Actually, the case you are asking about is easier to permit than the one that you assume is permitted. Let us develop the topic from the beginning.
Paying for something not at its “natural” time raises questions of ribbit. The normal time to pay for a purchase is at the time the buyer receives the merchandise. Therefore, it is forbidden for a seller to allow a buyer to pay on credit if he clearly charges him more for that privilege.[3] It is viewed as if the seller is lending money to the buyer during the credit period and receiving extra money for doing so.
There are nevertheless permitted ways of buying on credit; we will note a number. If, during the presentation and discussion before the sale, only the sales price for credit payment was given as an option, it is permitted to agree on the credit payment,[4] even if it would have in fact been cheaper had the purchaser bought with cash. This system has a couple of conditions, based on the need to ensure that 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 was exceeded with the credit agreement.[5] Another is that the increase in price for credit is not steep enough to be clearly related to the credit.[6] If one negotiates his own prices with suppliers, he can agree on a payment scheme before agreeing on a price and then negotiate one price accordingly. This is not a problem even if other customers are able to choose between different rates for cash and for credit.
Another possibility is to use a heter iska[7] for the transaction, which is particularly effective when the item is to be used for business, rather than for personal consumption.[8] A heter iska causes the late payment, which is considered like the seller’s loan to the buyer, to be viewed as the seller’s investment of the sales money in the buyer’s hands, with assumed joint profits.[9] (It is preferable but not absolutely required for the heter iska to be a written document.[10])
There is a distinguished but minority opinion[11] that if the accepted market price is the one the seller gave for credit and this seller gives a particularly cheap price for cash, it is permitted to buy on credit even when the two prices were presented together. The Pitchei Teshuva,[12] however, does not accept this leniency.
There is a more accepted opinion[13] that applies in many business settings. If the industry standard is to pay only 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 does not create a problem of ribbit.
Regarding your question, we might have thought that we should view the receiving of the money early as, in essence, a “loan” from the time the money is received until the time the payment was due. If so, the incentive for early payment could have been forbidden as interest on that “loan.” Nevertheless, the halacha is that it is permitted to pay early after a proper sale on credit in order to receive a discount.[14] The Rama[15] cautions that the offer of a discount should be presented only after a kinyan has made the sale final. Otherwise, it would be forbidden for the sides to stand by the credit deal, although it would be permitted for them to use the arrangement of a discount for immediate payment. While it is not always clear when it is that the kinyan takes place, if you have already received the merchandise, you can safely assume that the kinyan has already been completed. In any case, the answer to your question is that such a scenario is permitted.