Final answer:
Sydney Dukes-Miller earned $163.58 in simple interest from her deposit of $2,430 at 6.75%, calculated using the formula for simple interest over the period of one year. The correct option is A.
Step-by-step explanation:
The student in question, Sydney Dukes-Miller, deposited $2,430 at an interest rate of 6.75%. The formula to calculate simple interest is the principal amount (P) multiplied by the interest rate (r) in decimal form, multiplied by the time the money is invested or borrowed for (t), which is P × r × t. In this scenario, assuming that the deposit is for a period of one year (since no time frame is specified), the simple interest can be calculated by converting the percentage to a decimal and applying the formula. The interest rate of 6.75% as a decimal is 0.0675.
Consequently, the calculation for Sydney's interest would be $2,430 × 0.0675 × 1. The result of this calculation gives Sydney a simple interest earned of $163.925. Since this amount isn't available in the multiple-choice options and typically the interest earned is rounded to the nearest cent, the closest match from the given options would be $163.58 (option a).