Frequently Asked Questions about the Fisher Equation
What is the Fisher equation?
The Fisher equation links three quantities: the nominal interest rate (i), the real interest rate (r), and inflation (π) in the exact form (1+i) = (1+r)(1+π). Example: with an 8% nominal rate and 3% inflation, the exact real rate is 4.8544% — that is (1.08/1.03)−1.
Why is computing r ≈ i − π not enough?
The i − π formula is only an approximation that ignores the r×π cross term. For an 8% nominal rate and 3% inflation, the approximation gives 5% while the exact value is 4.8544% — a gap of 0.1456 percentage points. The gap widens when inflation is high: at i=12% and π=8% it reaches 0.2963 percentage points.
How do you compute inflation from nominal and real rates?
Rearrange the equation to π = (1+i)/(1+r) − 1. Example: a 5% nominal rate and a 1.5% real rate imply inflation of 3.4483% — that is (1.05/1.015)−1.
What happens to the real interest rate during deflation?
When inflation is negative (deflation), the real rate is actually larger than the nominal rate. Example: a 2% nominal rate with 1% deflation produces a real rate of 3.0303% — that is (1.02/0.99)−1. The purchasing power of unspent money grows as prices fall.
How does inflation erode the purchasing power of my money?
Rp1,000,000 at 5% inflation per year for 10 years is worth the equivalent of Rp613,913.25 in today’s purchasing power — that is 1,000,000/(1.05^10). About 38.61% of its purchasing power is eroded. To keep the same purchasing power, a nominal Rp1,628,894.63 would be needed after 10 years.
How is this tool different from the Raise Lab Calculator?
This tool is a general Fisher equation solver for three directions (nominal, real, inflation) with a scenario table and purchasing power calculator.
Raise Lab Calculator focuses on the payroll context — computing nominal versus real raises, multi-year projections, and after-tax salary. To compute your real raise, use the Raise Lab Calculator.
When does the i − π approximation exactly equal the exact result?
Only when inflation is zero — or when the nominal rate exactly equals inflation (zero real rate, both give 0%). Example: a 6% nominal rate with 0% inflation gives an exact real rate of 6% — identical to the approximation. With positive inflation and a positive real rate, the exact result is slightly lower than the approximation; but when the real rate is negative (inflation exceeds the nominal rate), the exact result is slightly higher instead. Under deflation, the exact result is also higher than the approximation.
Methodology
This tool uses the exact form of the Fisher equation (1+i) = (1+r)(1+π) for all three solution directions: r = (1+i)/(1+π) − 1, i = (1+r)(1+π) − 1, and π = (1+i)/(1+r) − 1. The approximation column uses the classic linear formula (r ≈ i − π) so you can see how large the deviation is. The purchasing power calculator uses the exact deflator (1+π)n, not the (1−π)n approximation used by some secondary sites.