[Permissibility of Selling Paper Currency for Paper Currency with a Premium]

Answer: What is meant by permitting the sale of paper currency one for another with an increase is that one of the two lots of notes is new while the other is near disintegration and tearing, or that one is in large denominations and the other in small denominations, and the like; thus the increase on one side is in exchange for the deficiency on the other side.
It is a condition of this exchange that it be hand-to-hand.
There is no doubt you see in the examples mentioned an added attribute in one of the two counter-values, and that added attribute is often sought and near-necessary at times—such as for a trader who carries money and travels for commerce: higher-denomination notes are lighter for him to carry, and he can conceal and hide them from covetous eyes, unlike lower denominations.
However, it is a condition that the exchange be hand-to-hand; as credit it is invalid and impermissible, because it is a means to ribā. The usurer would make such a thing a way to take usury—for example, [exchanging] new notes for ragged notes on credit—and say, “The increase is for the increased attribute,” whereas in reality he wants the increase in exchange for deferment.
Even if the seller’s intention were that the increase is for the increased attribute, that would still not be permitted, because the buyer typically accepts the increase and is lax about its amount on account of the credit.
If it is said: Why was this permitted in paper currency but not in gold and silver?
We say:
1. Because paper currency has no intrinsic value; its value is notional. The note, as such, has no value—unlike gold and silver.
2. Paper currency is neither measured by volume nor by weight, and it has no value from that standpoint; whatever is of that kind does not belong to the ribā-bearing categories.
3. The notes in circulation are qīmiyyāt (valued by appraisal), not mithliyyāt (fungibles); ribā does not attach to qīmiyyāt.
From here we said the foregoing transaction is permissible.
However, we have given it the rulings of the two currencies (gold and silver) in sales and debts that entail ribā. On that basis, it is permissible that you sell the commodity for cash at one hundred five thousand riyals if paid in 100-notes, and at one hundred thousand riyals if paid in 1,000-notes—all this when the price is paid cash. It is not permitted as a credit-sale, for the reason we mentioned: the possibility that the increase is in exchange for the term.
There is no objection to an employee consenting, for himself, to a reduction—say five hundred—in order to be paid in 1,000-notes, or to an agreed increase—say five hundred—so that he takes 100-notes.
Likewise, there is no harm if the creditor and debtor mutually agree, at settlement, that the creditor take his due from the debtor in 1,000-notes while reducing—say one thousand—in return; or that he take payment in extremely tattered notes—whose leaves barely hold together in a man’s hand due to their decay—with an agreed increase—say one thousand riyals.
All of this is unobjectionable, since it involves no injustice and is no means to injustice; ribā was only prohibited because of the injustice it inflicts upon one of the two contracting parties.
Source: Min Thimār al-ʿIlm wa al-Ḥikmah vol.2