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The Fisher equation relates the nominal interest rate i to the real interest rate r and expected inflation π^e: i = r + π^e. The real interest rate is what matters for consumption and investment decisions because it reflects the true return to saving in terms of purchasing power. If inflation rises unexpectedly, real returns to existing lenders fall while real costs to borrowers fall, creating a redistribution of wealth.
You already know the difference between nominal and real variables — nominal measures use current prices while real measures adjust for inflation to reflect actual purchasing power. Applying that distinction to interest rates produces one of the most important equations in macroeconomics: the Fisher equation, named for economist Irving Fisher. It says that the nominal interest rate equals the real interest rate plus expected inflation: i = r + π^e. Simple in form, but the implications run through monetary policy, investment decisions, and the distribution of wealth.
Start with the intuition. A bank offers you 6% annual interest on a savings deposit. You feel richer, but the question that matters is: after inflation erodes the value of your dollars, how much more *purchasing power* do you have? If inflation is 4%, your 6 nominal dollars at year's end buy only about 2% more goods than at the start. The real interest rate is approximately 2% — your actual gain in purchasing power. This is what a rational saver or investor cares about. A 6% nominal return in an economy with 10% inflation leaves you poorer in real terms; a 3% nominal return in an economy with 0% inflation leaves you meaningfully better off.
The Fisher equation is written as an *ex ante* (before the fact) relationship using expected inflation π^e, because when a loan is made, the actual future inflation rate is unknown. The nominal rate agreed upon in the contract embeds the lender's and borrower's best guess about inflation over the loan's life. The ex post real interest rate — the one actually realized — equals the nominal rate minus *actual* inflation. When inflation turns out higher than expected, borrowers win (their real debt burden is lower than anticipated) and lenders lose (their real return is lower than anticipated). This unexpected inflation creates a redistribution of wealth from creditors to debtors, which is why inflation expectations are so important in financial contracts and why central banks that lose control of inflation face intense pressure from the financial sector.
For monetary policy, the Fisher equation constrains what central banks can do. When the central bank raises nominal rates, what happens to real rates depends on whether inflation expectations adjust. In the short run, raising i tends to raise r as well — businesses and households face higher real borrowing costs, which slows investment and spending. This is the transmission mechanism of tight monetary policy. Over the long run, if the central bank credibly targets low inflation, the nominal rate will eventually reflect that lower π^e and a stable r. The distinction between nominal and real rates is also why deflation can be dangerous: when inflation is negative (deflation), real interest rates can be *higher* than nominal rates — even a 0% nominal rate implies a positive real rate, which discourages borrowing and investment at exactly the moment a struggling economy needs stimulus.