Do the rulings regarding gold for gold and silver for silver, concerning the necessity of equivalence and immediate possession, apply to paper money? If so, how is it permissible to incur a debt of identical paper currencies payable at a future date, while this is not permissible for gold?

Circulating currencies are treated like gold and silver in terms of the obligation of immediate exchange (qabḍ) and the prohibition of disparity when selling some of them for others. However, the prohibition of deferment and the obligation of immediate exchange are specific to sales, not loans. Thus, it is permissible to loan gold and silver for a term, on condition that the equivalent is returned. It is also permissible for someone who borrowed money to repay it with the equivalent value in another currency at the exchange rate on the day of repayment, provided there is immediate exchange and they do not part ways while anything is outstanding between them.