Final answer:
The new balance after a $250 payment on the credit card debt, taking into account the accrued interest for 45 days and a late fee, would be $147651.98. This includes the initial balance, accumulated interest, and the late payment fee subtracted by the amount paid.
Step-by-step explanation:
To calculate the new balance after a payment on a credit card debt, we need to account for any accrued interest and any fees for late payments. Initially, the student owes $145569 at an annual percentage rate (APR) of 12.8%, and they make a payment 45 days after the interest starts accruing. Since most credit card companies use a daily interest calculation, we'll first find the daily interest rate by dividing the APR by 365. The daily interest rate is 12.8% / 365 = 0.0350685%.
Next, we multiply the daily interest rate by the number of days interest has accrued (45 days) and then by the balance:
Interest = $145569 * 0.0350685% * 45 = $2297.98 (approximately)
We then add the late fee to find the total amount due before the payment:
Total Due = $145569 + $2297.98 (Interest) + $35 (Late Fee) = $147901.98
After a payment of $250, the remaining balance would be:
New Balance = Total Due - Payment = $147901.98 - $250 = $147651.98