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Answer: Actually, the case you ask about is easier to permit than that which you assume is permitted. Let us develop the topic from the beginning.
Paying for something not at its "natural" time raises issues of ribbit. The normal time to pay for a sales item is at the time he receives it. Therefore, it is forbidden for a seller to allow a buyer to pay on credit and clearly charge him more for the privilege (Bava Metzia 65a).
Therefore, one has to be careful when buying on credit. We will now mention some of the permitted ways of buying on credit. If during deliberations before the sale only the sales price for credit pay was on the table, it is permitted (ibid., Shulchan Aruch, Yoreh Deah 173:1) even if, in fact, it would have been cheaper if he bought with cash. This system has a couple of conditions, which are predicated on the need to ensure it is not clear that the seller is charging extra for waiting for payment. One is that there must not be a set price for the item that they exceeded with the credit agreement (ibid.). Another is that the increase in price for credit is not steep enough to be clearly related to the credit (ibid.). If you negotiate your own prices with suppliers, you can agree on a payment scheme before agreeing on a price and then negotiate one price accordingly. It is not a problem if other customers get to choose between different rates for cash and for credit.
Another possibility is to use a heter iska for the transaction, especially if the item is for business, not consumption use (Brit Yehuda 40:21). (It is preferable but not absolutely required for the heter iska to be a written document (Brit Yehuda 40:9; Torat Ribbit 16:2).) Then, the late payment, which is considered like the seller’s loan to the buyer, is viewed as the seller’s investment of the sales money in the buyer’s hands with assumed joint profits. One who regularly sells on credit would be wise to put up a clearly visible sign stating that all the transactions on credit are "according to the heter iska found in …"
Bemare Habazak - Rabbis Questions (654)
Rabbi Daniel Mann
273 - Reflecting on a Socio-Religious Trend
274 - Paying Earlier than the Payment Plan Prescribed
275 - When to Cut the Challa?
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There is a more accepted opinion (Imrei Yosher I:150; see Torat Ribbit 8:15, Brit Yehuda 22:8), although far from unanimous, that applies in many business settings. If the industry standard is to pay by credit, that becomes the normal payment time. Then, even if there is a known cheaper price for cash, paying on credit is normal and not an issue of ribbit.
Regarding your question, if after a proper sale on credit, you are offered to pay earlier than agreed for a discount, this is permitted (Shulchan Aruch, YD 173:3). Rishonim (see Tur and Beit Yosef, YD 173) compare this to someone who sells a debt for future payment to a third party for immediate cash but at a lower face value. The discount is not considered a new "loan" that the seller is requesting from the buyer, who owes him later. This is apparently because the payment still corresponds to the sale, which classically is paid immediately. The Rama (YD 173:3) warns that the offer of a discount should be made only after a kinyan has made the sale final. Otherwise, it will be forbidden for the buyer to stand by the credit deal. While it is not always clear when the kinyan is, if you already received the merchandise, the kinyan will presumably be complete.

Kuzari -Rabbi Ari Shvat Kuzari class 8- "Answering Questions on the Kuzari's Proof from Mass Revelation
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