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Lesson M02.L05: Real vs Nominal Interest Rates: The Fisher Equation

Module: Measuring the Price Level and Inflation; Savings and Wealth Level: intro Duration: 30 minutes Learning Objective: Derive the Fisher equation; calculate real interest rates from Australian cash rate and CPI data; explain the real interest rate's role in saving decisions. Provenance: OpenStax Macro 3e | MIT OCW 14.02

Explanation

An interest rate tells you how much you'll receive (or pay) in nominal (dollar) terms for lending (or borrowing) money. But what matters for economic decisions is the real return — how much extra purchasing power you gain.

Nominal interest rate (i): The rate stated on a loan or deposit — the "sticker price" of borrowing.

Real interest rate (r): The nominal rate adjusted for inflation. It measures the increase in purchasing power earned by the lender (or paid by the borrower).

The Fisher Equation (named for economist Irving Fisher):

r ≈ i − π

Where π (pi) is the inflation rate. (The precise form is (1+r) = (1+i)/(1+π), but the approximation r ≈ i − π is accurate for low-to-moderate rates.)

Why it matters for saving:

A household deciding whether to save is really asking: "Will I be able to buy more in the future?" The answer depends on the real rate. If your bank pays 4% interest but inflation is 5%, you are actually losing purchasing power by saving — the real rate is negative (−1%).

Distinction between ex-ante and ex-post: - Ex-ante real rate: Expected real rate = i − π_expected (used when deciding to borrow/save). - Ex-post real rate: Realised real rate = i − π_actual (calculated after the fact).

If inflation turns out higher than expected, borrowers gain and lenders lose (as we saw in Australia in 2022–23 when inflation surpassed most forecasts).

RBA cash rate context (approximate):

Period Cash Rate (i) CPI Inflation (π) Real Rate (r ≈ i − π)
2020–21 0.10% 1.1% −1.0%
2022 2.0% (avg, rising) 7.8% −5.8%
Late 2023 4.35% 4.1% +0.25%

Real rates were deeply negative during 2022, incentivising borrowing over saving. By late 2023, with the RBA's hiking cycle near complete and inflation falling, the real rate turned marginally positive.

Worked Example

Scenario: In January 2022, an Australian couple locks in a 2-year term deposit at a nominal rate of 1.2% per year. Actual inflation over those two years averages 6%.

Nominal return over 2 years: - Deposit: $50,000 - Interest earned: $50,000 × 1.2% × 2 = $1,200 - End balance: $51,200

Purchasing power check: - Price level rose 6% per year compounded: $50,000 × (1.06)² = $56,180 needed to maintain purchasing power. - Shortfall: $56,180 − \(51,200 = **−\)4,980**

Real interest rate: r ≈ 1.2% − 6.0% = −4.8% per year

Despite earning nominal interest, the couple's real wealth declined — their $51,200 buys significantly less than $50,000 did in 2022. This is exactly why the 2022 inflation surge was painful for savers on fixed-rate deposits.

Common Misconception

Misconception: A high nominal interest rate always means it's a good time to save.

Correction: What matters is the real interest rate. In 2022, Australian term deposit rates climbed but inflation climbed faster — the real rate was deeply negative. Savers earned more nominal dollars but could buy less with them. Conversely, when nominal rates are low but inflation is even lower (as in 2010–11), real rates can be reasonably positive and saving rewarding. Always subtract inflation before judging whether saving "pays."

Practice Prompts

  1. The RBA cash rate is 4.35% and annual CPI inflation is 3.8%. What is the approximate real interest rate? → Answer: r ≈ 4.35% − 3.8% = 0.55% — a slightly positive real rate, meaning savers are just barely growing their purchasing power.

  2. A borrower takes a mortgage at 6% nominal interest. Inflation turns out to be 8% (higher than expected). Who benefits — borrower or lender — and why? → Answer: The borrower benefits. They repay the loan with dollars that are worth less in real terms. The real interest rate is 6% − 8% = −2%, so the lender is effectively paying the borrower to hold their debt. This is unexpected inflation redistributing wealth from lender to borrower.

  3. Using the Fisher equation, if a saver requires a real return of 2% and expects inflation of 3.5%, what nominal interest rate must the bank offer? → Answer: i = r + π = 2% + 3.5% = 5.5% nominal.

Further Resources