What is the ruling on purchasing a house by installments with a declining profit rate called "Yusr" in Islamic banks?

It is not permissible for the seller and buyer in an installment sale to agree on a discount of part of the debt if the buyer expedites payment, because it falls under the issue of "da' wa ta'ajjal" (reduce and hasten), which is forbidden by most scholars.

However, it is permissible for the seller to forgive the buyer a portion of the debt without a prior condition if the buyer expedites payment.

It is also permissible for the seller to reward the buyer with a discount on a portion of the agreed price if the buyer commits to making payments at the specified times. This is considered a reward and an encouragement for their commitment.