Question

You owe $1,578.93 on a credit card at 12.8% APR. You pay 15 days after the due date and the late fee is $25.00,
making it 45 days of accrued interest. You pay $236.00. How much is your balance after the payment?

Answer 1

To calculate the balance after making a payment on the credit card, we need to first determine the interest accrued over the 45 days, along with the late fee, and then apply the payment amount.

### Step 1: Calculate Daily Interest Rate
The annual percentage rate (APR) is 12.8%. To find the daily interest rate, we can use the formula:

\[
\text{Daily Interest Rate} = \frac{\text{APR}}{365}
\]

So,

\[
\text{Daily Interest Rate} = \frac{12.8\%}{365} = \frac{0.128}{365} \approx 0.00035068493
\]

### Step 2: Calculate Interest for 45 Days
Now, we multiply the daily interest rate by the balance and the number of days (45 days) to find the total interest accrued:

\[
\text{Accrued Interest} = \text{Balance} \times \text{Daily Interest Rate} \times \text{Number of Days}
\]

\[
\text{Accrued Interest} = 1,578.93 \times 0.00035068493 \times 45 \approx 24.972
\]

### Step 3: Calculate Total Amount Owed
Now, add the accrued interest to the original balance and include the late fee of $25.00:

\[
\text{Total Amount Owed} = \text{Original Balance} + \text{Accrued Interest} + \text{Late Fee}
\]

\[
\text{Total Amount Owed} = 1,578.93 + 24.972 + 25 = 1,628.902
\]

### Step 4: Apply the Payment
Now, subtract the payment of $236.00:

\[
\text{New Balance} = \text{Total Amount Owed} - \text{Payment}
\]

\[
\text{New Balance} = 1,628.902 - 236.00 = 1,392.902
\]

### Step 5: Final Balance
Thus, the balance after the payment is approximately:

\[
\text{New Balance} \approx 1,392.90
\]

So, your balance after the payment would be **$1,392.90**.