Interest rate

Interest rates vary according to:

• the government's directives to the central bank to accomplish the government's goals
• the currency of the principal sum lent or borrowed
• the term to maturity of the investment
• the perceived default probability of the borrower
• supply and demand in the market
• the amount of collateral
• special features like call provisions
• reserve requirements
• compensating balance

as well as other factors.

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.

Base rate usually refers to the annualized effective interest rate offered on overnight deposits by the central bank or other monetary authority.

The annual percentage rate (APR) may refer either to a nominal APR or an effective APR (EAPR). The difference between the two is that the EAPR accounts for fees and compounding, while the nominal APR does not.

The annual equivalent rate (AER), also called the effective annual rate, is used to help consumers compare products with different compounding frequencies on a common basis, but does not account for fees.

A discount rate is applied to calculate present value.

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.

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.[2][3][4][5][6]

Germany experienced deposit interest rates from 14% in 1973 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,[7][8] and Germany experienced rates close to 90% in the 1920s down to about 2% in the 2000s.[9][10] During an attempt to tackle spiraling hyperinflation in 2007, the Central Bank of Zimbabwe increased interest rates for borrowing to 800%.[11]

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.[12]

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)

• 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.[13]
• 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.

The nominal interest rate is the rate of interest with no adjustment for inflation.

For example, suppose someone deposits $100 with a bank for one year, and they receive interest of $10 (before tax), so at the end of the year, their balance is $110 (before tax). In this case, regardless of the rate of inflation, the nominal interest rate 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.

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:

• The risk-free cost of capital
• Expected inflation
• Risk premium
• Transaction costs

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".[17] Current interest rates in savings accounts often fail to keep up with the pace of inflation.[18]

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.

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.

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.

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).[19][20] In the late 1970s, United States Treasury securities with negative real interest rates were deemed certificates of confiscation.[21]

On government bond yields

Ireland bond prices, Inverted yield curve in 2011,[34] And rates went negative after the European debt crisis

  15 year bond

  10 year bond

  5 year bond

  3 year bond

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).[35]

• Forward rate
• List of countries by central bank interest rates
• Macroeconomics
• Rate of return
• Short-rate model
• Spot rate

• Homer, Sidney; Sylla, Richard Eugene; Sylla, Richard (1996). A History of Interest Rates. Rutgers University Press. ISBN 978-0-8135-2288-3. Retrieved 2008-10-27.