What an interest rate measures
In Topic 4.1 you saw that a bond pays interest and that money pays little or none. An interest rate is the price of borrowing money, or the reward for lending (saving) it, expressed as a percentage of the amount per year.
A lender gives up spending today in order to spend more later. So what a lender really cares about is not the number of extra valdas she gets back, but how much more she can buy with them. That is the difference between a nominal and a real interest rate.
- Nominal interest rate: the interest rate paid on a loan, not adjusted for inflation. It is the rate written in the contract or shown on the bank’s website. It measures the return in money.
- Real interest rate: the interest rate adjusted for inflation. It measures the return in purchasing power: how much more goods and services the lender can buy at the end than at the start.
If prices did not change, the two rates would be the same. With inflation, part of the nominal interest only makes up for the fall in what each valda buys.
How lenders and borrowers set a nominal rate
When a loan is agreed, nobody knows what inflation will be. Both sides must use their expectations.
- The lender asks: what real return do I want for giving up my money for a year? And how much do I expect prices to rise? She wants both covered.
- The borrower asks: what real cost am I willing to pay? He accepts a higher nominal rate when he expects inflation, because he expects to repay with valdas that buy less.
So the nominal rate they agree is the sum of the two:
Nominal interest rate = expected real interest rate + expected inflation rate
This tells you how the rates move together.
| Change | Effect |
|---|---|
| Expected inflation rises by 2 percentage points; the expected real rate does not change | Nominal rate rises by 2 percentage points |
| Expected inflation falls; the expected real rate does not change | Nominal rate falls by the same amount |
| Nominal rate is fixed in a contract, and expected inflation rises | The real rate the lender now expects to earn falls |
Calculating a real rate in hindsight
Once the year is over, the actual inflation rate is known. Now you can calculate the real rate the lender actually earned:
Real interest rate (in hindsight) = nominal interest rate − actual inflation rate
The nominal rate was fixed in advance, so the real rate in hindsight depends on what inflation turned out to be.
- Inflation as expected: the real rate equals the expected real rate. Neither side is surprised.
- Inflation higher than expected: the real rate is lower than expected. The borrower repays in valdas that buy less than planned, so the borrower gains and the lender loses. This is the redistribution you met in Topic 2.5.
- Inflation lower than expected (or deflation): the real rate is higher than expected. The lender gains and the borrower loses.
A real rate can be negative. That happens whenever inflation is higher than the nominal rate.
Why the distinction matters. Saving and borrowing decisions depend on the real rate, because people care about what they can buy. A firm borrowing at 10% while prices rise by 8% faces a real cost of only 2%, which is low. A saver earning 1% while prices fall by 1% earns a real 2%, which is not bad at all. The nominal rate alone cannot tell you whether borrowing is cheap or saving is rewarding.
Our fictional economy: Valdoria
Valdoria is the fictional country used across the Marlbridge macroeconomics pages. Its currency is the valda (VD). All people, rates and index numbers below are fictional.
Worked example 1: setting the rate on a loan
Farah owns a bakery and borrows VD 24,000 for one year from a credit union to buy an oven. Both sides want a real interest rate of 3.5%, and both expect inflation of 4.5% over the year.
Question. (a) What nominal interest rate do they agree? How much does Farah repay? (b) Calculate the real interest rate in hindsight if actual inflation turns out to be 6.5%, 2.0% or 4.5%. In each case, who gains? (c) What nominal rate would they have agreed if they had expected 6.5% inflation?
(a) Nominal rate = 3.5% + 4.5% = 8.0%. Interest = 24,000 × 0.08 = VD 1,920, so Farah repays VD 25,920. This amount is fixed in the contract.
(b) Real rate in hindsight = 8.0% − actual inflation.
| Actual inflation | Real rate in hindsight | Compared with the 3.5% expected | Who gains |
|---|---|---|---|
| 6.5% | 8.0 − 6.5 = 1.5% | lower | Farah (the borrower) |
| 2.0% | 8.0 − 2.0 = 6.0% | higher | the credit union (the lender) |
| 4.5% | 8.0 − 4.5 = 3.5% | the same | neither: the deal went as planned |
(c) Nominal rate = 3.5% + 6.5% = 10.0%. If the higher inflation had been expected, it would have been built into the contract, and the credit union would still have earned a real 3.5%.
Interpretation. The 8% nominal rate is made of two parts. One part (3.5%) is the reward the lender expected for lending. The other part (4.5%) was meant only to make up for rising prices. When inflation turned out to be 6.5%, more of the 8% went on making up for inflation, and less was left as a real reward.
Worked example 2: real rates from price index data
A Valdorian bank sets the nominal rate on one-year savings deposits at the start of each year. The table shows those rates and Valdoria’s CPI at the end of each year.
| Year | CPI at end of year | Nominal rate on deposits made at the start of the year |
|---|---|---|
| 2022 | 150.00 | — |
| 2023 | 159.00 | 4.0% |
| 2024 | 163.77 | 4.5% |
| 2025 | 162.13 | 3.0% |
Question. (a) Calculate the inflation rate for 2023, 2024 and 2025. (b) Calculate the real interest rate earned by savers in each year. (c) In which year did savers do best in terms of purchasing power, and why? (d) At the start of 2023, the bank and its savers expected inflation of 1.5%. What real rate did they expect, and who gained from what actually happened?
(a) Inflation = (new CPI − old CPI) ÷ old CPI × 100, as in Topic 2.4.
- 2023: (159.00 − 150.00) ÷ 150.00 × 100 = 6.00%
- 2024: (163.77 − 159.00) ÷ 159.00 × 100 = 3.00%
- 2025: (162.13 − 163.77) ÷ 163.77 × 100 = −1.00% (deflation)
(b) Real rate = nominal rate − actual inflation.
- 2023: 4.0 − 6.00 = −2.00%
- 2024: 4.5 − 3.00 = 1.50%
- 2025: 3.0 − (−1.00) = 3.0 + 1.00 = 4.00%
(c) 2025, even though it had the lowest nominal rate. Prices fell, so every valda of savings, and of interest, bought more at the end of the year. In 2023 the highest-looking year was the worst: the real rate was negative, so savers ended the year able to buy less than when they started.
(d) Expected real rate = 4.0% − 1.5% = 2.5%. The actual real rate was −2.00%, far below that, because inflation (6.00%) was much higher than expected. The bank, as the borrower of savers’ money, gained; the savers, as lenders, lost.
Check. In 2025 subtracting a negative number raises the real rate. With deflation, the real rate is always above the nominal rate.
Background: why subtraction is close but not exact
The course uses real rate = nominal rate − inflation, and that is all you need. It is an approximation that works well when rates are small. A more exact method divides: (1 + nominal) ÷ (1 + inflation) − 1. For Farah’s loan with 6.5% inflation, this gives 1.08 ÷ 1.065 − 1 ≈ 1.41%, compared with 1.5% by subtraction. Use subtraction unless a question tells you otherwise.
Common misconceptions
- “The real rate is the nominal rate plus inflation.” It is the nominal rate minus inflation. Nominal = real + expected inflation; rearrange carefully.
- “A higher nominal rate always means a better deal for savers.” Only if inflation does not rise by more. In Worked example 2, 4.0% was the worst year and 3.0% was the best.
- “Lenders always lose from inflation.” Only from unexpected inflation. Expected inflation is built into the nominal rate.
- “Real interest rates cannot be negative.” They are negative whenever inflation exceeds the nominal rate.
- “In hindsight you subtract expected inflation.” The real rate in hindsight uses actual inflation. Expected inflation is used when the rate is set.
- Using the CPI level instead of the inflation rate. Subtract the percentage change in the index, not the index number.
- “Deflation lowers the real rate.” Subtracting a negative inflation rate raises the real rate above the nominal rate.
Where this leads
Next, Topic 4.3, Definition, Measurement, and Functions of Money, defines money itself. Later in Unit 4, the money market (Topic 4.5) determines the nominal interest rate, and the loanable funds market (Topic 4.7) determines the real interest rate. If bond prices and interest rates are not yet secure, go back to Topic 4.1, Financial Assets.
Now try the practice questions, then use the revision notes and the checklist to consolidate.
Quick questions
Can a real interest rate be negative?
Yes. If inflation is higher than the nominal rate, the real rate is negative. A lender is repaid more valdas than she lent, but they buy less than the valdas she gave up.
Is the real rate exactly the nominal rate minus inflation?
The course uses this subtraction, and it is very close when rates are small. A more exact method divides instead of subtracting, but you are not asked to use it.