To find the nominal rate of return using the exact formula, you can use the Fisher equation, which relates the nominal interest rate (\(i\)), the real interest rate (\(r\)), and the inflation rate (\(π\)):
\[ 1 + i = (1 + r)(1 + π) \]
Where:
- \( r \) is the real rate of return (4.13% or 0.0413),
- \( π \) is the inflation rate (6.92% or 0.0692).
Let's plug in the values into the formula:
\[ 1 + i = (1 + 0.0413)(1 + 0.0692) \]
Calculating \(1 + r\) and \(1 + π\):
\[ 1 + r = 1 + 0.0413 = 1.0413 \] \[ 1 + π = 1 + 0.0692 = 1.0692 \]
Now, multiply these two values:
\[ 1 + i = 1.0413 \times 1.0692 \]
Calculating this product:
\[ 1 + i \approx 1.11267796 \]
Now, subtract 1 to find \(i\):
\[ i \approx 1.11267796 - 1 = 0.11267796 \]
To express \(i\) as a percentage:
\[ i \approx 0.11267796 \times 100 \approx 11.27% \]
Thus, the nominal rate of return is approximately 11.27%.
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