AP® Macroeconomics review sheet from Aim for Five (aimforfive.com/macro/units/4/4-2)
Unit 4 · Topic 4.2
4.2 Nominal v. Real Interest Rates
The nominal interest rate is the rate a loan or account actually states. The real interest rate takes inflation out, so it shows how much more a lender can actually buy. When inflation turns out different from what people expected, the gains shift between borrowers and lenders.
Key terms
- nominal interest rate
- real interest rate
- expected inflation
- Fisher equation (nominal = real + expected inflation)
Nominal versus real
The nominal interest rate is the percentage a loan, bond or savings account actually pays, with no adjustment for inflation. If you lend $100 at 6%, you get back $106.
But if prices rose 4% that year, your $106 buys only about 2% more than your $100 did a year earlier. That 2% is the real interest rate: the gain in purchasing power (what your money can actually buy).
Real interest rate = nominal interest rate − inflation rate. This simple subtraction is an approximation, and it's the version AP uses.
Setting a rate ahead of time: the Fisher equation
When a loan is made, nobody knows what inflation will be. So the lender and the borrower agree on a nominal rate that covers the real return the lender wants plus the inflation both sides expect. This relationship is called the Fisher equation, after the economist Irving Fisher.
- Nominal interest rate = real interest rate + expected inflation rate.
- Planned real interest rate = nominal interest rate − expected inflation rate.
- Real interest rate after the fact = nominal interest rate − actual inflation rate.
Why expected inflation raises nominal rates
If lenders expect more inflation, they won't accept the same nominal rate, because the money they get back will buy less. So, holding the real rate the same, a 1 percentage point rise in expected inflation raises the nominal rate by about 1 percentage point. That's why nominal interest rates tend to be high in countries where people expect high inflation.
Who wins when inflation surprises
Once a loan's nominal rate is locked in, the real rate the lender actually earns depends on actual inflation. Inflation that everyone expected is already built into the nominal rate, so it doesn't shift wealth between borrowers and lenders. Surprises do. This connects to the costs of inflation in topic 2.5.
| What happens | Real rate actually earned | Who gains | Who loses |
|---|---|---|---|
| Inflation is higher than expected | Lower than planned | Borrower, who repays with dollars that buy less | Lender |
| Inflation is lower than expected | Higher than planned | Lender | Borrower |
| Inflation equals what was expected | Same as planned | Neither | Neither |
Where each rate shows up in the course
The money market (4.5) sets the nominal interest rate. The loanable funds market (4.7) sets the real interest rate. Investment decisions and international capital flows (6.6) depend on real rates, because firms and investors care about purchasing power.
In the short run, economists usually assume expected inflation doesn't change right away. So when the central bank pushes the nominal rate down, the real rate falls too.
A real rate can be negative. If your savings account pays 1% and inflation is 3%, your real return is −2%: your balance grows, but it buys less each year.
Worked examples
Try each one yourself first, then open the solution.
- Example 1
Finding the real rate after the fact
A bank charges 8% interest on a one-year car loan. During the year, the inflation rate turns out to be 5%. What real interest rate did the bank earn?
Show the solutionHide the solution
- Step 1: After the fact, use actual inflation: real rate = nominal rate − actual inflation.
- Step 2: Real rate = 8% − 5% = 3%.
Answer: 3%
- Example 2
Setting a nominal rate, then an inflation surprise
A lender wants a 3% real return and expects 2% inflation. (a) What nominal interest rate should it charge? (b) Inflation actually turns out to be 4%. What real rate did the lender earn, and who gained from the surprise?
Show the solutionHide the solution
- Step 1: (a) Before the loan, use expected inflation: nominal = real + expected inflation = 3% + 2% = 5%.
- Step 2: (b) After the fact, use actual inflation: real = 5% − 4% = 1%.
- Step 3: The lender planned on 3% but got 1%. Inflation was higher than expected, so the borrower repaid with dollars that bought less than both sides planned. The borrower gained and the lender lost.
Answer: (a) 5%. (b) 1%; the borrower gained and the lender lost.
- Example 3
A negative real rate (classic trap)
A savings account pays a nominal interest rate of 1.5%, and inflation is 4%. A student says the real interest rate is 2.5%. Is that right?
Show the solutionHide the solution
- Step 1: Real rate = nominal rate − inflation, in that order.
- Step 2: Real rate = 1.5% − 4% = −2.5%.
- Step 3: The student subtracted in the wrong order. A negative real rate means the saver's money buys less at the end of the year than at the start, even though the balance grew.
Answer: No. The real interest rate is −2.5%, so the saver loses purchasing power.
Common mistakes
- Subtracting in the wrong order. Real rate = nominal rate − inflation, and the answer can be negative.
- Using actual inflation when the question asks what nominal rate a lender should set. Before a loan is made, use expected inflation; after the fact, use actual inflation.
- Saying unexpected inflation hurts borrowers. Higher-than-expected inflation helps borrowers with fixed-rate loans and hurts lenders.
- Labeling the money market's vertical axis 'real interest rate'. The money market uses the nominal rate; loanable funds uses the real rate.
On the exam
- Free-response questions often give two of the three numbers (nominal rate, real rate, inflation) and ask for the third. Write the formula and show the subtraction or addition.
- You may be asked how a change in expected inflation affects the nominal interest rate. If the real rate doesn't change, higher expected inflation means a higher nominal rate.
Connected topics
Videos
Check yourself
5 questions on 4.2 Nominal v. Real Interest Rates. Pick an answer to see if you got it, and why.
A bank wants to earn a real return of 3 percent on its loans, and it expects inflation of 2 percent over the next year. What nominal interest rate should it charge?
A saver buys a one-year bond with a nominal interest rate of 6 percent. During that year, the actual inflation rate turns out to be 8 percent. What real interest rate did the saver earn?
In January, Lena borrows $10,000 from a credit union for one year at a nominal interest rate of 6 percent. When they sign the loan, both Lena and the credit union expect inflation of 2 percent during the year.
By December, actual inflation for the year has turned out to be 5 percent.
Hypothetical scenario
What real interest rate did Lena and the credit union expect when the loan was made?
What real interest rate did Lena actually pay on the loan?
Which of the following best describes the effect of the higher-than-expected inflation?
0 of 5 answered