Question

Assume the nominal rate of return is 5.91% and the inflation rate is 2.54%. Find the real rate of return using the exact formula.

Answer 1

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

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

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

In this case:
- \( i = 5.91\% = 0.0591 \)
- \( \pi = 2.54\% = 0.0254 \)

Substituting the values into the equation:

\[
1 + r = \frac{1 + 0.0591}{1 + 0.0254}
\]
\[
1 + r = \frac{1.0591}{1.0254}
\]

Now, calculate the fraction:

\[
1 + r \approx \frac{1.0591}{1.0254} \approx 1.0328
\]

Now, isolate \( r \):

\[
r \approx 1.0328 - 1
\]
\[
r \approx 0.0328
\]

Converting back to percentage:

\[
r \approx 0.0328 \times 100 \approx 3.28\%
\]

Therefore, the real rate of return is approximately **3.28%**.