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Let's go step by step to break down the problem involving Anne's earnings, taxes, expenses, and loans. 

### Step 1: Calculate Anne's **weekly income**  
- **Normal rate**: \$19.5/hour  
- **Weekly normal hours**: 33 hours  
- **Overtime hours at time-and-a-half**: 9 hours  
- **Overtime hours at double-time**: 5 hours  

#### Weekly income calculation:
1. **Regular pay**:  
   $33 \times 19.5 = 643.5$ dollars  

2. **Overtime pay at time-and-a-half**:  
   $1.5 \times 19.5 = 29.25$ dollars/hour  
   $9 \times 29.25 = 263.25$ dollars  

3. **Overtime pay at double-time**:  
   $2 \times 19.5 = 39$ dollars/hour  
   $5 \times 39 = 195$ dollars  

**Total weekly income**:  
\[
643.5 + 263.25 + 195 = 1101.75 \, \text{dollars}
\]

---

### Step 2: Calculate Anne’s **annual income**
\[
1101.75 \times 52 = 57,691 \, \text{dollars/year}
\]

---

### Step 3: Calculate **income tax** (using the provided table)
Anne's taxable income is \$57,691. Let's use the table to find her income tax.  
- **First \$34,000**: Tax = \$4681.25  
- **Next**: $\$57,691 - 34,000 = 23,691$ (falls within the next bracket)  
  Tax on this part = $0.25 \times 23,691 = 5922.75$  

**Total income tax**:  
\[
4681.25 + 5922.75 = 10,604 \, \text{dollars}
\]

---

### Step 4: **Other deductions**
- **Pension contributions**: 6% of \$57,691  
  \[
0.06 \times 57,691 = 3461.46 \, \text{dollars}
  \]

- **Unemployment and health insurance**: 3.5% of \$57,691  
  \[
0.035 \times 57,691 = 2019.19 \, \text{dollars}
  \]

---

### Step 5: **Net income calculation**
\[
\text{Net income} = 57,691 - 10,604 - 3461.46 - 2019.19 = 41,606.35 \, \text{dollars/year}
\]

---

### Step 6: **Hire purchase of the car**
- **Cost of car**: \$5000  
- **Deposit (15%)**:  
  \[
0.15 \times 5000 = 750 \, \text{dollars}
  \]  
- **Outstanding balance**:  
  \[
5000 - 750 = 4250 \, \text{dollars}
  \]
- **Interest rate**: 10% per annum  
- **Monthly payment** (12 installments with interest): Use the formula for loan installment:
  \[
M = \frac{P \times r}{1 - (1 + r)^{-n}}
  \]
  where:
  - $P = 4250$
  - $r = \frac{10\%}{12} = 0.00833$ (monthly rate)
  - $n = 12$ months  

---

### Step 7: **Loan for the house**
- Loan = \$10,000  
- **Interest**: Compound interest rate of 15% per annum  
- **Monthly installment**:  
   Use the same loan formula, with $P = 10,000$, $r = \frac{15\%}{12}$, and $n = 36$.

---

### Step 8: **House sale and rent**
- Anne **sells the house** after one year for \$13,000, making a profit of $13,000 - 10,000 = 3000$ dollars.
- She then **rents an apartment** for \$500/month.

---

Would you like me to:
1. Calculate the detailed monthly installment for the car and house loans?  
2. Work out Anne’s **total net income** after accounting for loans and rent?  
3. Analyze her **profit from the house sale** in more depth?  
4. Break down the formulas for compound interest if needed?  
5. Recheck any step for accuracy or explore another scenario?

---

**Tip**: For installment calculations, using the **loan repayment formula** simplifies managing payments with interest.

Anne works in a factory. The standard rate of pay is $19.5 per hour. Anne worked 33 normal hours, 9 hours of overtime at time-and-a-half, and 5 hours of overtime at double-time. She needs to calculate her weekly and annual income, along with taxes, pension, insurance, and hire purchase and loan payments.

Learn how to calculate the weekly and annual income of a factory worker, including overtime pay, taxes, pension contributions, and interest on loans. Detailed steps for calculating loan installments with interest rates and understanding tax brackets.

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