The nominal interest rate is the rate written on the loan. The real interest rate subtracts inflation, so it measures what the lender really earns in purchasing power. Set up a loan, then choose what inflation actually turns out to be and watch who gains and who loses. Finish with the calculator to practice the two AP calculations.
A lender and a borrower sign a one-year, fixed-rate loan. They set the nominal rate with the Fisher equation: nominal rate = real rate + expected inflation. After the year, the real rate the lender actually earns is nominal rate − actual inflation.
Pick a preset problem or type your own numbers. The work is shown the way you would write it on the exam.
The rate written on a loan, bond, or savings account. It tells you how many more dollars you get back, without adjusting for what those dollars can buy.
The nominal rate minus inflation. It tells you how much your purchasing power grows. A 5% nominal rate with 3% inflation is a 2% real rate. If inflation is higher than the nominal rate, the real rate is negative.
Lenders add expected inflation to the real return they want. When expected inflation rises, the nominal rate rises by the same amount and the expected real rate stays the same. This is the Fisher effect.
The ex ante real rate is planned: nominal rate minus expected inflation. The ex post real rate is realized: nominal rate minus actual inflation. They differ only when inflation surprises people.
If inflation is higher than expected, borrowers repay with dollars that buy less, so borrowers gain and lenders lose. If inflation is lower than expected, lenders gain and borrowers lose. Anticipated inflation is already built into the nominal rate, so it moves no purchasing power between them.
The money market graph has the nominal interest rate on its vertical axis. The loanable funds graph has the real interest rate. Using the wrong label costs a point on the FRQ.
Each row is a one-year, fixed-rate loan. Cover the last three columns and work them out yourself. Compare the ex post rate with the ex ante rate to see who gained.
| Nominal rate | Expected inflation | Actual inflation | Ex ante real rate | Ex post real rate | Who gains |
|---|---|---|---|---|---|
| 6% | 2% | 2% | 6 − 2 = 4% | 6 − 2 = 4% | Neither: inflation was anticipated |
| 6% | 2% | 5% | 6 − 2 = 4% | 6 − 5 = 1% | Borrower (inflation higher than expected) |
| 7% | 4% | 1% | 7 − 4 = 3% | 7 − 1 = 6% | Lender (inflation lower than expected) |
| 4% | 3% | 8% | 4 − 3 = 1% | 4 − 8 = −4% | Borrower; the lender loses purchasing power outright |
| 5% | 2% | −1% (deflation) | 5 − 2 = 3% | 5 − (−1) = 6% | Lender (prices fell instead of rising) |
| Find it: 3 + 6 = 9% | 6% | 6% | 3% wanted | 9 − 6 = 3% | Neither: the Fisher effect protected the lender |
AP-style multiple choice. Pick an answer to see the explanation.
The vocabulary for topic 4.2. Read the list, flip through flashcards, or quiz yourself. For every term in the unit, see the Unit 4 terminology guide.