Real vs Nominal Interest Rates: Adjusting for Inflation
The rate on a savings account or bond is a nominal rate: it tells you how fast the balance grows in money terms. The real rate tells you how fast your buying power grows, after rising prices have eaten into the gain.
The difference decides whether saving is actually moving you forward. This guide gives the exact formula and the quick approximation, works through a ten-year example, and explains when the shortcut stops being reliable.
The exact formula and the shortcut
The exact relationship compares growth factors. Your money grows by (1 + nominal) while prices grow by (1 + inflation), so the buying power grows by the ratio:
real rate = (1 + nominal) ÷ (1 + inflation) − 1All rates as decimals, so 4% is 0.04.
The shortcut is simply real ≈ nominal − inflation. It is quick and usually close when rates are low, but it always slightly overstates the real rate when it is positive.
| Nominal | Inflation | Exact real rate | Shortcut |
|---|---|---|---|
| 4% | 3% | 0.971% | 1.000% |
| 5% | 2% | 2.941% | 3.000% |
| 1.5% | 3% | −1.456% | −1.500% |
| 20% | 15% | 4.348% | 5.000% |
At ordinary rates the gap is a few hundredths of a point. At 20% nominal with 15% inflation it is more than half a point, which is why the exact formula is the safer habit.
Worked example: 10,000 for 10 years
Say 10,000 earns 4% a year while inflation runs at 3% a year.
- Nominal balance after 10 years: 10,000 × 1.0410 = 14,802.44.
- Prices after 10 years are 1.0310 = 1.3439 times as high.
- Balance in today's money: 14,802.44 ÷ 1.3439 = 11,014.41.
- Real gain: 1,014.41, or about 0.97% a year, which matches the exact real rate in the table.
The headline growth was 48.0%. After inflation, the buying power rose by about 10.1%. A saver who only looks at the nominal balance sees almost five times the improvement that actually happened.
The formula also works backwards. To earn a real 2% when inflation is 3%, you need a nominal rate of 1.02 × 1.03 − 1 = 5.06%, not 5%.
When the real rate is negative
If inflation is higher than the nominal rate, the real rate is below zero and the balance buys less every year even though it keeps growing.
Worked example: 10,000 at 1.5% with 3% inflation. After ten years the nominal balance is 10,000 × 1.01510 = 11,605.41, which looks like a gain. In today's money it is 10,000 × (1.015 ÷ 1.03)10 = 8,635.51, or about 13.6% less buying power than you started with.
Negative real rates are not a mistake or a scam, and some people accept them for safety or access to their cash. The point is to see the cost clearly.
A smaller positive example: an account paying 3.2% when inflation is 2.4% has a real rate of 1.032 ÷ 1.024 − 1 = 0.781%. On 25,000 over five years the nominal balance is 29,264.32, but in today's money it is about 25,991.94, a real gain of less than 1,000 despite a nominal gain of more than 4,000.
Caveats worth remembering
- Taxes. If interest is taxed, the after-tax nominal rate is lower. A 4% rate taxed at 25% leaves 3%, which is no real gain at 3% inflation. Tax rules differ widely, so treat this as an illustration only.
- Expected versus actual inflation. When you choose a savings product, you only know today's rate. The real rate you end up with is known only afterwards.
- Personal inflation. The official rate is an average. Your own costs may rise faster or slower.
- Borrowers see the mirror image. On a fixed-rate loan at 6% with 3% inflation, the real cost of borrowing is 1.06 ÷ 1.03 − 1 = 2.91%, because the fixed repayments are worth less in real terms as prices rise. This applies to loans whose rate stays fixed, not to variable rates that move with inflation.
For the underlying idea of prices rising over time, read inflation and purchasing power. To project the nominal balance, use the compound interest calculator, and to express a future amount in today's money, use the present value calculator.
This article is general education, not financial advice. Rates in the examples are illustrations and do not describe any real product or forecast.
- Compound Interest Calculator: Enter a starting balance, an interest rate and a term to see how money grows when interest is added to the balance. Add regular deposits or withdrawals to model a savings plan.
- Present Value Calculator: Enter a future amount, a discount rate and the number of periods. The calculator returns what that money is worth today and how much value discounting removes.
This article is general information, not professional advice. See our Disclaimer and Editorial Policy.
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