Final answer:
The likely reason for the court finding that the administrative agency violated the APA is the lack of a logical and rational explanation for the significant change in the proposed rule following public comments.
Step-by-step explanation:
A court finding that an administrative agency violated the Administrative Procedure Act (APA) typically implies that the agency has failed to follow proper rulemaking procedures as defined under the APA. In the scenario described, the agency provided a notice and a comment period, which are both in compliance with the APA. However, the most likely reason for the court's decision might be that the agency did not provide a logical and rational explanation for why it decided to change the proposed maximum interest rate from 40 percent to 20 percent in response to public comments. This sudden and significant alteration may appear arbitrary without an accompanying explanation of how the public's feedback influenced the agency's decision-making process. The APA requires agencies to consider and respond to significant comments received during the public comment period, thereby ensuring that the rulemaking process is open and based on a reasoned decision-making process.