AP Macroeconomics

## Learning Outcomes

- Distinguish clearly between the **nominal interest rate** and the **real interest rate**
- Explain why the nominal rate does not adjust for inflation
- Use the Fisher equation to calculate nominal, real, and expected inflation rates
- Analyse what happens when inflation changes but the nominal rate stays fixed
- Explain how inflation affects borrowers, savers, and lenders
- Apply this topic to AP-style multiple-choice and free-response questions

## AP Macroeconomics Syllabus

For the AP Macroeconomics, you are expected to understand nominal and real interest rates, with a focus on the following syllabus points:

- Know that the **nominal interest rate** is the stated or quoted interest rate and is not adjusted for inflation
- Identify the **real interest rate** as the inflation-adjusted rate that reflects purchasing power
- Explain the relationship **real interest rate ≈ nominal interest rate − inflation rate**
- Understand the Fisher relationship **nominal interest rate = real interest rate + expected inflation**
- Distinguish between **expected inflation** and **actual inflation**
- Explain how rising inflation lowers the real interest rate if the nominal rate is unchanged
- Recognise that quoted, advertised, and market rates in examples are usually nominal rates
- Apply the distinction between nominal and real rates in the money market and loanable funds market

## Test Your Knowledge

_Attempt these questions before reading this article. If you find some difficult or cannot remember the answers, look more closely at that area during your revision._

1. What is the difference between a nominal interest rate and a real interest rate?
2. If a bank pays 8% interest and inflation is 3%, what is the approximate real interest rate?
3. Why can a saver earn a positive nominal return but still lose purchasing power?
4. How does a rise in expected inflation affect the nominal interest rate if the real rate stays constant?
5. In AP Macroeconomics, which market usually uses the nominal interest rate and which uses the real interest rate?

## Introduction

Interest rates appear all over AP Macroeconomics. They matter in the money market, the loanable funds market, inflation questions, and monetary policy. A common student mistake is to treat every interest rate as if it means the same thing. It does not.

The key distinction is simple but very important: the **nominal interest rate** is the rate you see posted by a bank or lender, while the **real interest rate** adjusts that rate for inflation. That adjustment matters because what households and firms care about in the end is not just how many dollars they get back, but what those dollars can actually buy.

> **Key Term: nominal interest rate**
> The stated, quoted, or advertised interest rate on a loan or asset; it is not adjusted for inflation.

### What it means to say the nominal rate excludes inflation

When economists say the nominal rate excludes inflation, they mean it does **not remove** the effects of rising prices. It is measured in current dollars, not purchasing-power terms. If a savings account pays 6%, that 6% is the nominal return. It tells you how many more dollars you have later, but not whether those extra dollars buy more goods and services.

This is why nominal rates can be misleading if you stop there. Suppose you put $1,000 in a bank for one year at a nominal interest rate of 5%. At the end of the year, you have $1,050. In dollar terms, you gained $50. But if prices rose 4% during that year, many goods and services now cost more. Your money grew, but your purchasing power grew by much less than 5%.

> **Key Term: real interest rate**
> The interest rate adjusted for inflation; it measures the gain or cost in purchasing-power terms.

The real interest rate answers the question students often forget to ask: after prices change, how much better off is the lender or saver really?

For AP Macroeconomics, the working relationship is:

$$
\text{Real interest rate} \approx \text{Nominal interest rate} - \text{Inflation rate}
$$

Worked example:

- Nominal interest rate = 8%
- Inflation rate = 3%

Step 1: Write the formula

$$
r \approx i - \pi
$$

Step 2: Substitute values

$$
r \approx 8\% - 3\%
$$

Step 3: Calculate

$$
r \approx 5\%
$$

So the approximate **real interest rate** is **5%**.

This means the saver's purchasing power rose by about 5%, not 8%.

Now consider a second example:

- Nominal interest rate = 5%
- Inflation rate = 7%

$$
r \approx 5\% - 7\% = -2\%
$$

The saver got more dollars back, but those dollars buy less than before. That is a **negative real interest rate**.

> **Key Term: purchasing power**
> The quantity of goods and services money can buy.

Students often confuse "nominal excludes inflation" with "nominal ignores inflation." The safer wording is this: the nominal rate is **unadjusted for inflation**. The real rate is the one that removes inflation's effect.

> **Test Tip:** If a question gives you a posted, advertised, or quoted interest rate, assume it is the **nominal** rate unless the question says it is inflation-adjusted.

### The Fisher equation and expected inflation

A second source of confusion is that some questions use **actual inflation**, while others use **expected inflation**. This matters because borrowers and lenders make agreements before they know exactly what inflation will turn out to be.

The AP relationship usually presented is:

$$
\text{Nominal interest rate} = \text{Real interest rate} + \text{Expected inflation}
$$

This is often called the **Fisher equation** or **Fisher relationship**.

> **Key Term: Fisher equation**
> The relationship stating that the nominal interest rate is approximately equal to the real interest rate plus expected inflation.

In symbols:

$$
i = r + \pi^e
$$

where:

- $i$ = nominal interest rate
- $r$ = real interest rate
- $\pi^e$ = expected inflation

Why does expected inflation get added? Because lenders want compensation for two things:

- a real return for postponing consumption
- protection against the expected loss of purchasing power

If lenders want a 3% real return and expect inflation of 4%, they will want a nominal rate of about 7%.

Worked example:

- Desired real interest rate = 2%
- Expected inflation = 5%

Step 1: Write the formula

$$
i = r + \pi^e
$$

Step 2: Substitute values

$$
i = 2\% + 5\%
$$

Step 3: Calculate

$$
i = 7\%
$$

So the nominal interest rate should be **7%**.

This helps explain why nominal rates tend to rise when expected inflation rises. Lenders do not want inflation to eat away at their returns.

A useful distinction:

- **Ex ante real interest rate** uses expected inflation
- **Ex post real interest rate** uses actual inflation

Suppose:

- Nominal interest rate = 7%
- Expected inflation = 2%
- Actual inflation = 4%

Expected real return:

$$
7\% - 2\% = 5\%
$$

Actual real return:

$$
7\% - 4\% = 3\%
$$

The lender expected a 5% real return but actually got 3%.

This difference helps explain why unexpected inflation redistributes income.

> **Key Term: expected inflation**
> The rate of inflation borrowers and lenders think will occur in the future when they agree on a nominal interest rate.
>
> **Test Tip:** If the question says **expected inflation**, use the Fisher equation. If it gives actual inflation after the fact, you are usually finding the actual real return.

### How inflation changes who gains and who loses

This topic is not only about formulas. AP questions also test reasoning. If inflation changes while the nominal rate is fixed, the real rate changes automatically.

If the nominal interest rate stays at 6%:

- inflation 2% → real rate about 4%
- inflation 5% → real rate about 1%
- inflation 8% → real rate about -2%

So if inflation rises and the nominal rate does not, the real interest rate falls.

This matters because borrowers and lenders care about real value, not just money amounts.

#### Savers and lenders

Savers and lenders are helped by higher real returns. If inflation turns out lower than expected, they often do better than planned because the dollars repaid have more purchasing power.

If inflation turns out higher than expected, they lose. They still receive the nominal number of dollars promised, but those dollars buy less.

Example:

- Fixed loan nominal rate = 5%
- Expected inflation = 2%
- Actual inflation = 6%

Expected real return:

$$
5\% - 2\% = 3\%
$$

Actual real return:

$$
5\% - 6\% = -1\%
$$

The lender expected to gain purchasing power but actually lost it.

#### Borrowers

Borrowers tend to benefit from unexpectedly high inflation on fixed-rate debt. They repay with dollars that are worth less than expected.

That is why inflation can redistribute wealth from lenders to borrowers. On AP Macro, this is a standard application of nominal versus real rates.

#### Why banks try to protect themselves

Banks and other lenders know inflation is a risk. That is why nominal rates tend to include an inflation premium. They try to build expected inflation into the quoted rate.

But if inflation is higher than expected, even a bank can end up with a lower real return than intended.

### How this appears in AP graphs and exam questions

Students also mix up where each interest rate belongs in macro graphs.

In the **money market**:

- vertical axis = **nominal interest rate**
- horizontal axis = quantity of money

The money market uses the nominal rate because it is about the opportunity cost of holding money balances that are not inflation-adjusted in the graph.

In the **loanable funds market**:

- vertical axis = **real interest rate**
- horizontal axis = quantity of loanable funds

The loanable funds market uses the real rate because savers and borrowers care about the true reward to saving and the true cost of borrowing.

This distinction matters in free-response questions. If you label the wrong rate on the graph, your analysis can unravel even if your logic is partly right.

Side-by-side comparison:

| Market                | Vertical axis         | Why                                                      |
| --------------------- | --------------------- | -------------------------------------------------------- |
| Money market          | Nominal interest rate | Measures the opportunity cost of holding money           |
| Loanable funds market | Real interest rate    | Measures the true borrowing cost and true lending return |

Now connect this to inflation:

- If expected inflation rises, nominal rates tend to rise through the Fisher effect
- If nominal rates do not rise as fast as inflation, real rates fall
- Lower real rates can encourage borrowing
- Higher expected inflation can therefore affect saving and lending decisions even before actual inflation occurs

Common student errors:

1. Saying the nominal interest rate is inflation-adjusted  
   This is false. The **real** rate is inflation-adjusted.

2. Forgetting to subtract inflation from the nominal rate  
   A high nominal rate may still mean a low or negative real return.

3. Using actual inflation when the question clearly says expected inflation  
   Read carefully. AP questions may test this distinction directly.

4. Labeling the money market with a real rate  
   The money market uses the **nominal** interest rate.

5. Assuming a positive nominal rate means savers gain purchasing power  
    Not if inflation is higher than the nominal rate.
   > **Key Term: inflation-adjusted return**
   > The gain in value after accounting for inflation; another way of describing the real return.

A good FRQ chain of reasoning might look like this:

- The nominal interest rate is the quoted rate and is not adjusted for inflation.
- The real interest rate equals the nominal rate minus inflation, approximately.
- Therefore, if inflation rises while the nominal rate stays fixed, the real interest rate falls.
- As a result, savers receive a lower purchasing-power return and borrowers benefit from repaying in less valuable dollars.

That kind of step-by-step reasoning earns more credit than just writing a formula.

## Key Point Checklist

_This article has covered the following key knowledge points:_

- The **nominal interest rate** is the stated or quoted rate on a loan or asset
- The nominal rate is **not adjusted for inflation**
- The **real interest rate** measures the return or cost in purchasing-power terms
- The standard AP formula is **real interest rate ≈ nominal interest rate − inflation rate**
- The Fisher equation is **nominal interest rate = real interest rate + expected inflation**
- Expected inflation and actual inflation are not always the same
- If inflation rises while the nominal rate is fixed, the real interest rate falls
- If inflation is higher than the nominal rate, the real interest rate becomes negative
- Unexpected inflation tends to hurt lenders and help borrowers with fixed-rate loans
- In AP Macroeconomics, the **money market** uses the nominal interest rate
- In AP Macroeconomics, the **loanable funds market** uses the real interest rate
- Quoted, stated, and advertised interest rates in exam questions are usually nominal rates

## Key Terms and Concepts

- nominal interest rate
- real interest rate
- purchasing power
- Fisher equation
- expected inflation
- inflation-adjusted return


Nominal v. Real Interest Rates - Nominal rate excludes inflation