To solve the problem step-by-step:

Step 1: Calculate the weighted balance for each time period.

The finance charge calculation involves finding the average daily balance, weighted by the number of days the balance was at a specific level.

1. Days 1–3: $150
   Weighted balance: $3 \times 150 = 450$

2. Days 4–20: $200
   Weighted balance: $17 \times 200 = 3400$

3. Days 21–30: $50
   Weighted balance: $10 \times 50 = 500$

Step 2: Add the weighted balances.

Total weighted balance:
$450 + 3400 + 500 = 4350$

Step 3: Find the average daily balance.

Average daily balance = $\frac{\text{Total weighted balance}}{\text{Number of days}}$:
$\text{Average daily balance} = \frac{4350}{30} = 145$

Step 4: Calculate the finance charge.

The APR is 28.5%, so the monthly rate is: \frac{28.5\%}{12} = 0.02375\ \text{(or 2.375%)}

Finance charge: $\text{Finance charge} = 145 \times 0.02375 = 3.44$

Final Answer:

The finance charge is $3.44.

Let me know if you want further clarification!

Here are 5 related questions you may consider:

1. How does changing the APR affect the finance charge calculation?
2. What happens if a payment is made earlier in the cycle?
3. How would this calculation differ with compounding interest?
4. How do late fees factor into average daily balance calculations?
5. What is the difference between APR and APY?

Tip: To reduce finance charges, pay off balances as early as possible during the billing cycle.