An interest rate is the rate at which interest Interest is a fee paid on borrowed assets. It is the price paid for the use of borrowed money, or, money earned by deposited funds. Assets that are sometimes lent with interest include money, shares, consumer goods through hire purchase, major assets such as aircraft, and even entire factories in finance lease arrangements. The interest is is paid by a borrower for the use of money Money is any object that is generally accepted as payment for goods and services and repayment of debts in a given country or socio-economic context. The main functions of money are distinguished as: a medium of exchange; a unit of account; a store of value; and, occasionally, a standard of deferred payment that they borrow from a lender A loan is a type of debt. Like all debt instruments, a loan entails the redistribution of financial assets over time, between the lender and the borrower. For example, a small company borrows capital from a bank to buy new assets for their business, and in return the lender receives interest at a predetermined interest rate for deferring the use of funds and instead lending it to the borrower. Interests rates are fundamental to a capitalist Capitalism is an economic system in which the means of production are privately owned; supply, demand, price, distribution, and investments are determined mainly by private decisions in the free market, rather than by the state through central economic planning or through democratic planning; profit is distributed to owners who invest in society[dubious – discuss]. Interest rates are normally expressed as a percentage In mathematics, a percentage is a way of expressing a number as a fraction of 100 . It is often denoted using the percent sign, "%", or the abbreviation "pct". For example, 45% (read as "forty-five percent") is equal to 45 / 100, or 0.45 rate over the period of one year A year is the orbital period of the Earth moving around the Sun. For an observer on Earth, this corresponds to the period it takes the Sun to complete one course throughout the zodiac along the ecliptic[citation needed].

Interest rates targets are also a vital tool of monetary policy Monetary policy is the process by which the monetary authority of a country controls the supply of money, often targeting a rate of interest. Monetary policy is usually used to attain a set of objectives oriented towards the growth and stability of the economy. These goals usually include stable prices and low unemployment. Monetary theory and are taken into account when dealing with variables like investment Investment is the commitment of money or capital to purchase financial instruments or other assets in order to gain profitable returns in the form of interest, income, or appreciation of the value of the instrument. It is related to saving or deferring consumption. Investment is involved in many areas of the economy, such as business management, inflation In economics, inflation is a rise in the general level of prices of goods and services in an economy over a period of time. When the price level rises, each unit of currency buys fewer goods and services; consequently, inflation is also an erosion in the purchasing power of money – a loss of real value in the internal medium of exchange and unit, and unemployment Unemployment occurs when a person is able and willing to work but currently without work. The prevalence of unemployment is usually measured using the unemployment rate, which is defined as the percentage of those in the labor force who are unemployed. The unemployment rate is also used in economic studies and economic indices such as the United.

Contents

Historical interest rates

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, the federal funds rate is the interest rate at which private depository institutions lend balances (federal funds) at the Federal Reserve to other depository institutions, usually overnight. It is the interest rate banks charge each other for loans in the United States has varied between about 0.25% to 19% from 1954 to 2008, while the Bank of England The Bank of England is (despite its name) the central bank of the whole of the United Kingdom and is the model on which most modern, large central banks have been based. It was established in 1694 to act as the English Government's banker, and to this day it still acts as the banker for HM Government. The Bank was privately owned and operated from base rate varied between 0.5% and 15% from 1989 to 2009,[1][2] and Germany experienced rates close to 90% in the 1920s down to about 2% in the 2000s.[3][4] During an attempt to tackle spiraling hyperinflation in 2007, the Central Bank of Zimbabwe increased interest rates for borrowing to 800%.[5]

This section requires expansion.

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.[6]

Reasons for interest rate change

Real vs nominal interest rates

Further information: Fisher equation The Fisher equation in financial mathematics and economics estimates the relationship between nominal and real interest rates under inflation. It is named after Irving Fisher who was famous for his works on the theory of interest. In finance, the Fisher equation is primarily used in YTM calculations of bonds or IRR calculations of investments. In

The nominal interest rate is the amount, in money terms, of interest payable.

For example, suppose a household deposits $100 with a bank for 1 year and they receive interest of $10. At the end of the year their balance is $110. In this case, the nominal interest rate In finance and economics nominal interest rate or nominal rate of interest refers to the rate of interest before adjustment for inflation ; or, for interest rates "as stated" without adjustment for the full effect of compounding (also referred to as the nominal annual rate). An interest rate is called nominal if the frequency of is 10% per annum.

The real interest rate, which measures the purchasing power of interest receipts, is calculated by adjusting the nominal rate charged to take inflation In economics, inflation is a rise in the general level of prices of goods and services in an economy over a period of time. When the price level rises, each unit of currency buys fewer goods and services; consequently, inflation is also an erosion in the purchasing power of money – a loss of real value in the internal medium of exchange and unit into account. (See real vs. nominal in economics In economics, nominal value refers to any price or value expressed in money of the day, as opposed to real value, which adjusts for the effect of inflation. Changes in real value reflect only changes in the actual quantity, Q, of goods or services produced; whereas changes in the nominal value reflect the combined effect of changes in the quantity.)

If inflation in the economy has been 10% in the year, then the $110 in the account at the end of the year buys the same amount as the $100 did a year ago. The real interest rate The "real interest rate" is approximately the nominal interest rate minus the inflation rate . Since the inflation rate over the course of a loan is not known initially, volatility in inflation represents a risk to both the lender and the borrower, in this case, is zero.

After the fact, the 'realized' real interest rate, which has actually occurred, is given by the Fisher equation The Fisher equation in financial mathematics and economics estimates the relationship between nominal and real interest rates under inflation. It is named after Irving Fisher who was famous for his works on the theory of interest. In finance, the Fisher equation is primarily used in YTM calculations of bonds or IRR calculations of investments. In, and is

where p = the actual inflation rate over the year. The linear approximation In mathematics, a linear approximation is an approximation of a general function using a linear function . They are widely used in the method of finite differences to produce first order methods for solving or approximating solutions to equations

is widely used.

The expected real returns on an investment, before it is made, are:

where:

= nominal interest rate
= real interest rate
= expected or projected inflation over the year

Market interest rates

There is a market A market is any one of a variety of different systems, institutions, procedures, social relations and infrastructures whereby persons trade, and goods and services are exchanged, forming part of the economy. It is an arrangement that allows buyers and sellers to exchange things. Competition is essential in markets, and separates market from trade for investments which ultimately includes the money market The money market is a component of the financial markets for assets involved in short-term borrowing and lending with original maturities of one year or shorter time frames. Trading in the money markets involves Treasury bills, commercial paper, bankers' acceptances, certificates of deposit, federal funds, and short-lived mortgage- and asset-, bond market The bond market is a financial market where participants buy and sell debt securities, usually in the form of bonds. As of 2009, the size of the worldwide bond market (total debt outstanding) is an estimated $82.2 trillion , of which the size of the outstanding U.S. bond market debt was $31.2 trillion according to BIS (or alternatively $34.3, stock market A stock market or equity market is a public market for the trading of company stock and derivatives at an agreed price; these are securities listed on a stock exchange as well as those only traded privately and currency market The foreign exchange market is a worldwide decentralized over-the-counter financial market for the trading of currencies. Financial centers around the world function as anchors of trading between a wide range of different types of buyers and sellers around the clock, with the exception of weekends as well as retail financial institutions like banks Banking is generally a highly regulated industry, and government restrictions on financial activities by banks have varied over time and location. The current set of global bank capital standards are called Basel II. In some countries such as Germany, banks have historically owned major stakes in industrial corporations while in other countries.

Exactly how these markets function is a complex question. However, economists generally agree that the interest rates yielded by any investment take into account:

This rate incorporates the deferred consumption and alternative investments elements of interest.

Inflationary expectations

According to the theory of rational expectations Rational expectations is a hypothesis in economics which states that agents' predictions of the future value of economically relevant variables, is not systematically wrong in that all errors are random. An alternative formulation is that rational expectations are model-consistent expectations, in that the agents inside the model assume the model', people form an expectation of what will happen to inflation In economics, inflation is a rise in the general level of prices of goods and services in an economy over a period of time. When the price level rises, each unit of currency buys fewer goods and services; consequently, inflation is also an erosion in the purchasing power of money – a loss of real value in the internal medium of exchange and unit in the future. They then ensure that they offer or ask a nominal interest rate that means they have the appropriate real interest rate The "real interest rate" is approximately the nominal interest rate minus the inflation rate . Since the inflation rate over the course of a loan is not known initially, volatility in inflation represents a risk to both the lender and the borrower on their investment.

This is given by the formula:

where:

= offered nominal interest rate
= desired real interest rate
= inflationary expectations

Risk

The level of risk Risk concerns the deviation of one or more results of one or more future events from their expected value. Technically, the value of those results may be positive or negative. However, general usage tends to focus only on potential harm that may arise from a future event, which may accrue either from incurring a cost or by failing to attain some in investments is taken into consideration. This is why very volatile In finance, volatility most frequently refers to the standard deviation of the continuously compounded returns of a financial instrument within a specific time horizon. It is used to quantify the risk of the financial instrument over the specified time period. Volatility is normally expressed in annualized terms, and it may either be an absolute investments like shares In financial markets, a share is a unit of account for various financial instruments including stocks , and investments in limited partnerships, and REITs. The common feature of all these is equity participation (limited in the case of preference shares) and junk bonds In finance, a high yield bond is a bond that is rated below investment grade at the time of purchase. These bonds have a higher risk of default or other adverse credit events, but typically pay higher yields than better quality bonds in order to make them attractive to investors have higher returns than safer ones like government bonds A bond is a debt investment in which an investor loans a certain amount of money, for a certain amount of time, with a certain interest rate, to a company. A government bond is a bond issued by a national government denominated in the country's own currency. Bonds issued by national governments in foreign currencies are normally referred to as.

The extra interest charged on a risky investment is the risk premium A risk premium is the minimum difference a person requires to be willing to take an uncertain bet, between the expected value of the bet and the certain value that he is indifferent to. The required risk premium is dependent on the risk preferences of the lender.

If an investment is 50% likely to go bankrupt, a risk-neutral In economics, risk neutral behavior is in between risk aversion and risk seeking. If offered either €50 or a 50% chance of €100, a risk averse person will take the €50, a risk seeking person will take the 50% chance of €100, and a risk neutral person would have no preference between the two options lender will require their returns to double. So for an investment normally returning $100 they would require $200 back. A risk-averse Risk aversion is a concept in economics, finance, and psychology based in the behavior of humans whilst exposed to uncertainty lender would require more than $200 back and a risk-loving A risk lover is a person who has a preference for risk. While most investors are considered risk averse, one could view casino goers as risk loving. If a person has a discontinuous indifference curve they may also behave in risk loving ways lender less than $200. Evidence suggests that most lenders are in fact risk-averse.

Generally speaking a longer-term investment carries a maturity risk premium, because long-term loans are exposed to more risk of default during their duration.

Liquidity preference

Most investors prefer their money to be in cash Cash refers to money in the physical form of currency, such as banknotes and coins. The word has various claims for sources. Some claim that the word comes from the modern French word caisse, which means "money box", coming from Provençal word caissa, from the Italian cassa, from the Latin capsa which means "box". In the 18th than in less fungible Fungibility is the property of a good or a commodity whose individual units are capable of mutual substitution. Examples of highly fungible commodities are crude oil, wheat, orange juice, precious metals, and currencies 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. This is known as liquidity preference Liquidity preference in macroeconomic theory refers to the demand for money, considered as liquidity. The concept was first developed by John Maynard Keynes in his book The General Theory of Employment, Interest and Money to explain determination of the interest rate by the supply and demand for money. The demand for money as an asset was. A 1-year loan, for instance, is very liquid compared to a 10-year loan. A 10-year US Treasury bond A United States Treasury security is government debt issued by the United States Department of the Treasury through the Bureau of the Public Debt. Treasury securities are the debt financing instruments of the United States Federal government, and they are often referred to simply as Treasuries. There are four types of marketable treasury, however, is liquid because it can easily be sold on the market.

A market interest-rate model

A basic interest rate pricing model for an asset

Assuming perfect information, pe is the same for all participants in the market, and this is identical to:

where

in is the nominal interest rate on a given investment
ir is the risk-free return to capital
i*n = the nominal interest rate on a short-term risk-free liquid bond (such as U.S. Treasury Bills).
rp = a risk premium reflecting the length of the investment and the likelihood the borrower will default
lp = liquidity premium (reflecting the perceived difficulty of converting the asset into money Money is any object that is generally accepted as payment for goods and services and repayment of debts in a given country or socio-economic context. The main functions of money are distinguished as: a medium of exchange; a unit of account; a store of value; and, occasionally, a standard of deferred payment and thus into goods).

Interest rate notations

What is commonly referred to as the interest rate in the media is generally the rate offered on overnight deposits by the Central Bank or other authority, annualised.

The total interest on an investment depends on the timescale the interest is calculated on, because interest paid may be compounded Compound interest arises when interest is added to the principal, so that from that moment on, the interest that has been added also itself earns interest. This addition of interest to the principal is called compounding . A loan, for example, may have its interest compounded every month: in this case, a loan with $100 initial principal and 1%.

In finance Finance is the science of funds management. The general areas of finance are business finance, personal finance, and public finance. Finance includes saving money and often includes lending money. The field of finance deals with the concepts of time, money, and risk and how they are interrelated. It also deals with how money is spent and budgeted, the effective interest rate is often derived from the yield, a composite measure which takes into account all payments of interest and capital from the investment.

In retail finance, the annual percentage rate and effective annual rate concepts have been introduced to help consumers easily compare different products with different payment structures.

Money market mutual funds quote their rate of interest as the 7 Day SEC Yield.

Interest rates in macroeconomics

Elasticity of substitution

The elasticity of substitution (full name should be the marginal rate of substitution of the relative allocation) affects the real interest rate. The larger is the magnitude of the elasticity of substitution, the more is the exchange, and the lower the real interest rate.

Output and unemployment

Interest rates are the main determinant of investment on a macroeconomic scale. Broadly speaking, if interest rates increase across the board, then investment decreases, causing a fall in national income.

A government institution, usually a central bank, can lend money to financial institutions to influence their interest rates as the main tool of monetary policy. Usually central bank interest rates are lower than commercial interest rates since banks borrow money from the central bank then lend the money at a higher rate to generate most of their profit.

By altering interest rates, the government institution is able to affect the interest rates faced by everyone who wants to borrow money for economic investment. Investment can change rapidly in response to changes in interest rates and the total output.

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.

Mathematical note

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, eliminating higher order terms, are:

The formulae in this article are exact if logarithms of indices are used in place of rates.

Negative interest rates

Interest rates are usually positive, but not always. Given the alternative of holding cash (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.[7]

However, central bank rates can be negative; in July 2009 Sweden's Riksbank was the first central bank to use negative interest rates, lowering its deposit rate to −0.25%, a policy advocated by deputy governor Lars E. O. Svensson.[8] This negative interest rate is possible because Swedish banks, as regulated companies, must hold these reserves with the central bank – they do not have the option of holding cash.

Negative interest rates have been proposed in the past, notably in the late 19th century by Silvio Gesell.[9] 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.

External links

You can see a list of current interest rates at these sites:

Notes

  1. ^ moneyextra.com Interest Rate History. Retrieved 2008-10-27
  2. ^ news.bbc.co.uk UK interest rates lowered to 0.5%
  3. ^ (Homer, Sylla & Sylla 1996, p. 509)
  4. ^ Bundesbank. BBK - Statistics - Time series database. Retrieved 2008-10-27
  5. ^ worldeconomies.co.uk Zimbabwe currency revised to help inflation
  6. ^ (Homer, Sylla & Sylla 1996, p. 1)
  7. ^ Buiter, Willem (2009-05-07), Negative interest rates: when are they coming to a central bank near you?, Financial Times, http://blogs.ft.com/maverecon/2009/05/negative-interest-rates-when-are-they-coming-to-a-central-bank-near-you/
  8. ^ Ward, Andrew; Oakley, David (2009-08-27), Bankers watch as Sweden goes negative, Financial Times, http://www.ft.com/cms/s/0/5d3f0692-9334-11de-b146-00144feabdc0.html
  9. ^ Mankiw, Gregory (2009-04-18), It May Be Time for the Fed to Go Negative, New York Times, http://www.nytimes.com/2009/04/19/business/economy/19view.html

See also

Debt
Debt instruments
Bond Debenture · Corporate bond · Government bond · Municipal bond
Loan Usury · Consumer lending · Predatory lending · Loan shark
Managing debt Debt management plan · Consolidation · Debt-snowball method · Bankruptcy
Debt collection and evasion Debt compliance · Collection agency · Garnishment · Tax refund interception · Debt bondage · Debtors' prison · Phantom debt · Charge-off · Strategic default
Debt markets Fixed income · Consumer debt · Corporate debt · Government debt · Money market · Deposit account · Debt buyer · Securitization
Debt in economics Debt levels and flows · External debt · Internal debt · Consumer leverage ratio
Interest · Interest rate · Default · Insolvency

Categories: Mathematical finance | Interest rates | Monetary policy

 

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Q. I have floating rate SBA commercial borrowing with 30 year term. Right now, the interest rates are low and My cash flow from the operation covers interest very well. But if Interest rates go up, the equation can change dramatically. How can I hedge this risk? SBA does not allow fixed rates.
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A. Unfortunately, the only way to hedge against this risk is to get a fixed rate. The adjustable rate loans are definitely NOT to protect the consumer, it's how the bank protects themselves from interest rate risk. Refinancing to a fixed rate is really your only option.
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