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Interest rate
An interest rate is the price a borrower pays
for the use of money he does not own, and the return a lender receives
for deferring his consumption, by lending to the borrower. Interest
rates are normally expressed as a percentage over the period of
one year.
Interest rates are also a vital tool of monetary
policy and are used to control variables like investment, inflation,
and unemployment.
Contents
* 1 Causes of interest rates
* 2 Real vs nominal interest rates
* 3 Market interest rates
o 3.1 Risk-free cost of capital
o 3.2 Inflationary expectations
o 3.3 Risk
o 3.4 Liquidity preference
o 3.5 A market interest-rate model
o 3.6 Interest rate notations
* 4 Interest rates in macroeconomics
o 4.1 Output and unemployment
o 4.2 Open Market Operations in the United
States
o 4.3 Money and inflation
* 5 Mathematical note
* 6 See also
* 7 External links
Causes of 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, 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 realise.
* 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
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 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:
ir = in — p
where p = the actual inflation rate over the
year.
The expected real returns on an investment,
before it is made, are:
ir = in — pe
where:
in = nominal interest rate
ir = real interest rate
pe = 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 is a complex
question. 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
Risk-free cost of capital
The risk-free cost of capital is the real interest
on a risk-free loan. While no loan is ever entirely risk-free, bills
issued by major nations like the United States are generally regarded
as risk-free benchmarks.
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:
in = ir + pe
where:
in = offered nominal interest rate
ir = desired real interest rate
pe = 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 10-year loan, for instance, is very illiquid compared
to a 1-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
in = ir + pe + rp+ lp
Assuming perfect information, pe is the same
for all participants in the market, and this is identical to:
in = i*n + rp + lp
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 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.
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
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. Note that if interest rates are high,
that means the broad economy is doing well and thus people will
be willing to borrow money at higher interest rates.
Interest rates are set by a government institution,
usually a central bank, as the main tool of monetary policy. The
institution offers to buy or sell money at the desired rate and,
because of their immense size, they are able to effectively set
i*n.
By altering i*n, 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
to changes in interest rates, affecting national income.
Through Okun's Law changes in output affect
unemployment.
Open Market Operations in the United States
The effective federal funds rate charted over
fifty years
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, the
Open Market Desk at the Federal Reserve Bank of New York can supply
the market with dollars by purchasing T-notes, hence increasing
the nation's money supply. By increasing the money supply or Aggregate
Supply of Funding (ASF), interest rates will fall due to the excess
of dollars banks will end up with in their reserves. Excess reserves
may be lent in the Fed funds market to other banks, thus driving
down rates.
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. This means that interest
rates can affect inflation in the future.
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