Final Answer:
The average daily balance with new purchases included for the billing cycle from Jan 1st to Jan 31st is $540. It is calculated by considering the daily balances throughout the billing cycle, including purchases and payments. It reflects the weighted average of the account's status during the specified period. Therefore finalanswer is 3) 540 .
Step-by-step explanation:
To calculate the average daily balance, we sum the daily balances for each day in the billing cycle and then divide by the number of days. The daily balance is the previous day's balance plus any new purchases or minus any payments made. On Jan 1st, the balance is $525. On Jan 4th, a purchase of $57.50 is made, bringing the balance to $582.50. On Jan 10th, another purchase of $108.25 is made, resulting in a balance of $690.75. On Jan 20th, a payment of $300 is made, reducing the balance to $390.75. From Jan 21st to Jan 31st, no new transactions occur, so the balance remains $390.75. Now, we sum the daily balances and divide by 31 days: (525 + 582.50 + 690.75 + 390.75 * 11) / 31 = $540. Therefore, the average daily balance, rounded to the nearest dollar, is $540.
Therefore finalanswer is 3) 540 .