What this calculator does
A 6 per cent return with 3 per cent inflation is not a 3 per cent real gain. The exact figure is 2.91 per cent, because the inflation applies to the grown balance rather than to the original amount.
The gap is small at low rates and grows as rates rise. At 6 per cent inflation against 12 per cent nominal, the approximation says 6 per cent while the exact answer is 5.66 per cent, a difference of a third of a percentage point.
The formula
The Fisher equation divides one plus the nominal rate by one plus the inflation rate and subtracts one. The common approximation simply subtracts inflation from the nominal rate, which is close but always slightly high.
| Term | Meaning |
|---|---|
| Nominal rate | The stated interest rate, before adjusting for inflation. |
| Real rate | What the return is worth in purchasing power. |
| Fisher equation | The exact relationship between nominal rate, real rate and inflation. |
The inputs explained
| Field | What to enter |
|---|---|
| Nominal interest rate (%) | The nominal interest rate as quoted. |
| Expected inflation rate (%) | Expected inflation over the same period. |
When to use it
Assessing a savings account
An account paying below the inflation rate loses purchasing power, whatever the headline figure says.
Comparing across time periods
A 12 per cent rate in a high-inflation era may be worth less in real terms than 4 per cent today.
Setting a required return
Investment targets are more meaningful stated in real terms than in nominal ones.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
What is a 6 per cent return worth after inflation?
The same nominal rate against four inflation rates.
| Inflation rate | Real interest rate (exact) | Real interest rate (quick approximation) |
|---|---|---|
| 2% | 3.92% | 4.00% |
| 4% | 1.92% | 2.00% |
| 6% | 0.000% | 0.000% |
| 8% | -1.85% | -2.00% |
Questions
Why is the approximation always too high?
Because subtracting ignores that inflation erodes the interest earned as well as the principal. The exact calculation accounts for that compounding, which always leaves slightly less than simple subtraction suggests.
When does the difference matter?
When rates are high or the period is long. At 2 per cent inflation the gap is under a tenth of a percentage point; at 9 per cent against a 12 per cent nominal rate it is a quarter of a point, which compounds noticeably over decades.
Can the real rate be negative?
Yes, and it frequently is. When inflation exceeds the interest available on savings, money loses purchasing power while sitting in the account. This has been a common condition in many countries.
Should expected or actual inflation be used?
Expected inflation, when looking forward, since that is what determines the real return you are agreeing to. Actual inflation is used afterwards to work out what the real return turned out to be.
For how a nominal rate compounds over time, see the compound interest calculator. For the return a risk-free investment should offer, see the CAPM calculator.