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The problem provides a scenario where:

1. **Initial gross salary**: 4100 €/month.
2. **Tax rate**: 32%.
3. **Salary increase**: 4%.
4. **Tax increase**: 1.2 percentage points.
5. **Consumer price index (CPI)** rises from 100.35 to 103.55.

We are asked to calculate the **real percentage change in the net salary**.

### Step-by-step solution:

1. **Initial net salary**:
   The net salary is the gross salary after tax. The initial net salary is calculated as:
   \[
   \text{Initial net salary} = 4100 \times (1 - 0.32) = 4100 \times 0.68 = 2788 \, \text{€/month}
   \]

2. **New gross salary**:
   The salary increases by 4%, so the new gross salary is:
   \[
   \text{New gross salary} = 4100 \times 1.04 = 4264 \, \text{€/month}
   \]

3. **New tax rate**:
   The tax rate increases by 1.2 percentage points, from 32% to 33.2%. The new net salary is:
   \[
   \text{New net salary} = 4264 \times (1 - 0.332) = 4264 \times 0.668 = 2850.75 \, \text{€/month}
   \]

4. **Change in consumer price index (CPI)**:
   The CPI increases from 100.35 to 103.55. The percentage increase in CPI is:
   \[
   \text{CPI increase} = \frac{103.55 - 100.35}{100.35} \times 100 = \frac{3.2}{100.35} \times 100 \approx 3.19\%
   \]

5. **Real percentage change in net salary**:
   To calculate the real change in net salary, we first find the nominal percentage change in net salary:
   \[
   \text{Nominal net salary change} = \frac{2850.75 - 2788}{2788} \times 100 = \frac{62.75}{2788} \times 100 \approx 2.25\%
   \]

   The real change in net salary is adjusted for inflation:
   \[
   \text{Real change in net salary} = 2.25\% - 3.19\% = -0.94\%
   \]

Thus, the real percentage change in net salary is **-0.94%**, meaning the net salary has decreased in real terms.

Would you like further details on any part of this solution? Here are 5 related questions:

1. How is real salary adjusted for inflation?
2. How does a percentage point increase in tax affect net salary?
3. What does the Consumer Price Index (CPI) indicate?
4. Can you explain the relationship between nominal and real wage?
5. What are the factors that influence changes in net salary over time?

**Tip**: Real wage growth is crucial in understanding purchasing power, as inflation can offset nominal wage increases.

Henkilön bruttopalkka oli 4100 €/kk, josta hän maksaa veroa 32 %. Myöhemmin bruttopalkka nousee 4 % ja samalla verotus kiristyy 1,2 %-yksikköä. Samaan aikaan kuluttajahintaindeksi nousee 100,35 → 103,55. Kuinka monta prosenttia nettopalkka muuttui reaalisesti?

This problem explores how a gross salary increase of 4%, a tax rate increase from 32% to 33.2%, and an increase in the Consumer Price Index (CPI) affect the real percentage change in net salary. Detailed step-by-step calculations show how to adjust for inflation and determine the real wage growth, suitable for high school students.

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