Question

If the nominal interest rate is 5 percent and the real interest rate is 7 percent, then the inflation rate is
a. 12 percent.
b. −2 percent.
c. 0.4 percent.
d. 2 percent.

Answer 1

To find the inflation rate given the nominal interest rate and the real interest rate, we can use the Fisher equation, which states:

\[
(1 + i) = (1 + r)(1 + \pi)
\]

Where:
- \( i \) = nominal interest rate
- \( r \) = real interest rate
- \( \pi \) = inflation rate

For small values, we can approximate the equation as:

\[
i \approx r + \pi
\]

Rearranging this gives us:

\[
\pi \approx i - r
\]

Plugging in the given values:
- Nominal interest rate (\( i \)) = 5% or 0.05
- Real interest rate (\( r \)) = 7% or 0.07

Now substituting these values:

\[
\pi \approx 0.05 - 0.07 = -0.02
\]

This corresponds to an inflation rate of -2 percent. Therefore, the answer is:

**b. −2 percent.**