To determine how much interest an opening balance of [tex]$12,356 accrues during the month of October on a credit card with an APR of 28%, follow these steps:
1. Identify the given information:
- Opening balance: $[/tex]12,356
- Annual Percentage Rate (APR): 28%
- Number of days in October: 31 days
- Number of days in a year: 365 days
2. Convert the Annual Percentage Rate (APR) to a daily interest rate:
- The APR of 28% must be converted into a daily rate. To do this, divide the APR by the number of days in a year (365).
- Daily interest rate = [tex]\( \frac{28\%}{365} \)[/tex]
3. Calculate the daily interest rate:
- Daily interest rate = 0.28 / 365 ≈ 0.000767
4. Calculate the interest accrued in October:
- Use the daily interest rate and multiply it by the opening balance and the number of days in the month of October.
- Interest accrued = Opening balance Daily interest rate Number of days
- Interest accrued = [tex]$12,356 0.000767 31
5. Perform the multiplication:
- Calculate: $[/tex]12,356 0.000767 = 9.473852
- Then, 9.473852 31 ≈ 293.8358
Rounding to two decimal places, the interest accrued in October is approximately [tex]$293.84.
Hence, the correct answer is:
D. $[/tex]293.84
