Final answer:
The interest for the month calculated on an initial balance of $15,000 with a payment of $2,500 on the third day, and a 20% annual interest rate is approximately $212.48. This is none of the provided multiple-choice answers, indicating that additional information about the bank's interest calculation method might be necessary to select the correct option.
Step-by-step explanation:
The question is asking to calculate the interest for the month given an annual interest rate of 20% on an initial balance of $15,000, after a payment of $2,500 was made on the 3rd day of the month. To solve this, we need to understand how interest is computed on a reducing balance.
Firstly, since there are no details on a daily interest rate or specific information about the grace period's effect, we'll assume that the interest is calculated monthly at the end of the month. Given this, for the first 3 days, the interest is calculated on the initial balance:
($15,000 * 20%) / 12 months = $250 per month
$250 / 30 days = $8.33 per day for the first 3 days
Interest for first 3 days = 3 days * $8.33/day = $24.99
After the payment, the new balance is $15,000 - $2,500 = $12,500. Interest is then calculated on the new balance:
($12,500 * 20%) / 12 months = $208.33 per month
Interest for the remaining 27 days = 27 days * ($208.33 / 30 days) = $187.49
Finally, the total interest for the month is the sum of interest before and after the payment:
Total interest = $24.99 + $187.49 = $212.48
However, the closest answer provided in the question options is $300, but that would be the full interest charge on the initial $15,000 balance without considering the payment. Without more information on how the bank applies payments and calculates interest (e.g., daily balance method or average daily balance method), we can't provide a precise answer based on the provided answers (a) $300, (b) $500, (c) $1000, (d) $2500. Our calculated interest aligns with none of these options.