Unit 4 · Topic 4.2

Nominal v. Real Interest Rates

The nominal interest rate is the rate stated in dollars; the real interest rate is the gain in buying power, the nominal rate minus the expected inflation rate.

Practice 1: Principles and ModelsPractice 2: Interpretation

Part 1 · Hook

Why this matters

A bank account pays 4% a year, and you feel richer when the balance grows. But if prices rose 5% that year, your money buys less than it did a year ago. The 4% is real money in dollars, yet you lost buying power. Economists keep two interest rates for exactly this reason: one in dollars and one in what those dollars can buy.

Part 2 · Before you start

What this builds on

Part 3 · Prerequisite check

Quick check before you start

1. A price index rises from 200 to 210 over a year. What is the inflation rate?

  1. 5%
  2. 10%
  3. 2.1%
  4. 105%
Show the answer

Inflation is the percent change in the index: (210 - 200) / 200 x 100 = 5%.

  • Correct: 5%:
  • 10%:
  • 2.1%:
  • 105%:

2. What is an interest rate?

  1. The yearly cost of borrowing, as a percent of the amount borrowed
  2. The total a borrower repays
  3. The price of a share of stock
  4. The fee to open a bank account
Show the answer

The interest rate is the price of borrowing money for a year, as a percent.

  • Correct: The yearly cost of borrowing, as a percent of the amount borrowed:
  • The total a borrower repays:
  • The price of a share of stock:
  • The fee to open a bank account:

Part 4 · See it

See it first

A bar for a 7 percent nominal interest rate split into two parts: a 4 percent real interest rate, the gain in buying power, and a 3 percent expected inflation rate. The real rate equals the nominal rate minus the expected inflation rate.
The nominal interest rate is the real interest rate plus the expected inflation rate. LevlPrep original diagram.

Part 5 · Step by step

How it works, step by step

  1. Lenders expect inflationthey add the expected inflation rate to the real return they want, so nominal rates rise
  2. Inflation turns out higher than expected on a fixed-rate loanthe real interest rate actually earned is lower than agreed
  3. The real rate earned is lower than agreedthe borrower gains and the lender loses buying power

Part 6 · Key ideas

Key ideas

  • The nominal interest rate is the rate stated on a loan, in dollars. The real interest rate is the gain in buying power.
  • Real interest rate = nominal interest rate - expected inflation rate. With a 7% nominal rate and a 3% expected inflation rate, the real rate is 4%.
  • Lenders build the expected inflation rate into nominal rates, so when lenders expect more inflation, nominal rates rise.
  • If inflation is higher than expected, fixed-rate borrowers gain and lenders lose; if lower than expected, the reverse.

Part 7 · Misconception

A common mistake

The wrong idea: A higher nominal interest rate always means lenders earn more.

What actually happens: What lenders earn in buying power is the real rate. A 10% loan with 12% inflation earns -2% real, worse than a 4% loan with 1% inflation (3% real).

Part 8 · Check yourself

Check yourself

Exam-style questions. Anything you miss goes into your review queue.

1. What is a nominal interest rate?

  1. The rate stated on a loan, in dollars
  2. The rate after the expected inflation rate is subtracted
  3. The rate a central authority sets for banks
  4. The interest rate measured in goods instead of dollars
Show the answer

Nominal means "in dollars as stated." The real rate adjusts it for inflation.

  • Correct: The rate stated on a loan, in dollars: Right: the nominal rate is the rate written on the loan, before any adjustment for inflation.
  • The rate after the expected inflation rate is subtracted: That is the real interest rate.
  • The rate a central authority sets for banks: That describes one particular rate, not what "nominal" means.
  • The interest rate measured in goods instead of dollars: Measuring in buying power is the real rate; nominal is in dollars.

2. Which formula gives the real interest rate?

  1. Nominal rate plus the expected inflation rate
  2. Nominal rate divided by the expected inflation rate
  3. Nominal rate minus the expected inflation rate
  4. Expected inflation rate minus the nominal rate
Show the answer

Real interest rate = nominal interest rate - expected inflation rate.

  • Nominal rate plus the expected inflation rate: Adding inflation gives a larger number; inflation reduces the buying power gained, so subtract.
  • Nominal rate divided by the expected inflation rate: The real rate is a difference, not a ratio.
  • Correct: Nominal rate minus the expected inflation rate: Right: what is left after inflation is the gain in buying power.
  • Expected inflation rate minus the nominal rate: That is the real rate with its sign flipped.

3. A savings bond pays a nominal interest rate of 5%, and savers expect 2% inflation. What is the expected real interest rate, in percent?

Type a number (%). A four-function calculator is allowed, as on the exam.

Show the answer

5−2=3%5 - 2 = 3\%: savers expect their buying power to grow about 3% a year.

  • Answer: 3 %

4. Prices fall by 2% over a year, though everyone expected them to rise by 2%. A firm repays a loan at a fixed 5% nominal rate. How is the firm affected?

  1. It gains, because prices fell
  2. It is not affected, because its rate was fixed
  3. It loses, because its real rate rose
  4. It loses, because its nominal rate rose
Show the answer

Unexpected deflation is the reverse of unexpected inflation: it hurts fixed-rate borrowers and helps lenders.

  • It gains, because prices fell: Falling prices raise the buying power of each dollar the firm repays, which hurts the borrower.
  • It is not affected, because its rate was fixed: The fixed rate is why the surprise matters: the real rate rose from 3% to 7%.
  • Correct: It loses, because its real rate rose: Right: it repays with dollars worth more than expected; the real rate turned out 5 - (-2) = 7%, not the 3% the firm planned.
  • It loses, because its nominal rate rose: The nominal rate stayed at 5%; the real rate rose because prices fell.

Scenario

A fixed-rate car loan and a surprise in inflation

A bank in the invented country of Quentar lends Sam money for a car at a fixed nominal interest rate of 7% a year. When the loan is made, both Sam and the bank expect inflation of 3% a year. Over the next year, inflation turns out to be 6%.

5. What real interest rate did the bank actually earn over the year, in percent?

Type a number (%). A four-function calculator is allowed, as on the exam.

Show the answer

After the fact, use the inflation that happened: 7−6=1%7 - 6 = 1\%. The bank planned on 7−3=4%7 - 3 = 4\%.

  • Answer: 1 %

6. Who gained from the surprise in inflation, and why?

  1. The bank, because prices rose faster
  2. Sam, because his real rate fell
  3. Neither, because the nominal rate stayed at 7%
  4. Both, because incomes rose with prices
Show the answer

Unanticipated inflation helps fixed-rate borrowers and hurts lenders, because the real value of the repayment falls.

  • The bank, because prices rose faster: Faster inflation means the bank is repaid in dollars that buy less than it planned, so it loses.
  • Correct: Sam, because his real rate fell: Right: Sam repays with dollars that buy less than expected; his real rate fell from an expected 4% to 1%.
  • Neither, because the nominal rate stayed at 7%: The nominal rate is fixed, which is why the surprise moves buying power from the lender to the borrower.
  • Both, because incomes rose with prices: A surprise in inflation moves buying power between them: one side gains what the other loses.

7. If lenders in Quentar now expect inflation to stay at 6%, what most likely happens to the nominal rates they charge on new car loans?

  1. They rise, to keep the real rate lenders want
  2. They fall, because borrowers are gaining
  3. They stay at 7%, because the real rate fell
  4. They fall to the inflation rate of 6%
Show the answer

Nominal rate = real rate + expected inflation rate. When the expected inflation rate rises, nominal rates rise with it.

  • Correct: They rise, to keep the real rate lenders want: Right: to earn a 4% real rate with a 6% expected inflation rate, lenders ask about 10% nominal.
  • They fall, because borrowers are gaining: Lenders protect themselves from inflation by charging more, not less.
  • They stay at 7%, because the real rate fell: At 7% nominal and a 6% expected inflation rate lenders would earn 1% real, so they raise the nominal rate.
  • They fall to the inflation rate of 6%: At 6% nominal the real rate would be zero; lenders want a positive real return.

Part 9 · Summary

Summary

The nominal interest rate is the rate stated in dollars; the real interest rate is the gain in buying power, the nominal rate minus the expected inflation rate. Lenders add the expected inflation rate to the real return they want, so nominal rates rise when lenders expect more inflation. When inflation turns out higher than expected, fixed-rate borrowers gain and lenders lose, because the real rate actually paid falls.

Part 10 · Up next

What comes next

Part 11 · Connections

Connections

Question set for this topic