To calculate the finance charge on the average daily balance for the credit card over the period of the month, we follow these steps:
1. Determine the average daily balance:
- Calculate the balance for each period, multiplying the balance by the number of days in that period.
- Aggregate these weighted balances and then divide by the total number of days in the billing cycle.
- For days 1-5: A balance of \[tex]$200 for 5 days.
- For days 6-20: A balance of \$[/tex]350 for 15 days.
- For days 21-30: A balance of \[tex]$150 for 10 days.
Therefore, the calculation would be:
\[
\text{Average Daily Balance} = \frac{(5 \times 200) + (15 \times 350) + (10 \times 150)}{30}
\]
\[
= \frac{1000 + 5250 + 1500}{30}
\]
\[
= \frac{7750}{30}
\]
\[
\approx 258.33
\]
2. Calculate the daily interest rate:
- The Annual Percentage Rate (APR) is 10.5%. To find the daily interest rate, we divide this by the number of days in a year (365 days).
\[
\text{Daily Interest Rate} = \frac{10.5\%}{365} = \frac{0.105}{365} \approx 0.00028767
\]
3. Calculate the finance charge:
- The finance charge is the product of the average daily balance, the daily interest rate, and the number of days in the billing cycle (30 days).
\[
\text{Finance Charge} = 258.33 \times 0.00028767 \times 30
\]
\[
\approx 2.23
\]
After rounding to the nearest cent, the finance charge for the month is:
\[
\boxed{2.23}
\]
So, the finance charge on the credit card's average daily balance for this 1-month period is \$[/tex]2.23.
