Which of the following is an inflation-adjusted return on a loan or bond (i.e., the real interest rate) according to the Fisher relationship?

• A. The inflation rate $\pi$ (the rate of change in the price level)
• B. The nominal interest rate $i$ (the stated rate before adjusting for inflation)
• C. The real interest rate, approximately $r\approx i-\pi$, where $i$ is the nominal interest rate and $\pi$ is the inflation rate
• D. The sum $i+\pi$ (nominal interest rate plus inflation)

Answer: (C)

Verified step by step guidance

1. Understand the key variables involved: the nominal interest rate \(i\), the inflation rate \(\pi\), and the real interest rate \(r\). The nominal interest rate is the stated rate on a loan or bond, while the inflation rate measures how much prices increase over time.
2. Recall the Fisher equation, which relates these variables. The Fisher relationship states that the nominal interest rate approximately equals the sum of the real interest rate and the inflation rate: \(i \approx r + \pi\).
3. Rearrange the Fisher equation to solve for the real interest rate \(r\). This gives: \(r \approx i - \pi\), meaning the real interest rate is the nominal interest rate adjusted for inflation.
4. Interpret the real interest rate as the inflation-adjusted return on a loan or bond. It reflects the true increase in purchasing power that the lender receives after accounting for inflation.
5. Confirm that the correct expression for the real interest rate is \(r \approx i - \pi\), distinguishing it from just the nominal interest rate \(i\), the inflation rate \(\pi\), or their sum \(i + \pi\).