Question 1163408
```python?code_reference&code_event_index=2
def calculate_tax(annual_income):
    if annual_income <= 14800:
        return annual_income * 0.15
    elif annual_income <= 34000:
        return 14800 * 0.15 + (annual_income - 14800) * 0.20
    elif annual_income <= 120000:
        return 14800 * 0.15 + (34000 - 14800) * 0.20 + (annual_income - 34000) * 0.27
    else:
        return 14800 * 0.15 + (34000 - 14800) * 0.20 + (120000 - 34000) * 0.27 + (annual_income - 120000) * 0.35

monthly_income = 9000
annual_income = monthly_income * 12
tax = calculate_tax(annual_income)
print(f"{annual_income=}")
print(f"{tax=}")

# Checking bracket constants
print(f"Bracket 1 tax: {14800 * 0.15}")
print(f"Bracket 2 tax: {(34000 - 14800) * 0.20}")
print(f"Bracket 3 tax: {(120000 - 34000) * 0.27}")


```
```text?code_stdout&code_event_index=2
annual_income=108000
tax=26040.0
Bracket 1 tax: 2220.0
Bracket 2 tax: 3840.0
Bracket 3 tax: 23220.0

```
To calculate the annual income tax based on the 2018-2019 Turkish tax brackets, we can define a piecewise mathematical model and then apply it to your specific income.

### a) Mathematical Model
Let $I$ represent the **Annual Taxable Income** (in TRY) and $T(I)$ represent the **Annual Income Tax**. The progressive tax system is modeled as follows:

$$
T(I) = 
\begin{cases} 
0.15I & \text{if } 0 < I \le 14,800 \\
2,220 + 0.20(I - 14,800) & \text{if } 14,800 < I \le 34,000 \\
6,060 + 0.27(I - 34,000) & \text{if } 34,000 < I \le 120,000 \\
29,280 + 0.35(I - 120,000) & \text{if } I > 120,000 
\end{cases}
$$

**Derivation of constants:**
* **$2,220$:** Tax on the full first bracket ($14,800 \times 0.15$).
* **$6,060$:** Tax on the first bracket plus the full second bracket ($2,220 + [34,000 - 14,800] \times 0.20$).
* **$29,280$:** Tax on the first three brackets ($6,060 + [120,000 - 34,000] \times 0.27$).

---

### b) Calculation for TRY 9,000 Monthly Income

**Step 1: Determine Annual Taxable Income**
Since the brackets are annual, we first convert the monthly income:
$$I = 9,000 \text{ TRY/month} \times 12 \text{ months} = \mathbf{108,000 \text{ TRY}}$$

**Step 2: Identify the Correct Bracket**
The annual income of $108,000$ TRY falls into the **third bracket** ($34,001 - 120,000$).

**Step 3: Apply the Formula**
Using the third piece of our mathematical model:
$$T(108,000) = 6,060 + 0.27 \times (108,000 - 34,000)$$
$$T(108,000) = 6,060 + 0.27 \times (74,000)$$
$$T(108,000) = 6,060 + 19,980$$
$$T(108,000) = 26,040 \text{ TRY}$$

**Final Answer:**
If your monthly taxable income is TRY 9,000, you will have to pay an annual income tax of **TRY 26,040**.