To calculate the balance after the payment, we first need to determine the interest accrued over 45 days, including the late fee, before the $250 payment is applied.
Step 1: Calculate the daily interest rate.
The annual percentage rate (APR) is 12.8%, so the daily interest rate can be calculated as follows:
\[ \text{Daily Interest Rate} = \frac{12.8%}{365} = \frac{0.128}{365} \approx 0.0003506849 \]
Step 2: Calculate the interest accrued over 45 days.
Now we calculate the interest accrued over 45 days:
\[ \text{Interest Accrued} = \text{Principal} \times \text{Daily Interest Rate} \times \text{Number of Days} \]
Where:
- Principal = $1,455.69
- Daily Interest Rate = 0.0003506849
- Number of Days = 45
Calculating it step-by-step:
\[ \text{Interest Accrued} = 1,455.69 \times 0.0003506849 \times 45 \] \[ \text{Interest Accrued} \approx 1,455.69 \times 0.015795821 = 22.9783909 \]
Rounding to the nearest penny gives us:
\[ \text{Interest Accrued} \approx 22.98 \]
Step 3: Add the late fee.
Now, we add the late fee of $35 to the principal and the calculated interest:
\[ \text{Total Amount Owed} = \text{Principal} + \text{Interest Accrued} + \text{Late Fee} \] \[ \text{Total Amount Owed} = 1,455.69 + 22.98 + 35 = 1,513.67 \]
Step 4: Pay $250.
Now we deduct the payment of $250:
\[ \text{New Balance} = \text{Total Amount Owed} - \text{Payment} \] \[ \text{New Balance} = 1,513.67 - 250 = 1,263.67 \]
Final Result
The balance after the payment is:
\[ \text{Balance} = \boxed{1,263.67} \]