Round to the nearest penny.

You owe $1,350.00 on a credit card with a 14.25% APR. You
pay $300.00 at the beginning of the month.
How much interest do you save by paying at the beginning
of the month versus at the end of the month?

1 answer

To determine the interest saved by paying $300 at the beginning of the month versus at the end of the month, we will first calculate the interest charged for both cases.

  1. Calculate the daily interest rate: The APR is 14.25%, which is equivalent to a daily interest rate of: \[ \text{Daily Interest Rate} = \frac{14.25%}{365} = \frac{0.1425}{365} \approx 0.000390411 \]

  2. Paying at the beginning of the month: When you pay $300 at the beginning of the month, your new balance for the remainder of the month is: \[ \text{New Balance} = 1350 - 300 = 1050 \] Assuming a month has about 30 days, we calculate the interest for 30 days: \[ \text{Interest} = \text{New Balance} \times \text{Daily Interest Rate} \times \text{Days} \] \[ \text{Interest} = 1050 \times 0.000390411 \times 30 \approx 12.2984 \] Rounding to the nearest penny, this interest is approximately $12.30.

  3. Paying at the end of the month: If you assume the entire balance of $1,350 remains until the end of the month, the interest calculation is: \[ \text{Interest} = 1350 \times 0.000390411 \times 30 \approx 15.763 \] Rounding to the nearest penny, this interest is approximately $15.76.

  4. Calculating the interest saved: The interest saved by paying at the beginning versus the end of the month is: \[ \text{Interest Saved} = \text{Interest (end)} - \text{Interest (beginning)} = 15.76 - 12.30 = 3.46 \]

Thus, the total interest saved by paying at the beginning of the month versus the end is approximately $3.46.