Final answer:
The question is seeking the original principal balance of a loan with a 2.50% quarterly compounded interest rate. However, essential information to calculate the principal balance, such as the loan term or the total amount paid, is missing, making it impossible to determine the correct principal balance from the given options.
Step-by-step explanation:
The question asks for the principal balance of a loan which was used to finance the purchase of a machine.
The principal balance could be calculated using the formula for compound interest. However, the information provided does not include the required details such as the total amount paid or the duration of the loan.
With the given compounding rate of 2.50% compounded quarterly, several answers are listed, but without the necessary details about the loan term and the payments made, it is not possible to determine the correct principal balance from the options provided.
The concepts of compound interest, principal balance, and the workings of loan amortization are important for solving this kind of question. Without additional information, however, a definitive answer cannot be provided.