Fisher equation

In financial mathematics as well as economics, the Fisher equation expresses the relationship between nominal & real interest rates under inflation. Named after Irving Fisher, an American economist, it can be expressed as real interest rate ≈ nominal interest rate − inflation rate. In more formal terms, where r equals the real interest rate, i equals the nominal interest rate, and π equals the inflation rate, the Fisher equation is r = i - π. It can also be expressed as i = r + π or 1 + i = 1 + r 1 + π.

Applications

When loans are made, the amount borrowed and the repayments due to the lender are ordinarily stated in nominal terms, ago inflation. However, when inflation occurs, a dollar repaid in the future is worth less than a dollar borrowed today. To calculate the true economics of the loan, it is necessary to reconstruct the nominal cash flows to account for future inflation.

The Fisher equation can be used in the analysis of bonds. The real usefulness on a bond is roughly equivalent to the nominal interest rate minus the expected inflation rate. But if actual inflation exceeds expected inflation during the life of the bond, the bondholder's real improvement will suffer. This risk is one of the reasons inflation-indexed bonds such as U.S. Treasury Inflation-Protected Securities were created to eliminate inflation uncertainty. Holders of indexed bonds are assured that the real cash flow of the bond principal plus interest will non be affected by inflation.

As detailed by Steve Hanke, Philip Carver, and Paul Bugg 1975, cost benefit analysis can be greatly distorted whether the exact Fisher equation is not applied. Prices and interest rates must both be projected in either real or nominal terms.

The Fisher equation plays a key role in the ]