Core Concepts & Learning Goals
When you save money in a bank or take out a loan, the interest rate you see advertised is the nominal interest rate. However, the existence of inflation—a general rise in prices—means that the money you are paid back with is worth less than the money you originally lent. To understand the true return on savings or the true cost of a loan, we must account for this erosion of purchasing power.
This chapter introduces the critical distinction between nominal and real interest rates. The big idea is that rational economic decisions made by lenders and borrowers are based on the real interest rate, which reflects the change in purchasing power, not just the nominal rate.
After studying this topic, you will be able to:
Define the nominal interest rate and the real interest rate.
Explain how expected inflation influences the nominal interest rate set by lenders and borrowers.
Calculate both nominal and real interest rates using the Fisher equation.
Key Concepts Breakdown
1. Defining Nominal and Real Interest Rates
The first step is to distinguish between the two primary measures of interest.
Nominal Interest Rate: The rate of interest paid for a loan, unadjusted for inflation. This is the stated, or advertised, rate. If you deposit money into a savings account that offers a 5% annual interest rate, the nominal rate is 5%.
Real Interest Rate: The rate of interest paid for a loan, adjusted for the effects of inflation. The real interest rate measures the change in your purchasing power. If your savings account pays a 5% nominal rate, but the inflation rate is 2%, your ability to buy goods and services has only increased by approximately 3%. This 3% is the real interest rate.
The real interest rate provides a more accurate measure of the incentive to save and the cost of borrowing.
2. The Fisher Effect: Expected Inflation and Nominal Rates
Lenders and borrowers are forward-looking. When they agree on a loan, they do not know what the actual inflation rate will be over the course of the loan. Therefore, they must base their decisions on their expected inflation rate.
Lenders and borrowers establish nominal interest rates as the sum of their desired real interest rate and the inflation rate they expect over the loan's term. This relationship is often called the Fisher Effect.
The formula for setting the nominal rate is:
- Nominal Interest Rate = Expected Real Interest Rate + Expected Inflation
For example, if a bank wants to earn a real return of 3% on a loan, and it expects the inflation rate to be 2% over the next year, it will charge a nominal interest rate of 5%. This ensures the bank's return on the loan outpaces the expected loss of purchasing power due to inflation.
3. Calculating the Real Interest Rate in Hindsight
Once the term of a loan is complete, we can look back and calculate the actual or realized real interest rate. This is done by subtracting the actual inflation rate that occurred from the nominal interest rate that was charged.
The formula for calculating the realized real interest rate is:
- Real Interest Rate = Nominal Interest Rate – Actual Inflation Rate
This calculated real rate may differ from the expected real rate that the lender and borrower had in mind when they made the agreement.
If Actual Inflation > Expected Inflation, the lender is worse off and the borrower is better off. The real rate is lower than expected.
If Actual Inflation < Expected Inflation, the lender is better off and the borrower is worse off. The real rate is higher than expected.
4. Comparing Nominal and Real Interest Rates
The table below summarizes the key distinctions between these two concepts.
| Feature | Nominal Interest Rate | Real Interest Rate |
|---|---|---|
| Definition | The stated interest rate, unadjusted for inflation. | The interest rate adjusted for inflation. |
| What it Measures | The growth in the dollar amount of a deposit or loan. | The growth in the purchasing power of a deposit or loan. |
| How it is Set | Determined by the desired real rate plus the expected inflation rate. | Calculated by subtracting the actual inflation rate from the nominal rate. |
| Can it be Negative? | No, nominal rates are almost always positive. | Yes, if the inflation rate is higher than the nominal interest rate. |
Step-by-Step Example
Let's walk through a scenario involving a one-year loan to see how these concepts work in practice.
Scenario: A student takes out a $1,000 loan from a bank for one year. The bank wants to earn an expected real interest rate of 4%. Both the bank and the student expect the inflation rate for the upcoming year to be 2%.
Step 1: Setting the Agreed-Upon Nominal Interest Rate
The bank and the student form an agreement based on their expectations. They use the Fisher equation to determine the nominal rate for the loan.
Formula: Nominal Rate = Expected Real Rate + Expected Inflation
Calculation: Nominal Rate = 4% + 2% = 6%
Result: The bank charges the student a nominal interest rate of 6% on the $1,000 loan. The student agrees to pay back $1,060 at the end of the year.
Step 2: Calculating the Realized Real Interest Rate
Now, imagine the year has passed. The government announces that the actual inflation rate during that year was 5%, which was significantly higher than the 2% that the bank and student had expected. We can now calculate the actual real interest rate the bank earned.
Formula: Real Rate = Nominal Rate – Actual Inflation Rate
Calculation: Real Rate = 6% – 5% = 1%
Result: The bank's actual real return on the loan was only 1%.
Step 3: Determining Who Benefited
We compare the expected outcome to the actual outcome.
The bank expected to earn a real return of 4% but only actually earned 1%. The bank is worse off than it anticipated. The $1,060 it received has less purchasing power than it had planned for.
The student expected to pay a real cost of 4% but only actually paid 1%. The student is better off than anticipated because they repaid the loan with money that had lost more value to inflation than expected.
Conclusion: In this case, the unexpected-ly high inflation redistributed wealth from the lender (the bank) to the borrower (the student).
AP Exam Tips & Common Pitfalls
[FRQ Task]: You will frequently be asked to calculate a real interest rate given a nominal rate and an inflation rate. A common follow-up question is to identify whether the lender or the borrower is better off if the actual inflation rate differs from the expected rate.
[MCQ Task]: Multiple-choice questions often test your ability to correctly apply the Fisher equation. You might be given three of the four variables (nominal rate, real rate, expected inflation, actual inflation) and asked to solve for the missing one or to identify the relationship between them.
[Common Pitfall ①]: Mixing up expected and actual inflation. Remember that the nominal interest rate is set based on expected inflation. The realized real interest rate is calculated after the fact using actual inflation. Don't use the actual inflation rate to explain how the nominal rate was determined.
[Common Pitfall ②]: Assuming the real interest rate must be positive. The real interest rate can be negative. If the rate of inflation is higher than the nominal interest rate, the lender receives less purchasing power back than they originally lent out. For example, a 5% nominal rate with 7% inflation results in a -2% real interest rate.
Key Vocabulary
Nominal Interest Rate: The stated interest rate on a loan or financial asset, not adjusted for the rate of inflation. It reflects the percentage by which the dollar value of the asset increases over time.
Real Interest Rate: The interest rate corrected for the effects of inflation. It is calculated as the nominal interest rate minus the inflation rate and reflects the actual increase in purchasing power for a lender.
Inflation: A sustained increase in the general price level of goods and services in an economy over a period of time, resulting in a loss of purchasing power per unit of currency.