Question 1163381
Based on the 2018  -  2019 Turkish tax brackets provided, here is the mathematical model and the calculation for the specified 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 a piecewise function:

$$
T(I) = 
\begin{cases} 
0.15I & \text{if } 0 < I \le 14,800 \\
2,220 + 0.20(I - 14,800) & \text{if } 14,800 < I \le 34,000 \\
6,060 + 0.27(I - 34,000) & \text{if } 34,000 < I \le 120,000 \\
29,280 + 0.35(I - 120,000) & \text{if } I > 120,001 
\end{cases}
$$

**Breakdown of Cumulative Constants:**
* **$2,220$**: Tax on the first bracket ($14,800 \times 0.15$).
* **$6,060$**: Total tax through the second bracket ($2,220 + [34,000 - 14,800] \times 0.20$).
* **$29,280$**: Total tax through the third bracket ($6,060 + [120,000 - 34,000] \times 0.27$).

---

### b) Annual Income Tax Calculation

**1. Determine Annual Taxable Income**
Since the tax rates apply to annual income, we first convert the monthly taxable income:
$$I = 9,000 \text{ TRY/month} \times 12 \text{ months} = 108,000 \text{ TRY}$$

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

**3. Apply the Formula**
Using the third part of our piecewise model:
$$T(108,000) = 6,060 + 0.27 \times (108,000 - 34,000)$$
$$T(108,000) = 6,060 + 0.27 \times (74,000)$$
$$T(108,000) = 6,060 + 19,980$$
$$T(108,000) = 26,040$$

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