Nominal vs real: the gap that compounds.
A 7 % nominal return in a 3 % inflation environment is not 7 %. The Fisher equation makes the relationship exact, and the difference matters enormously over long horizons.
The Fisher equation
The exact relationship between nominal return, inflation, and real return:
(1 + rnominal) = (1 + rreal) × (1 + π)
where π is the inflation rate. Solving for real:
rreal = (1 + rnominal) / (1 + π) − 1
For 7% nominal and 3% inflation: 1.07 / 1.03 − 1 = 0.0388 = 3.88%.
The popular approximation
A common shortcut: real ≈ nominal − inflation. For 7% and 3%, that gives 4% (vs. the exact 3.88%). The approximation is fine at low rates and small inflation but breaks down at high rates:
| Nominal | Inflation | Approx (n − π) | Exact (Fisher) | Error |
|---|---|---|---|---|
| 5% | 2% | 3.00% | 2.94% | +0.06 |
| 7% | 3% | 4.00% | 3.88% | +0.12 |
| 10% | 4% | 6.00% | 5.77% | +0.23 |
| 15% | 8% | 7.00% | 6.48% | +0.52 |
| 25% | 15% | 10.00% | 8.70% | +1.30 |
| 50% | 30% | 20.00% | 15.38% | +4.62 |
For developed-market scenarios (sub-10% nominal returns, sub-5% inflation) the approximation is good enough for back-of-envelope work. For emerging-market or crisis-period analysis, use the exact Fisher equation.
Why long-horizon planning needs real
A 30-year retirement projection at 7% nominal will tell you your nest egg ends up at, say, $2 million. That figure is in future dollars. To translate to today's purchasing power for sensible planning, you need to deflate by 30 years of inflation: at 3%, that future $2 million is approximately $824,000 in today's purchasing power.
Working in real returns from the outset avoids this two-step. Set the calculator's expected-return input to a real rate (4% real instead of 7% nominal), and the projection is automatically in today's dollars.
What's a defensible long-run real-return assumption?
Historical real returns by asset class, US data 1928–2024:
| Asset class | Long-run real return | Standard deviation |
|---|---|---|
| US Treasury bills (cash) | ~0.5% | ~3% |
| 10-year US Treasury bonds | ~2.0% | ~8% |
| Corporate bonds (Baa) | ~3.5% | ~10% |
| S&P 500 (large-cap equities) | ~7.0% | ~18% |
| Small-cap equities | ~8.0% | ~22% |
| REITs (real estate investment trusts) | ~5.5% | ~16% |
| Gold | ~1.5% | ~17% |
For long-horizon planning, a 4–6% real return is defensible for a balanced equity-and-bond portfolio. Higher figures (7%+) require the equity allocation to remain high throughout retirement, which raises sequence-of-returns risk.
The compounding gap
Over a 30-year horizon, the difference between 7% nominal and 4% real is substantial: $10,000 grows to $76,123 nominal vs. $32,434 real. Both numbers are correct; they answer different questions. The nominal figure is what your portfolio statement will show in 30 years. The real figure is what that future dollar will actually buy.