Final answer:
The correct word to complete the sentence is 'dwindle', which means to gradually diminish or reduce in size, amount, or strength, and aptly describes what may happen to the investments without prudence.
Step-by-step explanation:
The correct answer to fill in the blank in the sentence "Unless he shows more prudence, his investments will _______ to nothing in a few months." is dwindle. The verb dwindle means to gradually diminish or reduce in size, amount, or strength. When it comes to investments, dwindling would convey the sense that the value is decreasing over time, which fits the context of the sentence perfectly.
Option 2, decrease, is a generic term that simply means to become smaller or less. Option 3, abate, generally refers to something that becomes less intense or widespread, more commonly used with things like storms or feelings, rather than investments. Option 4, diminish, is also close in meaning to dwindle, but diminish does not necessarily convey the gradual aspect that dwindle does.
Therefore, dwindle is the best choice as it implies a gradual reduction to almost nothing, which is what the sentence suggests will happen to the investments without more prudence.