Questions: Real Interest Rates and the Fisher Equation

Question 1

A retiree has her savings in an account earning 5% nominal interest. Annual inflation is 8%. She tells a friend she is earning 5% per year on her savings. What is she missing?

• A. She should be calculating compound interest rather than simple interest for accuracy
• B. Her real interest rate is approximately -3%, meaning her savings are losing purchasing power despite the nominal gain
• C. Nominal rates always equal real rates when inflation is below 10%
• D. The 5% nominal rate already adjusts for inflation — that is the purpose of nominal rates

Answer: (B)

The Fisher equation tells us that the real interest rate ≈ nominal rate − inflation rate. At 5% nominal and 8% inflation, the real rate is approximately -3%. The retiree is losing purchasing power: each year her account balance nominally grows, but the goods that balance can buy decline. What matters for actual standard of living is real return, not nominal return. This is the core insight: nominal rates can be deeply misleading without knowing inflation.

Question 2

A bond was issued with a 4% nominal interest rate when lenders expected 2% inflation. Actual inflation over the bond's life turns out to be 5%. Who benefits from this outcome?

• A. The bondholder, because they received the contracted 4% nominal return as agreed
• B. Both parties equally, since the nominal rate was set before inflation was known
• C. The bond issuer (the borrower), because the actual real interest rate they paid was lower than they anticipated when the contract was signed
• D. Neither party — unexpected inflation harms all participants in financial markets equally

Answer: (C)

The lender expected a real return of about 2% (4% nominal − 2% expected inflation). Actual inflation of 5% reduced the realized real return to about -1% — the lender lost purchasing power. The borrower, conversely, repaid in dollars that were worth less than expected, lowering their real cost of debt. Unexpected inflation redistributes wealth from creditors to debtors: borrowers win when inflation exceeds expectations; lenders lose. This is why inflation expectations are so central to financial contracts.

Question 3

During a period of deflation (negative inflation), the real interest rate can exceed the nominal interest rate — meaning even a 0% nominal rate implies a positive real borrowing cost.

• T. True
• F. False

Answer: True

From the Fisher equation: real rate ≈ nominal rate − inflation. If inflation is negative (say -2%), then even a 0% nominal rate produces a real rate of +2%. This is why deflation is economically dangerous: it raises real borrowing costs precisely when an economy is struggling, discouraging the investment and spending needed for recovery. Central banks at the 'zero lower bound' on nominal rates cannot cut below 0% easily, yet the real rate can still be positive and contractionary during deflation.

Question 4

The Fisher equation uses actual (realized) inflation rather than expected inflation because lenders can adjust the nominal rate after the loan is made if inflation surprises them.

• T. True
• F. False

Answer: False

The Fisher equation is an ex ante (before-the-fact) relationship: i = r + π^e, where π^e is expected inflation. The nominal rate is agreed upon when the loan contract is signed, embedding the parties' best forecast of future inflation. Once the contract is fixed, neither party can adjust it. The ex post (realized) real rate uses actual inflation and may differ significantly from what was anticipated — that discrepancy is precisely what creates the wealth redistribution between creditors and debtors.

Question 5

Why do real interest rates — rather than nominal interest rates — drive investment and savings decisions by rational households and businesses?

Model answer: Savers and investors care about how much more purchasing power they will have, not how many more nominal dollars. A 10% nominal return with 9% inflation produces only 1% more real buying power, while a 3% nominal return with 0% inflation produces 3% real purchasing power gain. Economic decisions — whether to build a factory, buy equipment, or save rather than spend — respond to the real return on capital. Using nominal rates ignores inflation's erosion effect and leads to systematically wrong assessments of the actual gain from investing or saving.

This is why the Fisher equation matters beyond the classroom. Monetary policy works through its effect on real rates: when a central bank raises nominal interest rates, the near-term effect is typically to raise real rates (slowing investment and borrowing). Over the long run, if inflation expectations adjust to a lower target, nominal rates fall and real rates stabilize. The real rate is also the relevant variable for comparing returns across countries with different inflation rates — a 20% nominal return in a high-inflation economy may be worse than a 4% return in a low-inflation economy.