https://file.aiquickdraw.com/mathbot/file/1726596431463yig797f5.jpg

The problem presented in the image can be summarized as follows:

Denise has:
- An annual salary of €47,500.
- A tax credit of €3,600.
- A standard rate cut-off point of €32,000.
- The standard tax rate is 20%, and the higher tax rate is 46%.

We are asked to find how much income tax Denise pays for the year.

### Step-by-step Calculation:

1. **Split Salary for Tax Rates**:
   - Denise's salary is €47,500.
   - The standard rate cut-off point is €32,000. This means the first €32,000 of her salary will be taxed at the standard rate (20%), and the remaining (€47,500 - €32,000) = €15,500 will be taxed at the higher rate (46%).

2. **Calculate Tax at Standard Rate**:
   - Tax on €32,000 at 20%: 
     \[
     32,000 \times 0.20 = 6,400 \, \text{(tax on standard rate)}
     \]

3. **Calculate Tax at Higher Rate**:
   - Tax on €15,500 at 46%:
     \[
     15,500 \times 0.46 = 7,130 \, \text{(tax on higher rate)}
     \]

4. **Total Tax Before Tax Credit**:
   - Total tax = Tax at standard rate + Tax at higher rate:
     \[
     6,400 + 7,130 = 13,530
     \]

5. **Apply Tax Credit**:
   - The tax credit is €3,600. So, the total tax payable after applying the tax credit is:
     \[
     13,530 - 3,600 = 9,930
     \]

Therefore, the total income tax Denise has to pay for the year is **€9,930**.

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Would you like more details or have any further questions?

Here are five related questions for further understanding:
1. How would Denise's tax change if her tax credit was reduced by €500?
2. What would her tax payable be if the higher rate was 40% instead of 46%?
3. If Denise's salary increased to €50,000, how would that affect her tax?
4. How much more would she save if the tax credit increased to €4,000?
5. What portion of her salary is taxed at the higher rate?

**Tip**: Understanding tax brackets is crucial to estimating tax liabilities accurately, especially in progressive tax systems where different portions of income are taxed at varying rates.

Denise has an annual salary of €47,500. She has a tax credit of €3,600 and a standard rate cut-off point of €32,000. If the standard rate is 20% and the higher rate is 46%, find how much income tax she pays for the year.

Learn how to calculate income tax for an individual with an annual salary of €47,500, a tax credit of €3,600, and a standard rate cut-off point of €32,000. This detailed solution explains how to apply the standard 20% tax rate and the 46% higher tax rate in a progressive tax system.

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