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## AP®︎/College Macroeconomics

### Unit 4: Lesson 2

Nominal vs. real interest rates

# Lesson summary: nominal vs. real interest rates

AP.MACRO:
MEA‑3 (EU)
,
MEA‑3.B (LO)
,
MEA‑3.B.1 (EK)
,
MEA‑3.B.2 (EK)
,
MEA‑3.B.3 (EK)
In this lesson summary review and remind yourself of the key terms and calculations related to the distinction between the real interest rate and the nominal interest rate.

## Lesson summary

What you see is what you get, right? Not when it comes to interest rates! When you see an ad saying a bank will pay 5, percent interest on savings accounts, it doesn’t necessarily mean you will be able to buy 5% more stuff with your money after a year.
When you put dollar sign, 100 in a savings account, the real value of that dollar sign, 100 is what you can buy with it. Therefore the real value of what you earn in interest is what you can buy with that interest. When there is inflation, the purchasing power of the interest you earn decreases. Your real interest is the nominal interest rate (the interest you get paid) minus the rate of inflation (the loss of purchasing power).

## Key Terms

Key termDefinition
nominal interest ratethe interest rate that you earn (or pay) on a loan; this is the amount you see on a sign advertising interest rates.
real interest ratethe nominal interest rate adjusted for inflation; this is the effective interest rate that you earn (or pay).
Fisher effectthe idea that an increase in expected inflation drives up the nominal interest rate, which leaves the expected real interest rate unchanged

## Key Takeaways

### Nominal interest is the sum of the expected real interest rate and the expected inflation rate

How does a bank decide what interest rate to charge? It needs to consider two important things: How much interest is enough to make it worthwhile for the bank to loan the money (the real interest rate they earn)? How much of the interest’s purchasing power might be lost to inflation?
For example, suppose a bank wants to earn 10, percent interest, but it thinks there will be 3, percent inflation. If they don’t factor that inflation into what they change in interest, they will effectively earn only 7, percent (because they will lose 3, percent of the purchasing power of an interest rate of 10, percent). Instead, banks factor inflation into their interest rates. To account for inflation, this bank would charge 13, percent interest.
Remember from a previous lesson that inflation results in winners and losers? Suppose the bank thought inflation would be 3, percent, but inflation turned out to be 4, percent. We can figure out the real interest that the bank actually earned in retrospect:
\begin{aligned}\text{real interest rate}&=\text{nominal interest rate}-\text{inflation}\\\\ &=13\%-4\%\\\\ &=9\%\end{aligned}
The bank was hurt by the unexpected inflation because they only got a return of 9, percent, not the 10, percent they hoped for. On the other hand, the borrower ended up only paying 9, percent real interest. The borrower got the better deal!
This is an important takeaway: it was the unanticipated aspect of the inflation that hurt the bank and helped the borrower. If the bank had anticipated the higher rate of inflation, they would have simply charged a higher nominal interest rate to ensure they got the real interest rate.
This is the basic idea behind something called the Fisher Effect. When expected inflation changes, the nominal interest rate will increase. However, inflation will not affect the real interest rate.

## Key Equations

### The interest rate borrowers pay and savers earn

start text, N, o, m, i, n, a, l, space, i, n, t, e, r, e, s, t, space, r, a, t, e, end text, equals, start text, r, e, a, l, space, i, n, t, e, r, e, s, t, space, r, a, t, e, end text, plus, start text, e, x, p, e, c, t, e, d, space, i, n, f, l, a, t, i, o, n, end text
Sometimes this equation is written using symbols:
i, equals, r, plus, start text, i, n, f, end text, start subscript, e, end subscript
Where:
\begin{aligned}i&=\text{nominal interest rate}\\\\ r&=\text{real interest rate}\\\\ \text{inf}_e &= \text{expected inflation}\end{aligned}
Note: sometimes you will see inflation abbreviated using the Greek symbol pi, and expected inflation abbreviated as pi, start subscript, e, end subscript.

### The real interest rate in retrospect

start text, R, e, a, l, space, i, n, t, e, r, e, s, t, space, r, a, t, e, end text, equals, start text, n, o, m, i, n, a, l, space, i, n, t, e, r, e, s, t, space, r, a, t, e, end text, minus, start text, i, n, f, l, a, t, i, o, n, space, r, a, t, e, end text
The actual interest earned (or paid) will depend on the nominal interest rate and how much the inflation rate turned out to be.
For example, the bank expects a real return of 4, percent to their earnings. They expect the inflation rate to be 1, percent, so they charge a nominal interest rate of 5, percent:
\begin{aligned} i&=r+\text{inf}_e\\\\ &=4\%+1\%\\\\ &=5\%\end{aligned}
However, it turns out that that inflation is 6%. In retrospect they only earned:
\begin{aligned} r&=i-\text{inf}\\\\ &=5\%-6\%\\\\ &=-1\%\end{aligned}
In this case, inflation was higher than they anticipated. They actually lost money, rather than earned it.

## Common misperceptions

• A point of confusion some people have is whether nominal and real interest rates can be negative. Real interest rates can be negative, but nominal interest rates cannot. Real interest rates are negative when the rate of inflation is higher than the nominal interest rate. Nominal interest rates cannot be negative because if banks charged a negative nominal interest rate, they would be paying you to borrow money! This is called the “zero bound” on interest rates: the nominal interest rate can only go down to 0, percent.

## Discussion questions

• Tywin knows he has a debt to repay soon. The bank charges him an interest rate of 6, percent. If the expected rate of inflation is 5, percent, how much interest is he effectively paying? Explain.
• Calculate the nominal rate of inflation that will be charged if the expected rate of inflation is 7, percent and the real return desired is 5, percent. Show all work.
If the rate of inflation is 3, percent instead, what happens to the value of the money paid back? Explain.
• The real interest rate paid on an asset was 10, percent, but the nominal rate was 9, percent. What was the rate of inflation?

## Want to join the conversation?

• is nominal interest rate always higher than the real interest rate?
• Most of the times, yes -- interest rates are always higher than real rates when the inflation rate is positive. This is because inflation takes a 'cut' into the real value of the money being returned at the end of the loan period, so the real (adjusted for inflation) rate of interest is less than the nominal rate. For example, if banks loan out money for 8% nominal interest per year and the inflation rate is 3%, the real interest rate is 8 - 3 = 5%.

However, you could imagine a scenario where inflation is actually negative and you have deflation. In this case, real interest rates are actually higher than nominal interest rates. So, if the rate of inflation is -2% (2% deflation), a bank that loans money out for a 3% rate of nominal interest actually gets 3 - (-2) = 5% real interest.

The second deflationary scenario is relatively rare and I doubt you would be asked test questions about nominal and real return in a deflationary environment. However, it still very much does happen (Japan is probably the best example of a country struggling with chronic deflation).

All in all, I wouldn't recommend you memorize relationships like these, but instead use the equation i = r + inf to think about what the real interest rate would be for different combinations of nominal interest and inflation.
(1 vote)
• In the 2nd discussion question of "Lesson Summary: Nominal Vs. Real Interest Rates", I think I have spotted an error. The error doesn't change the answer, but it might still be confusing to some? The error is this: I think the "real interest rate" and the "expected inflation rate" where switched in the answer.

The question states "the expected rate of inflation is 7%, and the real return desired is 5%". So r=5%, infe=7%.

The answer states "The real amount paid back (9%) is higher than the real amount that was anticipated (7%)." But this implies that r=7% instead of r=5%.
• Can you pinpoint when exactly real interest rate will be negative?
(1 vote)
• As of interest rate, it is no longer true that it is always greater or equal to zero. Today even Fed thinks about driving rate below zero. What a time to be alive!
(1 vote)
• Yes, subzero interest rates have been considered by the US government for some time, even stretching back to last fall!
(1 vote)
• Wasn't the ECB charging a negative nominal rate from 2013 to 2019?
(1 vote)
• Hardor borrowed $1000. The bank charges him 5% interest per year. At the end of the year he paid$50 in interest. During that year there was a 2% increase in the GDP deflator.
• Hardor borrowed $1000. The bank charges him 5% interest per year. At the end of the year he paid$50 in interest. During that year there was a 2% increase in the GDP deflator.