Suppose that in a given year, the rate of inflation is 3 percent, and the nominal interest rate is 2 percent. The real interest rate is:

Break Down the Problem

1. We need to determine the real interest rate using the provided nominal interest rate and the inflation rate.

Relevant Concepts

2. The relationship between nominal interest rate, real interest rate, and inflation rate can be expressed using the Fisher equation: $1 + r = \frac{1 + i}{1 + \pi}$ where:
   • $r$ = real interest rate
   • $i$ = nominal interest rate
   • $\pi$ = inflation rate

Analysis and Detail

3. Given:

   • Nominal interest rate, $i = 0.02$ (2%)
   • Inflation rate, $\pi = 0.03$ (3%)

   We need to calculate the real interest rate $r$.

   Using the Fisher equation: $1 + r = \frac{1 + 0.02}{1 + 0.03}$

   Now, calculating the right side: $1 + r = \frac{1.02}{1.03} \approx 0.9903$

   Thus, $r \approx 0.9903 - 1$ $r \approx -0.0097$

Verify and Summarize

4. The computed value indicates that the real interest rate is approximately $-0.0097$ or $-0.97\%$. This suggests that the purchasing power of money is decreasing given the inflation rate exceeds the nominal interest rate.

Final Answer

The real interest rate is approximately $-0.97\%$.