Real and nominal interest rates
What your savings really earn once rising prices are counted.
FinanceMankiw ch. 11About 3 min: 2 reading, 1 practiceUpdated
General education, not financial advice.
- Tell the nominal from the real interest rate
- Estimate a real rate as nominal minus inflation
- Say when savings lose buying power
Money over time: lesson 4 of 5
- Mankiw ch. 14
- Compound interest 5 min
- Present value 5 min
- Mankiw ch. 11
- Measuring inflation with a price index 4 min
- Real and nominal interest rates 3 min
- Bogle ch. 4
- Costs and the market return 3 min
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Pairs with Mankiw, Principles of Macroeconomics (6th ed.), chapter 11, "Measuring the Cost of Living": real and nominal interest rates
What it is
The nominal interest rate is the one you are quoted: how fast the number of coins in your account grows. The real interest rate is corrected for inflation: how fast what your money can buy grows.
They are linked, approximately, by:
real interest rate ≈ nominal interest rate − inflation rate
More detail: the exact relation
The exact link is (1 + real) = (1 + nominal) ÷ (1 + inflation). With a nominal rate of 5% and inflation of 3%: 1.05 ÷ 1.03 ≈ 1.0194, a real rate of about 1.94%, close to the shortcut's 2%. The subtraction shortcut gets less accurate as rates get higher: at 50% nominal and 40% inflation, the shortcut says 10% but the exact real rate is 1.50 ÷ 1.40 − 1 ≈ 7.1%.
Quick check
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Which rate tells you how much more you can buy?
- That only counts money, not what it buys
Show answer
The real rate. The real rate corrects for inflation.
Why it matters
What you care about is not the number on the statement but what it will buy. A savings rate that sounds good can still leave you worse off if prices are rising faster.
Worked example
You save 500 at 5% interest. A year later you have 525. Before, a cinema ticket cost 5, so your savings could buy 100 tickets. How many can you buy now?
| Inflation | Ticket price | Tickets you can buy | Real gain |
|---|---|---|---|
| 0% | 5.00 | 105 | +5% |
| 3% | 5.15 | about 102 | about +2% |
| 5% | 5.25 | 100 | 0% |
| 7% | 5.35 | about 98 | about −2% |
Each time, nominal 5% minus inflation gives roughly the real change.
Common mistake
Thinking you are richer because the balance went up. If inflation is higher than your interest rate, the balance rises while what it buys shrinks.
Key terms
- nominal interest rate
- the rate you are quoted, not corrected for inflation
- real interest rate
- the rate corrected for inflation: about nominal − inflation
- purchasing power
- how much your money can buy
- deflation
- falling prices
Practise the key terms
Tap a card to turn it over. 4 cards.
| Front | Back |
|---|---|
| nominal interest rate | the rate you are quoted, not corrected for inflation |
| real interest rate | the rate corrected for inflation: about nominal − inflation |
| purchasing power | how much your money can buy |
| deflation | falling prices |
Practice
Quick quiz
Tap an answer to check it.
Your savings earn 3% and inflation is 5%. What is your real interest rate, roughly?
- Added inflation instead of subtracting it
- Subtracted the wrong way round
Show answer
−2%. 3 − 5 = −2. You can buy about 2% less than before.
Which rate tells you how much more you can buy?
- Nominal counts money, not buying power
Show answer
Real.
In short
- Nominal: how fast the money grows. Real: how fast what it buys grows.
- Real ≈ nominal − inflation.
- If inflation beats your interest rate, you can buy less.
- With deflation, the real rate is above the nominal rate.
Mastery check
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What does the nominal interest rate measure?
Show answer
How fast the amount of money in the account grows, with no correction for prices.
Nominal rate 7%, inflation 4%. Roughly what is the real rate?
Show answer
About 3%.
When can a real interest rate be higher than the nominal rate?
Show answer
When prices are falling (deflation), because each unit of money then buys more.
Further reading
- N. Gregory Mankiw, Principles of Macroeconomics, 6th edition (South-Western, Cengage Learning, 2012), chapter 11.
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