To determine if the finance charge applied in Nia’s credit card statement is correct, we need to calculate the average daily balance for her billing cycle. Here is a detailed step-by-step solution for this:
1. Understand the Problem:
- We need to calculate the average daily balance for a 31-day billing cycle.
- Nia has balances and corresponding days as follows:
- 7 days with a balance of [tex]$745.00
- 10 days with a balance of $[/tex]585.15
- 7 days with a balance of [tex]$245.20
- 7 days with a balance of $[/tex]90.75
2. Calculate the Total Weighted Balance:
- We multiply each balance by the number of days it was held to get the total weighted balance.
- For the first entry: [tex]\(7 \times 745.00 = 5215.00\)[/tex]
- For the second entry: [tex]\(10 \times 585.15 = 5851.50\)[/tex]
- For the third entry: [tex]\(7 \times 245.20 = 1716.40\)[/tex]
- For the fourth entry: [tex]\(7 \times 90.75 = 635.25\)[/tex]
3. Sum Up the Total Weighted Balances:
- Total weighted balance = [tex]\(5215.00 + 5851.50 + 1716.40 + 635.25 = 13418.15\)[/tex]
4. Calculate the Average Daily Balance:
- To find the average daily balance, we divide the total weighted balance by the number of days in the billing cycle.
- [tex]\( \text{Average Daily Balance} = \frac{13418.15}{31} = 432.84354838709675 \)[/tex]
5. Match the Calculated Average Daily Balance to given options:
- Among the given options, the one that matches our calculated average daily balance (rounded to two decimal places) is:
- D. [tex]$432.84
Therefore, Nia’s average daily balance for the billing cycle is \$[/tex]432.84.
