Here's why:
* Adverbs modify verbs, adjectives, or other adverbs. "Promptly" describes how an action is performed (e.g., "He arrived promptly").
* They answer questions like "how," "when," "where," or "to what extent." "Promptly" answers the question "how" (how did he arrive? - promptly).
Let me know if you have any other word you'd like to analyze!