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To calculate the average daily balance and finance charge for this 30-day billing cycle, let's go through the step-by-step process of the solution.
### Step 1: Define the Information
We have the following information:
- Initial balance on 7/3: [tex]$400 - Payment on 7/18: $[/tex]100 (credit)
- Charge on 7/27: [tex]$250 ### Step 2: Calculate the Number of Days for Each Period 1. From 7/3 to 7/18 (exclusive): 18 - 3 = 15 days 2. From 7/18 to 7/27 (exclusive): 27 - 18 = 9 days 3. From 7/27 to the end of the month (7/30): 30 - 27 + 1 = 4 days ### Step 3: Calculate the Balance for Each Period 1. Period 1 (7/3 to 7/18): - Balance: $[/tex]400
- Number of days: 15 days
- Sum of balances: [tex]$400 * 15 = $[/tex]6000
2. Period 2 (7/18 to 7/27):
- Balance after payment on 7/18: [tex]$400 - $[/tex]100 = [tex]$300 - Number of days: 9 days - Sum of balances: $[/tex]300 * 9 = [tex]$2700 3. Period 3 (7/27 to 7/30): - Balance after charge on 7/27: $[/tex]300 + [tex]$250 = $[/tex]550
- Number of days: 4 days
- Sum of balances: [tex]$550 4 = $[/tex]2200
### Step 4: Calculate the Sum of Balances and Total Number of Days
- Sum of all balances for the billing cycle: [tex]$6000 (Period 1) + $[/tex]2700 (Period 2) + [tex]$2200 (Period 3) = $[/tex]10900
- Total number of days: 15 + 9 + 4 = 28 days
### Step 5: Calculate the Average Daily Balance
- Average daily balance = Total sum of balances / Total number of days
- Average daily balance = [tex]$10900 / 28 ≈ $[/tex]389.29
### Step 6: Calculate the Finance Charge
Assume an annual finance charge (APR) rate of 18%, which is converted to a monthly rate:
- Monthly rate = 18% / 12 = 1.5%
Now, calculate the finance charge based on the average daily balance:
- Finance charge = Average daily balance Monthly rate
- Finance charge = [tex]$389.29 * 0.015 ≈ $[/tex]5.84
### Conclusion
The average daily balance for the billing cycle is approximately [tex]$389.29, and the finance charge for the period is approximately $[/tex]5.84 when rounded to the nearest cent.
### Summary
- Average daily balance: [tex]$389.29 - Finance charge: $[/tex]5.84
These results are consistent with the given final outcome.
### Step 1: Define the Information
We have the following information:
- Initial balance on 7/3: [tex]$400 - Payment on 7/18: $[/tex]100 (credit)
- Charge on 7/27: [tex]$250 ### Step 2: Calculate the Number of Days for Each Period 1. From 7/3 to 7/18 (exclusive): 18 - 3 = 15 days 2. From 7/18 to 7/27 (exclusive): 27 - 18 = 9 days 3. From 7/27 to the end of the month (7/30): 30 - 27 + 1 = 4 days ### Step 3: Calculate the Balance for Each Period 1. Period 1 (7/3 to 7/18): - Balance: $[/tex]400
- Number of days: 15 days
- Sum of balances: [tex]$400 * 15 = $[/tex]6000
2. Period 2 (7/18 to 7/27):
- Balance after payment on 7/18: [tex]$400 - $[/tex]100 = [tex]$300 - Number of days: 9 days - Sum of balances: $[/tex]300 * 9 = [tex]$2700 3. Period 3 (7/27 to 7/30): - Balance after charge on 7/27: $[/tex]300 + [tex]$250 = $[/tex]550
- Number of days: 4 days
- Sum of balances: [tex]$550 4 = $[/tex]2200
### Step 4: Calculate the Sum of Balances and Total Number of Days
- Sum of all balances for the billing cycle: [tex]$6000 (Period 1) + $[/tex]2700 (Period 2) + [tex]$2200 (Period 3) = $[/tex]10900
- Total number of days: 15 + 9 + 4 = 28 days
### Step 5: Calculate the Average Daily Balance
- Average daily balance = Total sum of balances / Total number of days
- Average daily balance = [tex]$10900 / 28 ≈ $[/tex]389.29
### Step 6: Calculate the Finance Charge
Assume an annual finance charge (APR) rate of 18%, which is converted to a monthly rate:
- Monthly rate = 18% / 12 = 1.5%
Now, calculate the finance charge based on the average daily balance:
- Finance charge = Average daily balance Monthly rate
- Finance charge = [tex]$389.29 * 0.015 ≈ $[/tex]5.84
### Conclusion
The average daily balance for the billing cycle is approximately [tex]$389.29, and the finance charge for the period is approximately $[/tex]5.84 when rounded to the nearest cent.
### Summary
- Average daily balance: [tex]$389.29 - Finance charge: $[/tex]5.84
These results are consistent with the given final outcome.
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