Nominal versus Real Returns: What Inflation Actually Takes

Real return = (1 + nominal) ÷ (1 + inflation) − 1

At 7% nominal and 3% inflation: 1.07 ÷ 1.03 − 1 ≈ 3.88%, not 4%.

The gap comes from the denominator — purchasing power must be deflated by the higher price level, not subtracted. The higher the inflation, the worse the shortcut: at 10% nominal and 8% inflation, the real return is 1.10 ÷ 1.08 − 1 ≈ 1.85%, while subtraction gives 2%.

100,000 at 7% nominal for 20 years: 100000 × 1.07²⁰ ≈ 386,968.

But prices rise by 1.03²⁰ ≈ 1.806, so its real purchasing power is only 386,968 ÷ 1.806 ≈ 214,000 in today’s money.

Check the other way: 100000 × 1.0388²⁰ ≈ 214,000 — both routes agree. Nominally almost 4×, really only about 2.1×.

With a 20% tax on gains, 7% nominal becomes 5.6%; after 3% inflation: 1.056 ÷ 1.03 − 1 ≈ 2.52%.

Add a 1% management fee and the real figure may be near 1.5%. That is why fees and taxes are the most underestimated drag on compounding — they do not subtract from the final number, they reduce the growth base every single year.

Savings at 2% with 3% inflation: 1.02 ÷ 1.03 − 1 ≈ −0.97% — about 1% real loss per year. The balance grows while purchasing power shrinks.

The Rule of 72 in reverse: at 3% inflation, purchasing power halves roughly every 72 ÷ 3 = 24 years. This is not a reason to gamble the emergency fund — it is a reason to think about real returns for money sitting idle long term.

• When comparing products, convert to after-tax, after-fee, after-inflation real returns first.
• For long-term goals (retirement, education), model with real returns or you will systematically overestimate what the money buys.
• Inflation is an estimate; your own spending mix (rent, healthcare, education) can make experienced inflation quite different.