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Nominal v. Real
Interest Rates

Master the difference between stated rates and purchasing-power-adjusted rates: the Fisher equation and its real-world applications.

AP Macroeconomics

What Is an Interest Rate?

An interest rate is the price of borrowing money: the percentage a lender charges a borrower for using their funds over a period of time. It is also the reward for saving: the return you earn by letting someone else use your money.

For Borrowers
The cost of a loan: mortgage payments, credit card APR, student loan rates.
For Savers
The reward for depositing money: savings account yield, CD returns, bond coupons.

The Nominal Interest Rate

The nominal interest rate is the stated or advertised rate on a loan or savings account. It is the rate before adjusting for inflation. When your bank says your savings account earns 5%, that is the nominal rate.

Symbol
Typically denoted \( i \) in the Fisher equation.
Observable?
Yes: banks, the Fed, and bond markets all quote nominal rates directly.

The Real Interest Rate

The real interest rate adjusts the nominal rate for inflation. It measures the change in purchasing power: how much more (or less) you can actually buy with the money you earn from saving or owe from borrowing.

Symbol
Typically denoted \( r \) in the Fisher equation.
Observable?
Not directly: you must calculate it from the nominal rate and the inflation rate.

The Fisher Equation

Named after economist Irving Fisher, this equation links the three key variables. The AP-exam approximation is all you need:

\( r \;=\; i \;-\; \pi \)
\( r \)
Real interest rate
\( i \)
Nominal interest rate
\( \pi \)
Inflation rate (or expected inflation)

Visualising \( r = i - \pi \)

Nominal Rate \( (i) = 8\% \)
Inflation \( (\pi) = 3\% \)
Real Rate \( (r) = 5\% \)
\( 8\% - 3\% = 5\% \)

Nominal vs. Real: Side by Side

Nominal Rate \( i \) Real Rate \( r \)
Measures Growth in dollar amount Growth in purchasing power
Adjusts for inflation? No Yes
Directly observable? Yes No (must calculate)
Can be negative? Rarely (zero lower bound) Yes, when \( \pi > i \)
Used by Banks, bond markets Economists, policy analysis

Expected vs. Actual Inflation

There are actually two versions of the Fisher equation, depending on whether you use expected or actual inflation:

Ex Ante (Before)
\( r^e = i - \pi^e \)
Uses expected inflation. This is the rate borrowers and lenders agree on when signing a contract.
Ex Post (After)
\( r = i - \pi \)
Uses actual inflation. This is the rate you actually earned or paid after the fact.

Why Real Rates Matter

1
Investment decisions: Firms compare the real interest rate to the expected real return on capital. If \( r \) is low, more projects are profitable, so investment rises.
2
Saving decisions: Consumers care about purchasing power. A 10% nominal rate with 9% inflation barely rewards saving.
3
Monetary policy: The Fed targets the federal funds rate (nominal), but its effects on the economy depend on the real rate.
4
Loanable funds market: The supply and demand for loanable funds determine the real interest rate in equilibrium.

How to Apply the Fisher Equation

1
Identify the variables: Which two of \( r \), \( i \), and \( \pi \) are given? The third is what you solve for.
2
Write the equation: \( r = i - \pi \). Rearrange if needed: \( i = r + \pi \) or \( \pi = i - r \).
3
Plug in and solve: Substitute the known values and compute. All values are percentages.
4
Interpret the sign: A positive real rate means purchasing power grows. A negative real rate means inflation outpaces the nominal return.

Example 1: Finding \( r \)

A savings account pays a nominal rate of 6%. The current inflation rate is 2%. What is the real interest rate?

\( r = i - \pi \)
\( r = 6\% - 2\% \)
\( r = 4\% \)

Example 2: Finding \( i \)

A firm needs a real return of 3% on its bonds. Expected inflation is 5%. What nominal rate must the firm offer?

\( i = r + \pi \)
\( i = 3\% + 5\% \)
\( i = 8\% \)

Example 3: A Negative Real Rate

A bank offers a nominal rate of 2% on a CD, but inflation turns out to be 4%. What is the real interest rate?

\( r = i - \pi \)
\( r = 2\% - 4\% \)
\( r = -2\% \)

Connection to the Loanable Funds Market

Real Interest Rate (r) Quantity of Loanable Funds S D
\( r^* \)
\( Q^* \)

Common Mistakes

✕ Confusing the Two Rates
Saying "the interest rate is 6%" without specifying nominal or real. On the AP exam, always clarify which rate you mean.
✕ Wrong Sign on Inflation
Adding inflation when you should subtract: \( r = i - \pi \), not \( r = i + \pi \). Remember: inflation erodes purchasing power.
✕ Ignoring Negative Real Rates
Assuming \( r \) must be positive. When \( \pi > i \), the real rate is negative: savers lose purchasing power.

Summary of Key Formulas

Solving For Formula When to Use
Real rate \( r \) \( r = i - \pi \) Given nominal rate and inflation
Nominal rate \( i \) \( i = r + \pi \) Given real rate and inflation
Inflation \( \pi \) \( \pi = i - r \) Given both interest rates

Question 1 of 5

If the nominal interest rate is 7% and the inflation rate is 3%, what is the real interest rate?

Question 2 of 5

A bank offers a nominal interest rate of 3%. If expected inflation is 5%, what is the expected real interest rate?

Question 3 of 5

Investors require a real return of 4%. If expected inflation is 6%, what nominal interest rate must be offered?

Question 4 of 5

In the loanable funds market, the equilibrium interest rate determined by supply and demand is the:

Question 5 of 5

Unexpected inflation benefits which group?