"unexpected additional expenses," 1660s, from contingency in the "chance occurrence" sense.
Entries linking to contingencies
contingency n.
1560s, "quality of being contingent, openness to chance or free will, the possibility that that which happens might not have happened," from contingent + abstract noun suffix -cy. Meaning "a chance occurrence, an accident, an event which may or may not occur" is from 1610s.