Question 1163381: A. According to the Turkish tax legislation, there are two main types of tax statuses regulated on the basis of residence: resident taxpayers and non-resident taxpayers. Individual income tax rates applicable on resident taxpayers for 2018 - 2019 are as follows:
Income Scales (TRY) Rate (%)
Up to 14,800 15
14,801 - 34,000 20
34,001 - 120,000 27
120,001 and over 35
a) Create a Mathematical Model that represents the aforementioned information to calculate the annual income tax.
b) How much annual income tax you will have to pay if your monthly taxable income is TRY 9,000.
Answer by CPhill(2264)   (Show Source):
You can put this solution on YOUR website! 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**.
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