A charge account had a balance of $943 on May 5. A purchase of $295 was made on May 17, and a payment of $175 was made on May 20. The interest on the average daily balance is 1.1% per month. Find the finance charge on the June 5 bill. (Round your answer to the nearest cent.)

To calculate the finance charge based on the average daily balance, we can follow these steps:

### Step 1: Break the period into different sections
We are interested in calculating the average daily balance from May 5 to June 5 (31 days). Within this time, there are two transactions:
- May 17: A purchase of $295
- May 20: A payment of $175

### Step 2: Calculate the balance over the different periods
- From **May 5 to May 17 (12 days)**, the balance is $943.
- On **May 17**, the balance increases by $295, making it:
  \[
  943 + 295 = 1238
  \]
  So, from **May 17 to May 20 (3 days)**, the balance is $1238.
- On **May 20**, a payment of $175 is made, so the new balance is:
  \[
  1238 - 175 = 1063
  \]
  From **May 20 to June 5 (16 days)**, the balance is $1063.

### Step 3: Calculate the average daily balance
We now calculate the total weighted balance for the period:
\[
(943 \times 12) + (1238 \times 3) + (1063 \times 16)
\]
\[
= 11316 + 3714 + 17008 = 32038
\]
The total number of days in the billing cycle is 31. So, the average daily balance is:
\[
\frac{32038}{31} = 1033.48
\]

### Step 4: Calculate the finance charge
The finance charge is 1.1% per month, so the finance charge is:
\[
1.1\% \times 1033.48 = 0.011 \times 1033.48 = 11.37
\]

Thus, the finance charge on the June 5 bill is **$11.37**.

Would you like further details or have any questions?

Here are 5 related questions to expand on this concept:
1. How is average daily balance different from simple interest calculation?
2. What if the interest rate were compounded daily instead of monthly?
3. How would the finance charge change if the payment on May 20 was delayed until May 25?
4. How do promotional periods (0% interest for a certain time) affect the finance charge calculation?
5. What is the impact of higher interest rates on credit card balances over time?

**Tip**: Always aim to make payments early in the billing cycle to reduce the average daily balance and minimize finance charges.

Learn how to calculate the finance charge for a charge account using the average daily balance method and a monthly interest rate of 1.1%. This detailed solution involves transactions across a billing period and shows how to compute the final finance charge of $11.37. Suitable for high school students.

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