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## Interest rate

An interest rate is the rate at which interest is paid by a borrower for the use of money that they borrow from a lender. Specifically, the interest rate (I/m) is a percent of principal (I) paid at some rate (m). 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. Interest rates are normally expressed as a percentage of the principal for a period of one year.[1]

Interest rates targets are also a vital tool of monetary policy and are taken into account when dealing with variables like investment, inflation, and unemployment. Although most of the assumptions and expectations made by the Central Banks or Reserve Banks by countries (and economies) that by technically lowering the interest rate would produce the effect of increasing investments and consumptions, however, low interest rate by macro-economic policy is also risky and would also lead to the creation of massive economic bubble, when great amount of investments are poured into the real estate market and stock market, as what Japan experienced in the late 1980s and early 1990s that resulted in the large numbers of accounts of unpaid debts to the Japanese Banks and bankruptcy of these banks and caused stagflation to the local Japanese Economy (Japan being the second largest economy at the time), with exports becoming the last pillar for the growth of Japanese economy throughout the rest of 1990s and early 2000. The same scenario occurs to the United States' lowering of interest rate since late 1990s to present (see 2007 2012 global financial crisis) substantially by the decision of Federal Reserve System. Under Margaret Thatcher, United Kingdom's economy was maintaining stable growth by preventing to lower the interest rate by the Bank of England. For developed economies, the pace of the function of the interest rate therefore is inevitably argued either to be protecting the designated range of mild inflation in an economy for the health of economic activities or cap the interest rate concurrently with the economic growth to safeguard the economic momentum.[2][3][4][5][6][7]

## 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 has varied between about 0.25% to 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)

### Interest rates in the United States

In the United States, authority for interest rate decisions is divided between the Board of Governors of the Federal Reserve (Board) and the Federal Open Market Committee (FOMC). The Board decides on changes in discount rates after recommendations submitted by one or more of the regional Federal Reserve Banks. The FOMC decides on open market operations, including the desired levels of central bank money or the desired federal funds market rate. Currently, interest rates in the United States are at or near historical lows.

## Reasons for interest rate change

• 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 or money 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.

## Real vs nominal interest rates

The nominal interest rate is the amount, in percentage 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 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 into account. (See real vs. nominal in economics.) 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, in this case, is zero. After the fact, the 'realized' real interest rate, which has actually occurred, is given by the Fisher equation, and is r = \frac{1+i}{1+p}-1\,\! where p = the actual inflation rate over the year. The linear approximation r \approx i-p\,\! is widely used. The expected real returns on an investment, before it is made, are: i_r = i_n - p_e\,\! where: i_r\,\! = real interest rate i_n\,\! = nominal interest rate p_e\,\! = expected or projected inflation over the year ## Market interest rates There is a market for investments which ultimately includes the money market, bond market, stock market and currency market as well as retail financial institutions like banks. Exactly how these markets function are sometimes complicated. However, economists generally agree that the interest rates yielded by any investment take into account: • The risk-free cost of capital • Inflationary expectations • The level of risk in the investment • The costs of the transaction This rate incorporates the deferred consumption and alternative investments elements of interest. ### Inflationary expectations According to the theory of rational expectations, people form an expectation of what will happen to inflation in the future. They then ensure that they offer or ask a nominal interest rate that means they have the appropriate real interest rate on their investment. This is given by the formula: i_n = i_r + p_e\,\! where: i_n\,\! = offered nominal interest rate i_r\,\! = desired real interest rate p_e\,\! = inflationary expectations ### Risk The level of risk in investments is taken into consideration. This is why very volatile investments like shares and junk bonds have higher returns than safer ones like government bonds. The extra interest charged on a risky investment is the risk premium. 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 lender will require their returns to double. So for an investment normally returning$100 they would require $200 back. A risk-averse lender would require more than$200 back and a risk-loving 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 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. This 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 liquid because it can easily be sold on the market.

### A market interest-rate model

A basic interest rate pricing model for an asset

i_n = i_r + p_e + rp + lp\,\!

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

i_n = i^*_n + rp + lp\,\!

where

in is the nominal interest rate on a given investment
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 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, annualized.

The total interest on an investment depends on the timescale the interest is calculated on, because interest paid may be compounded.

In finance, 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.

## 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 the magnitude of the elasticity of substitution, the more the exchange, and the lower the real interest rate.

### Output and unemployment

Interest rates are the main determinant of investment on a macroeconomic scale. The current thought is that if interest rates increase across the board, then investment decreases, causing a fall in national income. However, the Austrian School of Economics sees higher rates as leading to greater investment in order to earn the interest to pay the depositors. Higher rates encourage more saving and thus more investment and thus more jobs to increase production to increase profits. Higher rates also discourage economically unproductive lending such as consumer credit and mortgage lending. Also consumer credit tends to be used by consumers to buy imported products whereas business loans tend to be domestic and lead to more domestic job creation [and/or capital investment in machinery] in order to increase production to earn more profit.

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.

## Impact on savings and pensions

Financial economists such as World Pensions Council (WPC) experts 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 [14]

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

This potentially long-lasting collapse in returns on government bonds is taking place against the backdrop of a protracted fall in returns for other core-assets such as blue chip stocks, and, more importantly, a silent demographic shock. Factoring in the corresponding longevity risk , pension premiums could be raised significantly while disposable incomes stagnate and employees work longer years before retiring. [14]

## Mathematical note

Because interest and inflation are generally given as percentage increases, the formulae above are (linear) approximations.

For instance,

i_n = i_r + p_e\,\!

is only approximate. In reality, the relationship is

(1 + i_n) = (1 + i_r)(1 + p_e)\,\!

so

i_r = \frac {1 + i_n} {1 + p_e} - 1\,\!

The two approximations, eliminating higher order terms, are:

\begin{align} (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{align}

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

## Negative interest rates

Nominal interest rates are normally positive, but not always. 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.[15]

However, central bank rates can, in fact, 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.[16] 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.

During the European sovereign-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).[17]

More often, 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).[18][19] In the late 1970s, United States Treasury securities with negative real interest rates were deemed certificates of confiscation.[20]

Negative interest rates have been proposed in the past, notably in the late 19th century by Silvio Gesell.[21] 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 approving cited the idea of a carrying tax on money,[21] (1936, The General Theory of Employment, Interest and Money) but dismissed it due to administrative difficulties.[22] 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, with the tax based on how the bill had been held.[22]

It has been proposed that a negative interest rate can in principle be levied on existing paper currency via a serial number lottery: choosing a random number 0 to 9 and declaring that bills whose serial number end in that digit are worthless would yield a negative 10% interest rate, for instance (choosing the last two digits would allow a negative 1% interest rate, and so forth). This was proposed by an anonymous student of N. Gregory Mankiw,[21] though more as a thought experiment than a genuine proposal.[23]

A much more simplistic method to ultimately achieve negative interest rate and provide disincentive to holding cash would be for governments to encourage inflationary monetary policy.

## Notes

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

Historical interest rates can be found at:

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