To determine the finance charge on the average daily balance for this credit card over a month, we need to follow several steps, broken down as follows:
1. Determine the total of the balances over all days:
- For the first 5 days, the balance is [tex]$200$[/tex]. Thus, for 5 days: [tex]\(200 \times 5 = 1000\)[/tex].
- For the next 15 days (6-20), the balance is [tex]$350$[/tex]. Thus, for 15 days: [tex]\(350 \times 15 = 5250\)[/tex].
- For the final 10 days (21-30), the balance is [tex]$150$[/tex]. Thus, for 10 days: [tex]\(150 \times 10 = 1500\)[/tex].
Summing these amounts gives the total balance over the 30 days:
[tex]\[
1000 + 5250 + 1500 = 7750
\][/tex]
2. Calculate the total number of days in the period:
The total number of days is [tex]\(5 + 15 + 10 = 30\)[/tex] days.
3. Calculate the average daily balance:
The average daily balance is given by dividing the total balance over all days by the total number of days:
[tex]\[
\text{Average Daily Balance} = \frac{7750}{30} = 258.33
\][/tex]
4. Determine the monthly interest rate:
The annual percentage rate (APR) is 12%. To find the monthly rate, divide the APR by 12 (since there are 12 months in a year):
[tex]\[
\text{Monthly Interest Rate} = \frac{12\%}{12} = 1\% = 0.01
\][/tex]
5. Calculate the finance charge:
The finance charge is determined by multiplying the average daily balance by the monthly interest rate:
[tex]\[
\text{Finance Charge} = 258.33 \times 0.01 = 2.58
\][/tex]
Therefore, the finance charge on the average daily balance for this card over this 1-month period is:
[tex]\[
\boxed{2.58}
\][/tex]
