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).
- First, plug in the values:
\[ 1 + r = \frac{1 + 0.0991}{1 + 0.0749} \]
- Calculate \( 1 + i \) and \( 1 + \pi \):
\[ 1 + 0.0991 = 1.0991 \] \[ 1 + 0.0749 = 1.0749 \]
- Now substitute these values into the equation:
\[ 1 + r = \frac{1.0991}{1.0749} \]
- Perform the division:
\[ 1 + r \approx \frac{1.0991}{1.0749} \approx 1.0224 \]
- Finally, solve for \( r \):
\[ r \approx 1.0224 - 1 \approx 0.0224 \]
- 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%.
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