What is incumbent upon one who vowed to pay a sum of money to deter himself from performing ghusl, fearing that he might have exited Islam, but he performed ghusl and only paid part of the amount?

The ruling regarding paying money upon performing ghusl (ritual bath): the questioner is not obligated to pay anything, as long as it was not issued in the form of a binding vow (nadhr). Such a formulation, if it occurred to prevent oneself from doing something, is considered a "vow of obstinacy" (nadhr lajaj), and its violation only requires an expiation for breaking an oath (kaffarat yamin).