All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
Based on what you have said, the offer from the dealer is apparently not included in Al-‘Eenah trade (underlined in Fatwa 5987), which is forbidden, due to a number of considerations. The most important one is that the goods have changed from their original state during the first sale upon the lapse of the mentioned period, so there is nothing wrong with swapping the old car for the new car with the same dealer or any other dealer provided that this is not for the sake of paying the first debt, as this would consist in canceling a debt with a debt, which is forbidden in Islam. This includes anything that results in an increase in the debt for the debtor in return for an increase in the period (of repayment) or anything that leads to it according to a resolution from the Islamic Fiqh Committee at its sixteenth session held in Makkah from 21-26/10/1422 A.H. (5-10 January, 2002 A.D.) on the subject of trading off a debt.
The resolution states that among the prohibited methods of incorporating an outstanding debt into a new debt, is “to cancel a debt with a debt by a transaction occurring between the debtor and a creditor by whose terms and conditions a new debt is created on the debtor in order to repay the first debt with a condition, a custom, or renouncement or an organized procedure, whether the debtor is solvent or in financial difficulties; and whether the first debt is immediate or deferred and the purpose is to accelerate repayment of the first debt from the new one; and whether the debtor and creditor agreed on this in the first debt agreement or it was a later agreement; and whether this is by request from the creditor or from the debtor. The prohibition also includes transactions between the debtor and another party, not the creditor, if it is by the arrangement of the creditor himself or a guarantee from him for the debtor in order to repay his debt.”
Allaah Knows best.