All perfect praise be to Allah, The Lord of The Worlds, and may His blessings and peace be upon our Prophet Mohammad and upon all his family and companions.
Waiving a portion of debt in what`s called "Debt Contracts" in return for early settlement is called by Muslim jurists "Da` wa Ta`ajjal" i.e. when the creditors "waive or forgive" a portion of the debt in return for early settlement of the rest of the money."
In this regard, there are five cases:
First: Waiving a portion of debt is conditioned in the original contract. In this case, this is considered Riba(interest and/or usury). It is like making two transactions combined in one bargain, and this is forbidden since The Prophet (PBUH) said: "If anyone makes two transactions combined in one bargain, he should have the lesser of the two or it will involve usury." {Related by Abi Dawud}.
Second:Waiving a portion of debt in return of early settlement of the rest of the money is agreed upon after having concluded the original contract. In fact, the majority of the Muslim scholars have forbidden this based on the preponderant opinion of the four schools of thought. They have based their view on the Hadith reported by Al-Miqdad Bin Al-Aswad who said, "I lent a man one hundred dinars. I said to him: "Pay me ninety as early as you could against waiving ten dinars from the original sum." The man replied, " Okay."Later, Al-Miqdad mentioned that to the Prophet(PBUH). He, peace and blessings be upon him, said, "You have dealt in usury."{Related by Al-Baihaqi}. Since waiving against early settlement is similar to addition against delayed settlement; both give financial value to the time factor. On the other hand, Ibn Abbas, may Allah bless them both, Al-Nokha`i, Ibn Serene and Zufar permitted waiving a portion of the debt against early settlement of the rest of the money based on the narration of Ibn abbas where it is stated that when the Prophet(PBUH) wanted to make Bani An-Nadeer leave Madinah, they said to him, "O` Messenger of Allah! You ordered us to leave although we haven`t collected our money from debtors because the time of settlement isn`t due yet." He, peace be upon him, said "Da`oo wa Ta`ajjaloo" i.e. "waive or forgive" a portion of that debt in return for immediate settlement of the rest of your money by debtors."{Related by Al-Hakim, but Al-Baihaqi considered it a weak narration}. Because usury is addition against delay in settlement, it totally harms the debtor and differs from "Da`oo wa Ta`ajjaloo" where both parties(Creditor and debtor) benefit from that transaction. The latter view was adopted by the International Islamic Fiqh academy in its resolution No.(66), but stipulated that no prior agreement was reached to that end.
Third: The waiving is made from the debts which the debtor has failed to settle on time. In this case, it is permissible to waive a portion of that debt against early settlement of the rest of the money in order to be cleared from the debt.
Fourth: The waiving wasn`t conditioned by the contracting parties; rather, it was a donation/gift from the creditor because the debtor had settled the rest of the money or the deferred payments earlier than agreed in the original contract.
Fifth: It is permissible for the debtor to give the creditor a commodity against his debt, even if its value was less than that of the debt, and this was permitted by the majority of the Muslim scholars. For further details, please refer to the books {Bedayat Al-Mojtahid by Ibn Roshd & Al-Qawaneen Al-Fiqhia by Ibn Jazzi}.
In conclusion, waiving a portion of the deferred debt, upon request of debtor or creditor, in return for early settlement of the rest of the money is permissible, and isn`t Riba so long as it wasn`t conditioned in the original contract. And Allah knows best.