Which word describes being rashly or wastefully extravagant?

The term that describes being rashly or wastefully extravagant is "prodigal." This word is often used to depict someone who spends resources, especially money, in a lavish or reckless manner without much regard for the consequences. The concept of prodigality is closely tied to excessive generosity that ultimately leads to wastefulness.

In a broader sense, "prodigal" can also relate to someone who may waste not only financial resources but also time or efforts. Its root is famously associated with the "Prodigal Son" parable, where a young man squanders his inheritance and experiences dire consequences.

The other options do not carry the same meaning; "profound" typically refers to something deep or intense, "pretext" relates to a reason given in justification of a course of action that is not the real reason, and "presumptuous" describes an attitude of overstepping bounds or taking liberties. Thus, "prodigal" is the most fitting choice to describe extravagance in a reckless manner.