To determine the finance charge on the average daily balance for the given credit card over this 1-month period, follow these steps:
1. Identify the Number of Days in Each Period:
- For days 1 to 3, there are 3 days.
- For days 4 to 20, there are [tex]\(20 - 4 + 1 = 17\)[/tex] days.
- For days 21 to 30, there are [tex]\(30 - 21 + 1 = 10\)[/tex] days.
2. Identify the Balance for Each Period:
- The balance from days 1 to 3 is \[tex]$200.
- The balance from days 4 to 20 is \$[/tex]300.
- The balance from days 21 to 30 is \[tex]$150.
3. Calculate the Total Number of Days in the Month:
- The total number of days is \(3 \, (days\ 1 \ to\ 3) + 17 \, (days\ 4 \ to\ 20) + 10 \, (days\ 21 \ to\ 30) = 30\ days\).
4. Calculate the Weighted Sum of the Balances:
- The sum of the balances weighted by the number of days in each period is:
\[
(200 \, \text{dollars} \times 3 \, \text{days}) + (300 \, \text{dollars} \times 17 \, \text{days}) + (150 \, \text{dollars} \times 10 \, \text{days}) = 600 + 5100 + 1500 = 7200 \, \text{dollar-days}.
\]
5. Calculate the Average Daily Balance:
- The average daily balance is:
\[
\frac{7200 \, \text{dollar-days}}{30 \, \text{days}} = 240 \, \text{dollars}.
\]
6. Determine the Monthly Interest Rate:
- Given the annual percentage rate (APR) is 12%, the monthly interest rate is:
\[
\frac{12\%}{12} = 1\%.
\]
7. Calculate the Finance Charge:
- The finance charge is:
\[
240 \, \text{dollars} \times 1\% = 240 \, \text{dollars} \times 0.01 = 2.40 \, \text{dollars}.
\]
8. Round to the Nearest Cent:
- The finance charge rounded to the nearest cent is already \$[/tex]2.40.
Therefore, the finance charge for this credit card over the 1-month period is [tex]\(\$2.40\)[/tex].
