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Encyclopedia > Interest rates

An interest rate is the 'rental' price of money. When a resource or asset is borrowed, the borrower pays the lender for the use of it. The interest rate is the price paid for the use of money for a period of time. One type of interest rate is the yield on a bond.


When money is loaned the lender defers consumption (or other use of the money) for a specific period of time. The lender does this in exchange for an expected increase in future income. The expected increase in real income (relative to the amount loaned) is the real interest rate. Note that the real interest rate is calculated by adjusting the actual rate charged (known as the money or nominal interest rate) to take inflation into account. (See real vs. nominal in economics.) A first approximation for the real interest rate for a one-year loan is:

ir = inpe

where:

in = nominal interest rate
ir = real interest rate
pe = expected or projected inflation over the year.

After the fact, there is the realized or ex post real interest rate:

ir = inp

where p = the actual inflation rate over the year.


Thus, if the (expected) inflation rate is 5% and the nominal interest rate is 7%, the (expected) real interest rate is 2%.


If financial markets have adjusted for the effects of expected inflation and the real interest rate is given, then the nominal rate approximately equals:

ir + pe

Thus, if the real interest rate is 3% and the inflation rate equals 5%, the nominal interest rate = 8%. The theory of rational expectations is sometimes applied to say that this equation applies in most cases. Most economists would agree that it applies over several years, as financial markets adjust: higher inflation leads to higher nominal rates, all else being equal.


Irving Fisher proposed a better approximation of the relationship between nominal interest rate, inflation and real interest rate. For a one-year bond, the expected real rate equals

ir = [(1 + in)/(1 + pe)] — 1

Using the first numerical example above, the expected real rate equals [1.07/1.05]-1 = 0.19 or 1.9%, which is similar to (but not the same as) the 2% calculated above.


When comparing different interest rates on different kinds of loans, a different kind of formula is used. For the nominal rate on a single type of asset,

in = i*n + d + mrp + lp

where

i*n = the nominal interest rate on a short-term risk-free liquid bond (such as U.S. Treasury Bills).
d = default premium (reflecting the likelihood of default by the borrower)
mrp = maturity risk premium (risk factor for length of borrowing period)
lp = liquidity premium (reflecting the perceived difficulty of converting the asset into money and thus into goods).
Contents

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External links

  • Grant's Online - Home Page - Grant's Interest Rate Observer (http://www.grantspub.com/)

  Results from FactBites:
 
Interest rate - Wikipedia, the free encyclopedia (1410 words)
Interest rates are normally expressed as a percentage over the period of one year.
Interest rates are the main determinant of investment on a macroeconomic scale.
Interest rates are set by a government institution, usually a central bank, as the main tool of monetary policy.
Interest rate parity - Wikipedia, the free encyclopedia (1354 words)
The interest rate parity is the basic identity that relates interest rates and exchange rates.
The covered interest parity states that the interest rate difference between two countries' currencies is equal to the percentage difference between the forward exchange rate and the spot exchange rate.
Thus the basic idea of covered interest arbitrage is to borrow in the country with lower interest rate and invest in the country with higher interest rate.
  More results at FactBites »

 
 

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