To find the nominal rate of return using the exact formula that accounts for both the real rate of return and the inflation rate, we use the Fisher equation, which is expressed as:
\[ (1 + r) = (1 + i) \times (1 + \pi) \]
Where:
- \( r \) is the nominal rate of return
- \( i \) is the real rate of return
- \( \pi \) is the inflation rate
Given:
- Real rate of return, \( i = 0.0126 \) (1.26%)
- Inflation rate, \( \pi = 0.0560 \) (5.60%)
We can plug these values into the formula:
\[ (1 + r) = (1 + 0.0126) \times (1 + 0.0560) \]
Calculating the right side:
- Calculate \( (1 + 0.0126) = 1.0126 \)
- Calculate \( (1 + 0.0560) = 1.0560 \)
- Now multiply these results:
\[ 1.0126 \times 1.0560 = 1.0709576 \]
Now we have:
\[ 1 + r = 1.0709576 \]
To find \( r \), we subtract 1 from both sides:
\[ r = 1.0709576 - 1 = 0.0709576 \]
Converting \( r \) back to a percentage gives:
\[ r \approx 0.07096 \times 100 = 7.096% \]
Therefore, the nominal rate of return is approximately 7.10%.
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