To find the finance charge, we can calculate the average daily balance for the period and then apply the monthly interest rate of 1.15%. Here’s the process broken down step-by-step:

1. Define the Timeline and Balances

• August 10: Starting balance is $\$365$.
• August 15: A purchase of $\$66$ and a payment of $\$71$ are made.
  • New balance: $365 + 66 - 71 = 360$
• August 27: An additional charge of $\$165$ is made.
  • New balance: $360 + 165 = 525$

2. Calculate the Daily Balance for Each Period

1. August 10 to August 15 (5 days): Balance = $\$365$
2. August 15 to August 27 (12 days): Balance = $\$360$
3. August 27 to September 10 (14 days): Balance = $\$525$

3. Compute the Average Daily Balance

To find the average daily balance, we’ll sum the products of each balance and the number of days it was held, then divide by the total number of days in the period.

$\text{Average Daily Balance} = \frac{(365 \times 5) + (360 \times 12) + (525 \times 14)}{5 + 12 + 14}$

Calculating each part:

• $365 \times 5 = 1825$
• $360 \times 12 = 4320$
• $525 \times 14 = 7350$

Total balance-days:

$1825 + 4320 + 7350 = 13495$

Total days:

$5 + 12 + 14 = 31$

So,

$\text{Average Daily Balance} = \frac{13495}{31} = 435.32$

4. Calculate the Finance Charge

The finance charge is 1.15% of the average daily balance.

$\text{Finance Charge} = 435.32 \times 0.0115 = 5.01$

Answer:

The finance charge on the September 10 bill is $5.01.

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Would you like further clarification on any steps?

Here are related questions for further exploration:

1. How would the finance charge change if the interest rate were different?
2. What effect would an additional payment have on the average daily balance?
3. How does changing the payment date affect the finance charge?
4. How is the average daily balance method different from other finance charge calculation methods?
5. What happens to the finance charge if purchases are made on the last day of the billing period?

Tip: Tracking balance changes by day can help predict finance charges more accurately.