SOLUTION: 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 in

Question 1163408: 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!
```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**.
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