To calculate the finance charge on the average daily balance over the 1-month period for the given credit card, we need to take the following steps:
1. Calculate the daily balances for each period:
- For days 1-3 (3 days), the balance is [tex]$150.
- For days 4-20 (17 days), the balance is $[/tex]200.
- For days 21-30 (10 days), the balance is [tex]$50.
2. Compute the total weighted balance:
- Multiply each balance by the number of days it was held:
\[
\text{Total Balance} = (3 \times 150) + (17 \times 200) + (10 \times 50)
\]
\[
\text{Total Balance} = 450 + 3400 + 500 = 4350
\]
3. Determine the total number of days:
- Sum the days:
\[
\text{Total Days} = 3 + 17 + 10 = 30
\]
4. Calculate the average daily balance:
- Divide the total balance by the total number of days:
\[
\text{Average Daily Balance} = \frac{\text{Total Balance}}{\text{Total Days}} = \frac{4350}{30} = 145
\]
5. Convert the Annual Percentage Rate (APR) to a monthly rate:
- Given APR is 15.5%, convert this to a monthly interest rate:
\[
\text{Monthly Interest Rate} = \frac{\text{APR}}{12} = \frac{15.5\%}{12} = \frac{0.155}{12} \approx 0.01291667
\]
6. Calculate the finance charge using the average daily balance and the monthly interest rate:
- Multiply the average daily balance by the monthly interest rate:
\[
\text{Finance Charge} = \text{Average Daily Balance} \times \text{Monthly Interest Rate} = 145 \times 0.01291667 \approx 1.872917
\]
7. Round the finance charge to the nearest cent:
- The finance charge rounded to the nearest cent is:
\[
\text{Finance Charge} \approx \$[/tex]1.87
\]
Thus, the finance charge on the average daily balance for this card over the 1-month period is [tex]$\( \$[/tex]1.87 \).
