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The Fisher equation

Calculate a real interest rate from a nominal rate and inflation, and say who gains

Key terms
Real interest rate
The real interest rate is the nominal interest rate minus the rate of inflation, so it measures the gain in buying power from lending.
Nominal interest rate
The nominal interest rate is the rate actually charged on a loan or paid on a deposit, made up of the real rate plus expected inflation.

The real interest rate is the nominal rate minus inflation

A saver who earns interest ends the year with more pounds, but if prices have risen, each pound buys less. The real interest rate takes inflation out to show what has happened to buying power. The Fisher equation, named after the economist Irving Fisher, links the two rates:

nominal interest rate ≈ real interest rate + inflation

so real interest rate ≈ nominal interest rate − inflation. It is not the same as Fisher's equation of exchange, MV = PT, which links the money supply to the price level and belongs to the quantity theory of money. If a bank account pays 4% and inflation is 5%, the real interest rate is −1%: the saver has more pounds but can buy less with them.