A perquisite is a payment or profit given in addition to regular wages or salary. The word is easy to remember because it is the source of the word perk.
A prerequisite is something that is required as a prior condition.
Prerequisite vs. requisite
Prerequisite is often used were requisite would make more sense. Requisite is a synonym of requirement, whereas a prerequisite is something that must be achieved prior to something else. In these sentences, for instance, requisite would work in place of prerequisite because the required thing doesn’t necessarily precede another required thing:
For some types of music, sheer volume is a prerequisite for true understanding. [AV Club]
The story concludes happily – a prerequisite of the genre – with a Vera Wang wedding dress and an Armani tuxedo. [Telegraph]
Everyone seems to agree that two stars are a prerequisite for NBA success. [Wall Street Journal]
And in these examples, prerequisite works well because it denotes a required thing that precedes another required thing:
States that want to pursue their own reforms shouldn’t have to toe the federal government’s line for three years as a prerequisite. [Los Angeles Times]
The new zzusis system, previously student information system (SIS), will check student course registrations to confirm that prerequisites are met. [WSU Today]
[F]or many young men owning a property is a prerequisite for attracting a wife. [The Economist]