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%.
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