Real Interest Rate
Compare exact inflation-adjusted interest, the Fisher approximation and their percentage-point gap over the same period.
Question, try, then observe
More interest, more purchasing power?
Raise inflation and see whether the extra interest still preserves purchasing power.
Hypothetical teaching scenario; results update immediately.
This illustration uses a same-period inflation assumption; expected versus realized inflation is explained below.
What did you just see?
Suppose 100 grows to 105 while the same basket rises from 100 to 103. Purchasing power follows 105/103, not a subtraction of currency amounts.
Expected and realized inflation answer different questions
Both inputs must cover the same period and price measure. Ex ante estimates depend on your inflation assumption; ex post adjustments depend on realized price changes. This tool does not forecast inflation.
Another example
- Enter 5% nominal interest and 3% inflation for the same year.
- Divide 1.05 by 1.03, then subtract one.
- Compare 1.9417% with 2%; 0.0583 pp is not a relative percentage error.
Show formal definition and formula
The real rate is the nominal growth factor divided by the same-period price growth factor, minus one. The nominal factor equals the product of the real and price factors; rates in the formulas are decimals.
Exact real interest rate
Fisher approximation
Exact multiplicative relation
The real rate is the nominal growth factor divided by the same-period price growth factor, minus one. The nominal factor equals the product of the real and price factors; rates in the formulas are decimals.
- i
- Same-period nominal interest rate
- π
- Same-period inflation rate
- r
- Exact inflation-adjusted real interest rate
- Units
- Formula rates use decimals: 5% = 0.05. Inputs and displayed rates use percentages; both inputs cover the same period.
Common mistakes
Subtracting inflation is an approximation. Expected inflation gives an ex ante real-rate illustration; realized inflation gives an ex post real return. Substituting expected inflation is not an identity for expected real returns under uncertainty or a causal model of interest-rate determination.
Frequently asked questions
Can inflation be negative?
Yes. Both nominal interest and inflation must exceed −100% to keep amount and price factors positive.
You can now explore…
- Separate exact real interest from the Fisher approximation
- Distinguish expected and realized inflation
Term reference1 terms
Open a term when you need a reminder. Underlined words in the article work too.