Question

Know if you are making a % more or less if there is a n% raise but m% inflation

Answer 1

To determine if you're making a percentage more or less after a raise while accounting for inflation, you can follow these steps:

1. **Calculate the New Salary After the Raise:**
If your current salary is \( S \) and you receive a raise of \( n\% \), your new salary \( S_{\text{new}} \) will be:
\[
S_{\text{new}} = S \times (1 + \frac{n}{100})
\]

2. **Adjust for Inflation:**
If inflation is \( m\% \), the value of money effectively decreases. To find out how much your salary needs to increase to keep up with inflation, calculate the inflation-adjusted salary \( S_{\text{adjusted}} \):
\[
S_{\text{adjusted}} = S \times (1 + \frac{m}{100})
\]

3. **Compare the New Salary to the Adjusted Salary:**
To find the real change in your income considering inflation, you can calculate the difference in percentage terms:
\[
\text{Real Change} = \left(\frac{S_{\text{new}} - S_{\text{adjusted}}}{S_{\text{adjusted}}}\right) \times 100
\]

4. **Substituting the Values:**
Replacing \( S_{\text{new}} \) and \( S_{\text{adjusted}} \) in the equation gives:
\[
\text{Real Change} = \left(\frac{S \times (1 + \frac{n}{100}) - S \times (1 + \frac{m}{100})}{S \times (1 + \frac{m}{100})}\right) \times 100
\]
Once simplified, it results in:
\[
\text{Real Change} = \left(\frac{1 + \frac{n}{100} - (1 + \frac{m}{100})}{1 + \frac{m}{100}}\right) \times 100
\]
\[
= \left(\frac{\frac{n}{100} - \frac{m}{100}}{1 + \frac{m}{100}}\right) \times 100
\]
\[
= \frac{n - m}{1 + \frac{m}{100}}
\]

5. **Outcome:**
- If \( n > m \), you're effectively making more money in real terms.
- If \( n < m \), you're making less in real terms.
- If \( n = m \), your purchasing power remains unchanged.

This formula lets you determine the actual change in your purchasing power after accounting for both the raise and the inflation.