Fisher Equation Calculator
From nominal rate and inflation, compute the real rate: real = (1 + nominal) ÷ (1 + inflation) − 1, to see true post-inflation return.
Input Data
Results
At a glance:The Fisher Equation (Irving Fisher) links nominal rate, real rate and inflation: (1 + nominal) = (1 + real)(1 + inflation). This calculator inverts it to the real rate: real = (1 + nominal) ÷ (1 + inflation) − 1, the true purchasing-power gain. The approximation real ≈ nominal − inflation slightly overstates; the exact division is used here. If nominal is below inflation, the real rate is negative — purchasing power shrinks.
Formula
(1 + nominal) = (1 + real)(1 + inflation).
Real = (1 + nominal) ÷ (1 + inflation) − 1.
Approx: real ≈ nominal − inflation.
$$$(1+i) = (1+r)(1+\\pi)$$$$$$r = \\dfrac{1+i}{1+\\pi} - 1$$$$$$\\dfrac{1.05}{1.02} - 1 \\approx 2.94\\%$ $i-\\pi=3\\%$$$How to Use
- Enter the nominal rate.
- Enter the inflation rate.
- View the post-inflation real rate.
Real rate from nominal and inflation (exact Fisher)
| Nominal i | Inflation π | Real (exact) | Approx i−π | Real return |
|---|---|---|---|---|
| 5% | 2% | 2.9412% | 3% | Positive (growing) |
| 2% | 5% | −2.8571% | −3% | Negative (shrinking) |
| 8% | 3% | 4.8544% | 5% | Positive (growing) |
Case Studies
Case 1: Nominal and inflation to real return
Time deposit: nominal i = 5%, inflation π = 2%. True purchasing-power gain?
Exact: real = (1 + 5%) ÷ (1 + 2%) − 1 = 1.05 ÷ 1.02 − 1 ≈ 2.9412%. Approx: 5% − 2% = 3%, a ~0.06pp gap.
Interpretation: the 5% face gain, after 2% prices, really adds about 2.94% purchasing power. The exact division (not naive subtraction) is the truer real return — judge fixed income by real, not nominal.
Case 2: Beware negative real rate — earning yet losing purchasing power
Compare: A nominal 5%, inflation 2% → real ≈ +2.94% (growing). B nominal 2%, inflation 5% → real ≈ −2.86%. C no interest (nominal 0), inflation 3% → real ≈ −2.91%.
B and C show a rising balance yet shrinking purchasing power.
Interpretation: that is the negative real rate — nominal numbers deceive. When inflation exceeds nominal, low-interest cash erodes wealth; that is why high-inflation periods drive demand for inflation-beating assets. For borrowers the reverse: unexpected inflation repays fixed nominal debt with thinner money, easing real burden, so fixed-rate long loans favour borrowers in high-inflation expectations. Inflation is expected/actual; educational use only.
FAQ
What is the Fisher equation; real vs nominal rate?
The Fisher equation links nominal rate, real rate and inflation. Nominal is the rate you see on deposits/bonds, ignoring inflation; real is the purchasing-power gain after inflation — what your money actually buys more of. Example: nominal 5%, inflation 2%, real ≈ 2.94% (exact), not 3%. Equation: (1 + nominal) = (1 + real)(1 + inflation). This calculator inverts to real = (1 + nominal) ÷ (1 + inflation) − 1.
Why use the real rate, not just nominal?
Nominal numbers mislead — a high nominal rate in high inflation can be near zero or negative in real terms. Money's worth is what it buys, not the account figure. Inflation erodes purchasing power, so if interest lags price rises, even a rising balance loses real wealth. Examples: nominal 5%, inflation 2% → real +2.94% (growing); nominal 2%, inflation 5% → real −2.86% (shrinking); nominal 0%, inflation 3% → real −2.91%. All fixed-income evaluation must adjust for inflation to see if real return is positive.
What does it imply for investing and borrowing?
The key frame: what matters is real cost/return, not nominal. For savers/investors: focus on real return; if negative, the 'safe' deposit erodes purchasing power — consider inflation-beating assets. For borrowers: unexpected inflation helps them — a fixed nominal debt is repaid with 'thinner' money, lowering real burden; fixed-rate long loans favour borrowers in high-inflation expectations. For comparison: always compare real rates across periods/markets. See also the Fisher effect calculator (real → nominal).
Why division, not just nominal minus inflation? And the gap?
The shortcut real ≈ nominal − inflation is good for small numbers but not exact — the Fisher equation uses division: real = (1 + nominal) ÷ (1 + inflation) − 1. Reason: inflation erodes purchasing power proportionally, so you divide by (1 + inflation) to recover it, not subtract percentage points. Algebra: (1+i) = (1+r)(1+π) → i = r + π + rπ, so r = i − π − rπ ≈ i − π (when rπ is tiny); the dropped rπ is the gap. Small rates: nominal 5%, inflation 2% → exact 2.94% vs approx 3%, ~0.06pp, negligible. Large: nominal 20%, inflation 15% → exact 4.35% vs approx 5%, 0.65pp, material. So: at low rates the approximation is fine; at high inflation/high rates use the exact division or you systematically overstate real return. This calculator always uses the exact form.
How to use it in Hong Kong's inflation/rate setting?
Apply it to Hong Kong decisions: (1) judge if deposits/time deposits are truly worthwhile — HK rates track US rates (Linked Exchange Rate), inflation is the CPI; enter the deposit nominal rate as i and expected inflation as π to get real; positive means it preserves purchasing power, negative means the 'safe' deposit erodes wealth in low-rate/high-inflation times. (2) Compare returns across periods — nominal alone is unfair (6% with 8% inflation is negative real; 2% with 0.5% inflation is positive). (3) Understand mortgage real cost — HK mortgages are mostly floating H/P plans; real borrowing cost = nominal − inflation; high inflation vs mortgage rate can make real cost negative (repay with thinner money), favouring borrowers; low inflation/high rates raises real cost. (4) Asset allocation — persistently low/negative real rates push investors toward equities, property, inflation-protected assets (with higher risk). Build the emergency fund and clear high-interest debt before heavy investing. Use real returns and keep medical cover. Inflation is expected/actual and shifts; this calculator is for education/estimation, not advice — consult a licensed professional.
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References
Content review: Calculatorism Finance Team. Results are for reference only; please refer to the relevant authorities for the official figures.