Question

Round any decimals to the nearest penny.
You owe $1,455.69 on a credit card at 12.8% APR.. You pay 15 days after the due date and the late fee is $35, making it 45 days
of accrued interest. You pay $250. How much is your balance after the payment?

Answer 1

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:

\[
\text{Balance} = \boxed{1,263.67}
\]