Interest rate(Redirected from Interest rates)
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. 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.
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.
Factors influencing interest ratesEdit
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
as well as other factors.
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.
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.
Historical interest ratesEdit
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, and Germany experienced rates close to 90% in the 1920s down to about 2% in the 2000s. During an attempt to tackle spiraling hyperinflation in 2007, the Central Bank of Zimbabwe increased interest rates for borrowing to 800%.
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.
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 interest rate changesEdit
- 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.
- 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.
Real vs nominal interest ratesEdit
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:
where p is the inflation rate. For low rates and short periods, the linear approximation applies:
Market interest ratesEdit
Interest rates reflect:
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.
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.
A maturity risk premium applied to a longer-term investment reflects a higher perceived risk of default.
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 modelEdit
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:
- 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 and thus into goods).
The spread of interest rates is the lending rate minus the deposit rate. 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.
Interest rates in macroeconomicsEdit
Elasticity of substitutionEdit
The elasticity of substitution (full name is 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 unemploymentEdit
Higher interest rates increase the cost of borrowing which can reduce investment and output and increase unemployment. Expanding businesses, especially entrepreneurs tend to be net debtors. However, the Austrian School of Economics sees higher rates as leading to greater investment in order to earn the interest to pay its creditors. Higher rates encourage more saving and reduce inflation.
Open Market Operations in the United StatesEdit
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 inflationEdit
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 pensionsEdit
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” 
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.
Because interest and inflation are generally given as percentage increases, the formulae above are (linear) approximations.
is only approximate. In reality, the relationship is
The two approximations, eliminating higher order terms, are:
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. Most elegantly, if the natural logarithm is used, yielding the neper as logarithmic units, scaling by 100 to obtain the centineper yields units that are infinitesimally equal to percentage change (hence approximately equal for small values), and for which the linear equations hold for all values.
Zero interest rate policyEdit
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 interest ratesEdit
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). In the late 1970s, United States Treasury securities with negative real interest rates were deemed certificates of confiscation.
On central bank reservesEdit
A so-called "negative interest rate policy" (NIRP) is a negative (below zero) central bank target interest rate.
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.
Negative interest rates have been proposed in the past, notably in the late 19th century by Silvio Gesell. 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, (1936, The General Theory of Employment, Interest and Money) but dismissed it due to administrative difficulties. 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.
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, though more as a thought experiment than a genuine proposal.
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.
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.
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%. 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. This is not technically an example of "negative interest on excess reserves," because Sweden does not have a reserve requirement, but imposing a reserve interest rate without reserve requirements imposes an implied reserve requirement of zero. The Riksbank studied the impact of these changes and stated in a commentary report that they led to no disruptions in Swedish financial markets.
On bond yieldsEdit
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).
The classical theory of the determination of the interest rateEdit
The classical theory was developed by a number of authors, including Ricardo, Mountifort Longfield, J. S. Mill, and Irving Fisher. It was strongly criticised by Keynes whose remarks nonetheless made a positive contribution to it.
Mill’s theory is set out the chapter “Of the rate of interest” in his “Principles of political economy”. He says that the interest rate adjusts to maintain equilibrium between the demands for lending and borrowing. Individuals lend in order to defer consumption or for the sake of the greater quantity they will be able to consume at a later date owing to interest earned. They borrow in order to anticipate consumption, but entrepreneurs also borrow to fund investment and governments borrow for their own reasons. The three sources of demand compete for loans.
For entrepreneurial borrowing to be in equilibrium with lending:
The interest for money... is... regulated... by the rate of profits which can be made by the employment of capital...
Ricardo’s and Mill’s ‘profit’ is made more precise by the concept of the marginal efficiency of capital (the expression, though not the concept, is due to Keynes), which may be defined as the annual revenue which will be yielded by an extra increment of capital as a proportion of its cost. So the interest rate r must be equal to the marginal efficiency of capital r'. It is possible to work with r and r' as separate variables, but since the economy is constrained to lie on the line along which they are equal, we let the single variable r denote their common value.
The efficiency schedule of capital Io (r ) is a function which shows how much investment is possible with a return of at least r. In a stationary economy it will resemble the blue curve in the diagram. The step shape arises from the assumption that opportunities to invest with yields greater than r̂ have been largely exhausted while there is untapped scope to invest with a lower return. Capital carves its own efficiency schedule the way a river carves its own bed.
The shape of the efficiency schedule is almost enough by itself to ensure that the interest rate will remain close to r̂. If we want to be more rigorous we may plot a curve showing the demand Sd for saving (which is equal to the demand for investment) as a function of r for the current income Ŷ. This gives the solid red curve in the diagram. Saving is the excess of deferred over anticipated consumption, and its demand function is much like that given by Keynes (see Keynesian economics), but in classical theory definitely an increasing function of r (the dependence of Sd on Y was not relevant to classical concerns prior to the development of theories of unemployment). The rate of interest is given by the intersection of the solid red curve with the efficiency schedule of capital. But because the schedule is almost vertical in the relevant region, a change in income (leading in extreme cases to the broken red curve) will make little difference to the interest rate.
In some cases the analysis will be less simple. The introduction of a new technique, leading to demand for new forms of capital, will shift the base of the step to the right and change the shape of the blue curve. Or a sudden increase in the desire to anticipate consumption (perhaps through military spending in time of war) will absorb most available loans; the interest rate will increase and investment will be reduced to the amount whose return exceeds it. This is illustrated by the dotted red demand curve.
In the case of extraordinary spending in time of war the government may wish to borrow more than the public would be willing to lend at a normal interest rate. If the dotted red curve started negative and showed no tendency to increase with r then the government would be trying to buy what the public was unwilling to sell at any price. Keynes mentions this possibility as a point “which might, perhaps, have warned the classical school that something was wrong” (p182).
He also points out (on the same page) that the classical theory doesn’t explain the usual supposition that “an increase in the quantity of money has a tendency to reduce the rate of interest, at any rate in the first instance”.
Keynes’s diagram of the efficiency schedule lacks the step shape which underpins the classical theory. He objects that
the functions used by classical theory... do not furnish material for a theory of the rate of interest; but they could be used to tell us... what the rate of interest will have to be, if the level of employment [which determines income] is maintained at a given figure.
The comment loses much of its strength when the efficiency schedule can be thought of as vertical.
Later (p184) he claims that “it involves a circular argument” to construct a theory of interest from the efficiency schedule since “the ‘marginal efficiency of capital’ partly depends on the scale of current investment, and we must already know the rate of interest before we can calculate what this scale will be”.
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- Isolated remarks in the chapters “Effects of accumulation on profits and interest” and “On currency and banks” in “Principles of political economy and taxation”.
- “Lectures on political economy”, IX.
- “The rate of interest.”
- “The general theory of employment, interest and money”, especially the appendix to Chapter 14. Page numbers refer to the widely available edition published by Macmillan for the Royal Economic Society as part of Keynes’s collected writings.
- See also his chapters “Of the law of the increase of capital” and “Of profits”.”
- “Of the rate of interest”, §1.
- Ricardo, chapter “On currency and banks”
- Keynes’s official term for this function was the ‘schedule of the marginal efficiency of capital’. Fisher described it as the ‘investment opportunity side of interest theory’ (p155) – hence the ‘o‘ in Io .
- Mill, §3; Longfield.
- Mill §3, Longfield.