Question

Assume the nominal rate of return is 9.91% and the inflation rate is 7.49%. Find the real rate of return using the exact formula.

Answer 1

To find the real rate of return using the exact formula, you can use the Fisher equation, which is given by:

\[
1 + r = \frac{1 + i}{1 + \pi}
\]

Where:
- \( r \) is the real rate of return,
- \( i \) is the nominal rate of return,
- \( \pi \) is the inflation rate.

In this case, the nominal rate of return \( i \) is 9.91% (or 0.0991 as a decimal), and the inflation rate \( \pi \) is 7.49% (or 0.0749 as a decimal).

1. First, plug in the values:

\[
1 + r = \frac{1 + 0.0991}{1 + 0.0749}
\]

2. Calculate \( 1 + i \) and \( 1 + \pi \):

\[
1 + 0.0991 = 1.0991
\]
\[
1 + 0.0749 = 1.0749
\]

3. Now substitute these values into the equation:

\[
1 + r = \frac{1.0991}{1.0749}
\]

4. Perform the division:

\[
1 + r \approx \frac{1.0991}{1.0749} \approx 1.0224
\]

5. Finally, solve for \( r \):

\[
r \approx 1.0224 - 1 \approx 0.0224
\]

6. Convert \( r \) back to a percentage:

\[
r \approx 0.0224 \times 100 \approx 2.24\%
\]

Therefore, the real rate of return is approximately **2.24%**.