payment rate vs rate of payment

payment rate and rate of payment both are nouns.

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

As nouns, payment rate and rate of payment are synonyms defined as:

payment rate and rate of payment: the amount of money paid out per unit time

Other synonyms of payment rate include installment rate, repayment rate.

payment rate (noun)	rate of payment (noun)
the amount of money paid out per unit time	the amount of money paid out per unit time