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:
- \( r \) is the real rate of return,
- \( i \) is the nominal rate of return (9.65% or 0.0965),
- \( \pi \) is the inflation rate (5.14% or 0.0514).
First, convert the rates to their decimal forms:
- Nominal rate \( i = 0.0965 \)
- Inflation rate \( \pi = 0.0514 \)
Now, we plug these values into the Fisher equation:
\[ 1 + r = \frac{1 + 0.0965}{1 + 0.0514} \]
Calculating the numerator and denominator:
- \( 1 + 0.0965 = 1.0965 \)
- \( 1 + 0.0514 = 1.0514 \)
Now, calculate the fraction:
\[ 1 + r = \frac{1.0965}{1.0514} \approx 1.0428 \]
Now, to find \( r \), we subtract 1:
\[ r \approx 1.0428 - 1 \approx 0.0428 \]
To express this as a percentage:
\[ r \approx 0.0428 \times 100 \approx 4.28% \]
Thus, the real rate of return is approximately 4.28%.
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