Naoko has these daily balances on his credit card for September's billing period. He paid his balance from the August billing in full.
2 days @ $99.78
15 days @ $315.64
11 days @ $515.64
2 days @ $580.32


a. His APR is 15.4%. How much is the finance charge on his September bill? Round to the nearest cent. 


To calculate the finance charge for Naoko's credit card, we need to determine the average daily balance and then apply the APR. Here’s how to do it step by step:

1. **Calculate the Total Daily Balance:**
   - For 2 days at $99.78:
     \[
     2 \times 99.78 = 199.56
     \]
   - For 15 days at $315.64:
     \[
     15 \times 315.64 = 4734.60
     \]
   - For 11 days at $515.64:
     \[
     11 \times 515.64 = 5672.04
     \]
   - For 2 days at $580.32:
     \[
     2 \times 580.32 = 1160.64
     \]

2. **Sum of All Daily Balances:**
   \[
   199.56 + 4734.60 + 5672.04 + 1160.64 = 11766.84
   \]

3. **Calculate the Average Daily Balance:**
   - Total days in September = 30
   \[
   \text{Average Daily Balance} = \frac{11766.84}{30} = 392.2292 \text{ (approximately } 392.23\text{)}
   \]

4. **Calculate the Finance Charge:**
   - APR = 15.4%, or 0.154 as a decimal
   - Monthly interest rate = $\frac{0.154}{12}$
   \[
   \text{Monthly interest rate} = 0.0128333
   \]
   \[
   \text{Finance Charge} = \text{Average Daily Balance} \times \text{Monthly interest rate}
   \]
   \[
   \text{Finance Charge} = 392.23 \times 0.0128333 \approx 5.04
   \]

**Final Answer:**
The finance charge on Naoko's September bill is approximately **$5.04**.

Would you like details on any specific part of the calculation, or do you have any questions? Here are some related questions you might consider:

1. How is the APR used to calculate monthly finance charges?
2. What are the implications of carrying a balance on a credit card?
3. How does the length of time a balance is carried affect finance charges?
4. What are some strategies to minimize finance charges on credit cards?
5. How can average daily balance be calculated in different billing cycles?

**Tip:** Always pay off your balance in full to avoid finance charges!

Naoko has these daily balances on his credit card for September's billing period. He paid his balance from the August billing in full. 2 days @ $99.78, 15 days @ $315.64, 11 days @ $515.64, 2 days @ $580.32. His APR is 15.4%. How much is the finance charge on his September bill? Round to the nearest cent.

Discover how to calculate the finance charge on a credit card with a 15.4% APR using daily balances over September. Learn the steps to find the total daily balance, average daily balance, and finance charge, resulting in a finance charge of approximately $5.04.

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