To determine the difference in the amount of interest accrued by the end of the month depending on whether the payment is made at the beginning or the end of the month, we can follow these steps:
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Calculate the daily interest rate.
- The annual percentage rate (APR) is 14.5%, so the daily interest rate is: \[ \text{Daily interest rate} = \frac{14.5%}{365} \approx 0.039726% \approx \frac{0.145}{365} \approx 0.0003967 \]
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Calculate the interest accrued with payment made at the end of the month.
- For one month (30 days), the total interest on the balance of $3,489.35 would be: \[ \text{Interest} = \text{Principal} \times \text{Daily interest rate} \times \text{Number of days} \] \[ \text{Interest} = 3489.35 \times 0.0003967 \times 30 \approx 41.52 \]
- After paying $500 at the end of the month, the new balance will be: \[ \text{New balance} = 3489.35 + 41.52 - 500 = 3030.87 \]
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Calculate the interest accrued with payment made at the beginning of the month.
- If you make the payment at the beginning, you effectively reduce the balance before interest accrues: \[ \text{New balance after payment} = 3489.35 - 500 = 2989.35 \]
- Now calculate the interest on this new balance for the entire month: \[ \text{Interest} = 2989.35 \times 0.0003967 \times 30 \approx 35.52 \]
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Compare the interest for both scenarios.
- Interest with payment at the end: Approximately $41.52
- Interest with payment at the beginning: Approximately $35.52
- Difference in interest accrued: \[ \text{Difference} = 41.52 - 35.52 = 6.00 \]
Thus, the difference in the amount of interest accrued by the end of the month if you pay at the beginning of the month versus the end of the month is $6.00.