rate of payment vs rate

rate of payment and rate both are nouns.

Word	Noun	Adjective	Verb	Adverb
rate of payment	Yes	No	No	No
rate	Yes	No	Yes	No

As nouns, rate is a hypernym of rate of payment; that is, rate is a word with a broader meaning than rate of payment:

Other hypernyms of rate of payment include charge per unit.

rate of payment (noun)	rate (noun)
the amount of money paid out per unit time	the relative speed of progress or change
	amount of a charge or payment relative to some basis
	a quantity or amount or measure considered as a proportion of another quantity or amount or measure
	a magnitude or frequency relative to a time unit

rate of payment (verb)	rate (verb)
	assign a rank or rating to
	estimate the value of
	be worthy of or have a certain rating