To find the inflation rate of return using the exact formula, we can use the Fisher equation, which relates the nominal interest rate, the real interest rate, and the inflation rate. The formula is:
\[ 1 + i = (1 + r)(1 + \pi) \]
Where:
- \( i \) is the nominal interest rate,
- \( r \) is the real interest rate,
- \( \pi \) is the inflation rate.
We can rearrange the formula to solve for the inflation rate (\( \pi \)):
\[ \pi = \frac{1 + i}{1 + r} - 1 \]
Given:
- Nominal rate (\( i \)) = 6.33% = 0.0633
- Real rate (\( r \)) = 1.45% = 0.0145
Now we can substitute the values into the formula:
\[ \pi = \frac{1 + 0.0633}{1 + 0.0145} - 1 \]
Calculating the numerator:
\[ 1 + 0.0633 = 1.0633 \]
Calculating the denominator:
\[ 1 + 0.0145 = 1.0145 \]
Now plug these values into the equation:
\[ \pi = \frac{1.0633}{1.0145} - 1 \]
Calculating the fraction:
\[ \frac{1.0633}{1.0145} \approx 1.0482 \]
Now subtract 1:
\[ \pi \approx 1.0482 - 1 \approx 0.0482 \]
To express this as a percentage:
\[ \pi \approx 0.0482 \times 100 \approx 4.82% \]
Thus, the inflation rate is approximately 4.82%.
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