Skip to content
Marlbridge

AP® Macroeconomics · Unit 4 · Topic 4.2

Nominal v. Real Interest Rates: Revision Notes (Macroeconomics 4.2)

One-page recap of nominal and real interest rates, how expected inflation enters the nominal rate, and how to calculate a real rate in hindsight, with the sign errors to avoid.

Short on time? This page is the recap. For explanations and worked examples, use the full study guide.

Recap

  • The nominal interest rate is the rate paid on a loan, not adjusted for inflation. It measures the return in money.
  • The real interest rate is adjusted for inflation. It measures the return in purchasing power.
  • When a loan is agreed, lenders and borrowers set the nominal rate as the expected real rate plus expected inflation.
  • After the event, the real rate in hindsight is the nominal rate minus the actual inflation rate.
  • Unexpected inflation makes the real rate lower than planned (borrowers gain). Unexpectedly low inflation, or deflation, makes it higher (lenders gain).
  • The real rate is negative whenever inflation is above the nominal rate.

Key relationships

Relationship Formula Use it to
Setting the nominal rate nominal = expected real + expected inflation find the rate written in a new loan
Real rate in hindsight real = nominal − actual inflation find what a lender actually earned
Expected real rate expected real = nominal − expected inflation find what both sides planned
Inflation from a price index (new index − old index) ÷ old index × 100 get the inflation rate to subtract
Expected inflation ↑ (expected real unchanged) nominal ↑ by the same number of points predict changes in nominal rates

Assumptions behind the numbers

  • The nominal rate is fixed for the whole loan.
  • “Inflation” means the percentage change in a price index such as the CPI over the period of the loan.
  • The course uses subtraction. The exact division method gives slightly different answers and is background only.

Mistakes to avoid

  1. Adding inflation to get the real rate. Real = nominal minus inflation.
  2. Using expected inflation for a real rate in hindsight. Use actual inflation.
  3. Subtracting the CPI level instead of the inflation rate.
  4. Forgetting that subtracting negative inflation (deflation) raises the real rate.
  5. Saying all inflation hurts lenders. Only unexpected inflation does.
  6. Judging a savings account by its nominal rate alone.

Quick self-check

  1. Lenders want a real rate of 2% and expect 5% inflation. What nominal rate do they charge? (7%)
  2. A loan has a nominal rate of 6%. Inflation turns out to be 9%. What is the real rate in hindsight? (−3%)
  3. A deposit pays 4% nominal and prices fall by 1%. What is the real rate? (5%)
  4. Expected inflation rises from 3% to 5% and the expected real rate stays at 2%. What happens to the nominal rate? (It rises from 5% to 7%.)

Next: practice questions.

AP® and Advanced Placement® are trademarks registered by the College Board, which is not affiliated with, and does not endorse, this website. Marlbridge is an independent tuition provider. It is not an authorized AP course provider, an AP school or an exam centre, and these resources are not official College Board materials. Reading them or doing simulations does not meet the laboratory requirement of an AP science course.