Question

Assume the nominal rate of return is 9.65% and the inflation rate is 5.14%. Find the real rate of return using the exact formula.

Answer 1

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%**.