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To solve this problem using the **average daily balance method** for calculating finance charges on the credit card account, we follow these steps:

### 1. **Identify the transactions and their impact on the balance:**
   The initial balance on August 1st is $260. The following transactions occur:

   - **August 3:** Payment of $82 reduces the balance.
   - **August 6:** Charge of $135 increases the balance.
   - **August 16:** Charge of $25 increases the balance.
   - **August 28:** Charge of $30 increases the balance.

### 2. **Calculate the daily balances for each period:**

   - **From August 1 to August 2 (2 days):**
     Initial balance = $260.

   - **From August 3 to August 5 (3 days):**
     Balance after payment of $82:  
     New balance = $260 - $82 = $178.

   - **From August 6 to August 15 (10 days):**
     Balance after charge of $135:  
     New balance = $178 + $135 = $313.

   - **From August 16 to August 27 (12 days):**
     Balance after charge of $25:  
     New balance = $313 + $25 = $338.

   - **From August 28 to August 31 (4 days):**
     Balance after charge of $30:  
     New balance = $338 + $30 = $368.

### 3. **Compute the average daily balance:**

   The average daily balance is computed by multiplying the balance for each period by the number of days it remains at that balance, then dividing by the total number of days (31).

   \[
   \text{Average daily balance} = \frac{(260 \times 2) + (178 \times 3) + (313 \times 10) + (338 \times 12) + (368 \times 4)}{31}
   \]

   Let's compute this step by step:

   - $ 260 \times 2 = 520 $
   - $ 178 \times 3 = 534 $
   - $ 313 \times 10 = 3130 $
   - $ 338 \times 12 = 4056 $
   - $ 368 \times 4 = 1472 $

   Total = $ 520 + 534 + 3130 + 4056 + 1472 = 9496 $

   So, the average daily balance is:
   \[
   \frac{9496}{31} = 306.32
   \]

### 4. **Calculate the finance charge:**

   The finance charge is based on the average daily balance, the annual interest rate (21%), and the billing period (1 month or 31 days). To compute the monthly finance charge:

   \[
   \text{Finance charge} = 306.32 \times \frac{21\%}{12} = 306.32 \times 0.0175 = 5.36
   \]

Thus, the finance charge for the month of August is **$5.36**.

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Would you like further clarification on any step? Here are five related questions:

1. How does the average daily balance method differ from other finance charge methods?
2. What effect would an additional payment have on the finance charge?
3. How does the interest rate impact the finance charge calculation?
4. What if the interest rate were compounded daily instead of monthly?
5. How would the calculation change if there were additional transactions within the month?

**Tip:** Keep track of transaction dates and amounts carefully to accurately calculate finance charges using the average daily balance method.

Use the average daily balance method to compute the finance charge on the credit card account for the month of August (31 days). The starting balance from the previous month is $260. The transactions on the account are: August 3 - payment of $82, August 6 - charge of $135 for hiking boots, August 16 - charge of $25 for gasoline, August 28 - charge of $30 for a restaurant meal. Assume an annual interest rate of 21% and that the billing date is August 1st. Round to the nearest cent.

Learn how to compute the finance charge for a credit card account using the average daily balance method. With a starting balance of $260, payments and charges made throughout the month, and an annual interest rate of 21%, this step-by-step solution breaks down the process for accurate financial management.

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