Inflation and Real Interest Rates
Your savings earn 2% and prices rise 4%: do you have more money or less? Tell nominal from real interest rates to see what a rate truly means.
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Text version · Interest Rates & Swaps, lesson 7: “Inflation and Real Interest Rates”
Your savings earn 2% and prices rise 4%: do you have more money or less? Tell nominal from real interest rates to see what a rate truly means.
Real rate = nominal − inflation
Banks pay a nominal rate; how fast prices rise is the inflation rate. Subtract one from the other and you get how fast your purchasing power really grows: the real interest rate.
Negative real rate: the more you save, the “less” you have
With a 2% deposit rate and 4% inflation, the number in your account grows every year, but it buys less and less. Both compound, so over time the gap widens.
Why central banks watch it
When inflation is high, the central bank raises the policy rate to make real rates positive: saving pays more, borrowing costs more, demand cools and price rises slow down. Non-interest-bearing assets like gold are especially sensitive to real rates.
Key takeaways
- Real interest rate ≈ nominal rate − inflation; the exact formula is (1 + nominal) ÷ (1 + inflation) − 1.
- When the real rate is negative, your savings balance grows on paper while its purchasing power shrinks.
- Both inflation and interest compound: the longer the time, the wider the gap from "losing to inflation".
- Central banks often hike to push real rates positive and cool the economy. Non-yielding assets like gold are especially sensitive to real rates.
Try it yourself
You can do these exercises in this lesson's interactive simulation:
- Click “Example: 2% · 4%” and press ▶: after 10 years, what are the account balance and the price of a basket? How many baskets can you still buy?
- Click “5% · 3%”: what's the exact value on the “Real interest rate” card? How far is it from the 2% approximation?
- Drag both the deposit rate and inflation to 3%: how many baskets can you buy after 10 years? Why did the balance grow but the number of baskets stay the same?
- Click “High inflation 1% · 6%”, then drag “Years saved” to 30: what fraction of today's purchasing power is left?
Quiz and explanations
- 1. The nominal rate is 5% and inflation is 3%. Roughly what's the real interest rate?
- Answer: 2%.Approximately 5% − 3% = 2% (exactly about 1.94%).
- 2. Savings earn 2% and inflation runs at 4% a year. After 10 years, roughly what's the purchasing power of this money compared with today?
- Answer: About 82%.1.02¹⁰ ÷ 1.04¹⁰ ≈ 1.219 ÷ 1.480 ≈ 0.82. The balance grew 22%, but prices rose 48%.
- 3. In which case does holding cash savings cost you the most?
- Answer: Nominal 1%, inflation 6%.The real rate is about 1% − 6% = −5%, so purchasing power shrinks fastest.
Terms in this lesson
- inflation (Inflation): A broad, ongoing rise in prices, so the same money buys less; the inflation rate is how much prices rise in a year.
- interest rate (Interest Rate): The price of borrowing money, usually shown as an annual percentage.
- policy rate (Policy Rate): The benchmark rate set by a central bank, which drives borrowing costs across the economy.
- purchasing power (Purchasing Power): How much a sum of money can actually buy; if your savings rate trails inflation, the number grows but its purchasing power shrinks.
- real interest rate (Real Rate): Nominal interest rate − inflation, the true return after inflation.