A bond or a bank account pays a nominal interest rate in dollars. But inflation shrinks what each dollar buys. To know what a saver really earns, combine the two, using interest rates and price changes.
Key idea
$$\text{real interest rate} \approx \text{nominal interest rate} - \text{inflation rate}$$ The nominal rate is the growth of your dollars; the real rate is the growth of your buying power. A lender who wants a real return of $r$ and expects inflation $\pi^e$ charges about $r + \pi^e$.
Why it works
Lend \$100 at 5% for a year: you get \$105 back. If prices rose 3%, something that cost \$100 now costs \$103, so your \$105 buys only about 2% more than before. Exactly, $\dfrac{1.05}{1.03} - 1 \approx 1.94\%$; for small rates, subtracting is close enough, and this course uses the subtraction rule. If inflation is higher than the nominal rate, the real rate is negative: savers lose buying power even though their balance grows.
Worked examples
Worked example: Finding the real rate
A savings account pays 4.5% and inflation is 3%. What is the real interest rate?
- $4.5\% - 3\% = 1.5\%$.
- Your buying power grows about 1.5% a year, not 4.5%.
Answer: About 1.5%
Worked example: Expected versus actual
A loan is made at 7%, when both sides expect 2% inflation. Inflation turns out to be 5%. Who gains?
- Expected real rate: $7\% - 2\% = 5\%$. Actual: $7\% - 5\% = 2\%$.
- The borrower pays a lower real rate than planned and gains; the lender loses.
Answer: The borrower
Real rates matter for decisions. A firm deciding whether to borrow for a new machine compares the machine's return with the real cost of borrowing, because the machine's output will sell at future prices. Savers deciding between spending now and later care about how much more they can buy later: the real return.
Common mistake
Adding inflation instead of subtracting it, or thinking a lender earning 5% gains 5% in buying power when inflation is 3%. Check: if prices rise faster than your balance, your buying power falls, so the real rate must be below the nominal rate when inflation is positive.
See it with real data: the 10-year Treasury yield (nominal) and the 10-year inflation-protected Treasury yield (a market real rate) on the Economic Data page. The gap between them is roughly the inflation that markets expect.