https://file.aiquickdraw.com/mathbot/file/1729493423124zorayvba.jpg

Let's go through the case in detail based on the image content:

### Problem Breakdown:

1. **Anne's Work Information:**
   - Standard hourly wage: **$19.5** per hour.
   - Weekly work:
     - Normal hours: **33**.
     - Overtime (time-and-a-half): **9** hours.
     - Overtime (double-time): **5** hours.
   - Year: **52 weeks**.

2. **Deductions:**
   - Pension contributions: **6%**.
   - Unemployment and health insurance: **3.5%**.
   - **Income tax table** (as shown in the image) to calculate tax based on her income.

3. **Additional Info:**
   - Anne bought a **car loan** for **$5000**, with **15% deposit** and an **interest rate of 10% per annum**.
   - She also took a **home loan** of **$10000** at **15% compounded interest** over **3 years**, repaid in **36 equal installments**.

4. **End-of-year transactions:**
   - Sold house for **$13000**.
   - Rented an apartment for **$500 per month** after selling the house.

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### We can now solve this step by step:

#### **1. Calculate Anne's Weekly Income:**

- **Normal pay**: $ 33 \times 19.5 = 643.5 $
- **Overtime (time-and-a-half)**: $ 9 \times (19.5 \times 1.5) = 9 \times 29.25 = 263.25 $
- **Overtime (double-time)**: $ 5 \times (19.5 \times 2) = 5 \times 39 = 195 $

- **Total weekly pay**: $ 643.5 + 263.25 + 195 = 1101.75 $

#### **2. Calculate Annual Income:**

- **Annual Income**: $ 1101.75 \times 52 = 57291 $

#### **3. Apply Deductions:**

- **Pension (6%)**: $ 57291 \times 0.06 = 3437.46 $
- **Unemployment & Health Insurance (3.5%)**: $ 57291 \times 0.035 = 2005.19 $

- **Total deductions**: $ 3437.46 + 2005.19 = 5442.65 $

- **Taxable Income**: $ 57291 - 5442.65 = 51848.35 $

#### **4. Calculate Income Tax (Based on the table):**

For income **$51848.35**:
- From **$0 to $8,375**, tax is **$837.50**.
- From **$8,375 to $34,000**, tax is $ 15\% $ of the amount over **$8,375**: 
  $ (34000 - 8375) \times 0.15 = 25625 \times 0.15 = 3843.75 $.
- From **$34,000 to $82,400**, tax is $ 25\% $ of the amount over **$34,000**:
  $ (51848.35 - 34000) \times 0.25 = 17848.35 \times 0.25 = 4462.09 $.

- **Total tax payable**: 
  \( 837.5

Anne works in a factory. If the standard rate of pay is $19.5 per hour. Anne worked 33 normal hours, 9 hours overtime at time-and-a-half, and 5 hours overtime at double-time for the week. There are 52 weeks in a year. Anne needs to pay income tax (use the given table), 6% for pension contributions, 3.5% for unemployment and health insurance. Anne buys a car for $5000 on hire purchase. A deposit of 15% is paid and interest is paid on the outstanding balance for 1 year at an interest rate of 10% per annum. She didn't pay from net income for deposit. Anne also takes a home loan for $10000 at a compound interest rate of 15% per annum, repaid in 36 equal installments. After one year, she sold her house for $13000 then rented an apartment for $500 per month.

Calculate Anne's income, taxes, and deductions based on her work hours and overtime. Learn to compute pension contributions, unemployment insurance, and income tax. Solve compound interest calculations for a home loan and determine annual deductions. Suitable for Grades 10-12 students learning algebra and finance-related concepts.

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