You can "make" a payment -- that much is fine. However, "The account for making the payment" is not a good phrase in my opinion. The word "for" seems vague and unsatisfactory, especially since you can make payments both to and from an account.
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AnonymousNamely, is it correct to say: The account to which the payment must be madeIt is correct English, but check whether "must" is correct in your situation.