A vested interest means a personal benefit or strong stake in an outcome. The correct answer is this meaning because the expression is used figuratively, not only by its literal words.

Examples:

• He had a vested interest in keeping the old system.
• In an HSC essay, A vested interest can express this meaning: a personal benefit or strong stake in an outcome.
• When this expression appears in a passage, connect A vested interest with the idea of a personal benefit or strong stake in an outcome.