values. When deciding between projects in which to invest, the choice can be made by comparing respective present values of such projects by means of discounting the expected income streams at the corresponding project interest rate, or rate of return. The project with the highest present value, i.e. that is most valuable today, should be chosen.

Risk-free interest rate

The risk-free interest rate is the rate of return of a hypothetical investment with no risk of financial loss, over a given period of time.Since the risk-free rate can be obtained with no risk, any other investment having some risk will have to have a higher rate of return in order to induce any investors to hold it.

In practice, to infer the risk-free interest rate in a particular situation, a risk-free bond is usually chosen—that is, one issued by a government or agency whose risks of default are so low as to be negligible.

Swap (finance)

A swap is a derivative in which two counterparties exchange cash flows of one party's financial instrument for those of the other party's financial instrument. The benefits in question depend on the type of financial instruments involved. For example, in the case of a swap involving two bonds, the benefits in question can be the periodic interest (coupon) payments associated with such bonds. Specifically, two counterparties agree to exchange one stream of cash flows against another stream. These streams are called the legs of the swap. The swap agreement defines the dates when the cash flows are to be paid and the way they are accrued and calculated. Usually at the time when the contract is initiated, at least one of these series of cash flows is determined by an uncertain variable such as a floating interest rate, foreign exchange rate, equity price, or commodity price.The cash flows are calculated over a notional principal amount. Contrary to a future, a forward or an option, the notional amount is usually not exchanged between counterparties. Consequently, swaps can be in cash or collateral.

Swaps can be used to hedge certain risks such as interest rate risk, or to speculate on changes in the expected direction of underlying prices.Swaps were first introduced to the public in 1981 when IBM and the World Bank entered into a swap agreement. Today, swaps are among the most heavily traded financial contracts in the world: the total amount of interest rates and currency swaps outstanding was more than \$348 trillion in 2010, according to Bank for International Settlements (BIS).

Most swaps are traded over-the-counter (OTC), "tailor-made" for the counterparties. Some types of swaps are also exchanged on futures markets such as the Chicago Mercantile Exchange, the largest U.S. futures market, the Chicago Board Options Exchange, IntercontinentalExchange and Frankfurt-based Eurex AG.

The Bank for International Settlements (BIS) publishes statistics on the notional amounts outstanding in the OTC derivatives market. At the end of 2006, this was USD 415.2 trillion, more than 8.5 times the 2006 gross world product. However, since the cash flow generated by a swap is equal to an interest rate times that notional amount, the cash flow generated from swaps is a substantial fraction of but much less than the gross world product—which is also a cash-flow measure. The majority of this (USD 292.0 trillion) was due to interest rate swaps. These split by currency as:

Source: "The Global OTC Derivatives Market at end-December 2004", BIS, [1], "OTC Derivatives Market Activity in the Second Half of 2006", BIS, [2] Usually, at least one of the legs has a rate that is variable. It can depend on a reference rate, the total return of a swap, an economic statistic, etc. The most important criterion is that it comes from an independent third party, to avoid any conflict of interest. For instance, LIBOR is published by Intercontinental Exchange.

Usury

Usury () is the practice of making unethical or immoral monetary loans that unfairly enrich the lender. The term may be used in a moral sense—condemning, taking advantage of others' misfortunes, or in a legal sense, where an interest rate is charged in excess of the maximum rate that is allowed by law. A loan may be considered usurious because of excessive or abusive interest rates or other factors defined by a nation's laws. Someone who practices usury can be called a usurer, but in contemporary English may be called a loan shark.

Originally, usury meant the charging of interest of any kind and, in some Christian societies and even today in many Islamic societies, charging any interest at all was considered usury. Some of the earliest known condemnations of usury come from the Vedic texts of India. Similar condemnations are found in religious texts from Buddhism, Judaism, Christianity, and Islam (the term is riba in Arabic and ribbit in Hebrew). At times, many nations from ancient Greece to ancient Rome have outlawed loans with any interest. Though the Roman Empire eventually allowed loans with carefully restricted interest rates, the Catholic Church in medieval Europe banned the charging of interest at any rate (as well as charging a fee for the use of money, such as at a bureau de change). Religious prohibitions on usury are predicated upon the belief that charging interest on a loan is a sin.

Zero interest-rate policy

Zero interest-rate policy (ZIRP) is a macroeconomic concept describing conditions with a very low nominal interest rate, such as those in contemporary Japan and December 2008 through December 2015 in the United States. ZIRP is considered to be an unconventional monetary policy instrument and can be associated with slow economic growth, deflation, and deleverage.

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