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Kurs: Makroekonomia > Rozdział 4

Lekcja 2: Nominal v. real interest rates

Lesson summary: nominal vs. real interest rates

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.

Podsumowanie

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 %

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

$ 100

in a savings account, the real value of that

$ 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).

Podstawowe pojęcia

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

Do zapamiętania — najważniejsze zagadnienia

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 %

interest, but it thinks there will be

3 %

inflation. If they don’t factor that inflation into what they change in interest, they will effectively earn only

7 %

(because they will lose

3 %

of the purchasing power of an interest rate of

10 %

). Instead, banks factor inflation into their interest rates. To account for inflation, this bank would charge

13 %

interest.

Remember from a previous lesson that inflation results in winners and losers? Suppose the bank thought inflation would be

3 %

, but inflation turned out to be

4 %

. We can figure out the real interest that the bank actually earned in retrospect:

\begin{aligned} real interest rate & = nominal interest rate - inflation \\ = 13 % - 4 % \\ = 9 % \end{aligned}

The bank was hurt by the unexpected inflation because they only got a return of

9 %

, not the

10 %

they hoped for. On the other hand, the borrower ended up only paying

9 %

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.

Najważniejsze równania

The interest rate borrowers pay and savers earn

Nominal interest rate = real interest rate + expected inflation

Sometimes this equation is written using symbols:

i = r + {inf}_{e}

Gdzie:

\begin{aligned} i & = nominal interest rate \\ r & = real interest rate \\ {inf}_{e} & = expected inflation \end{aligned}

Note: sometimes you will see inflation abbreviated using the Greek symbol

π

, and expected inflation abbreviated as

π_{e}

The real interest rate in retrospect

Real interest rate = nominal interest rate - inflation rate

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 %

to their earnings. They expect the inflation rate to be

1 %

, so they charge a nominal interest rate of

5 %

\begin{aligned} i & = r + {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 - inf \\ = 5 % - 6 % \\ = - 1 % \end{aligned}

In this case, inflation was higher than they anticipated. They actually lost money, rather than earned it.

Częste błędy

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 $0 %$ ‍.

Pytania do dyskusji

Tywin knows he has a debt to repay soon. The bank charges him an interest rate of $6 %$ ‍. If the expected rate of inflation is $5 %$ ‍, 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 $7 %$ ‍ and the real return desired is $5 %$ ‍. Show all work.

If the rate of inflation is

3 %

instead, what happens to the value of the money paid back? Explain.

\begin{aligned} i & = r + {inf}_{e} \\ = 7 % + 5 % \\ = 12 % \end{aligned}

If the actual rate of inflation turns out to be

3 %

, then the real interest earned from a nominal interest rate of

12 %

is:

\begin{aligned} r & = i - inf \\ = 12 % - 3 % \\ = 9 % \end{aligned}

In this case, because the inflation was lower than expected, the real amount paid back (

9 %

) is higher than the real amount that was anticipated (

7 %

). Lenders benefits from this unanticipated disinflation and borrowers are hurt.

The real interest rate paid on an asset was $10 %$ ‍, but the nominal rate was $9 %$ ‍. What was the rate of inflation?

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