Which preposition should be used in the following situations — on, to or of?
- payment on/to/of something.
- Here is the money to/of it.
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Payment is a nominalization of the verb pay, and therefore it inherits properties of the verb, including some prepositional usages. And pay is a particularly complex verb (it's the short verbs that tend to cause problems in English; they're really common and develop all kinds of idioms and special usages).
Pay is part of the Commercial Transaction Frame (CTF), which means that it involves not just two noun phrases (like a transitive verb), or three (like a bitransitive verb), but four noun phrases (NPs), each with a very specific semantic role in this frame.
These NPs (also featured in other CTF usages, like buy, spend, and sell) are:
With pay, the action starts with the Payer possessing the Money and the Payee possessing the Commodity; paying means moving the Money to the Payee and the Commodity to the Payer, so that the possession relations are reversed at the end of (and as a result of) the action.
This is fine with a verb, since subject, direct object, and indirect object all have places in the structure, and can even participate in the Dative Alternation:
So that's two prepositions accounted for: to marks the indirect object of pay (in this case, the Payee) and for marks the Commodity; these preposition choices are inherited by payment:
But nouns can't have subjects or direct objects, either, so more prepositions are necessary.
When a transitive verb is nominalized (the rules are different for intransitives, but pay is, if anything, super-transitive), of marks the direct object of pay (i.e, the Money), and by its subject (the Payer):
which is unwieldy but grammatical and unambiguous.
There are other ways to do this; for instance, the subject can possess the nominalization:
And they can appear by themselves
or in any combination -- one rarely needs to specify all four NPs with a nominalization, in context.
I'm not following your use of "sth". But, maybe this will help in any case:
"Payment is due on the 5th."
"Payments are made to ABC Corp Ltd."
"I made a payment of $400."
"Here is the money for it."
"Here is the $400 for this month's rent."