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. We ask Allaah to exalt his mention as well as that of his family and all his companions.
The method by which a bank which deals with Ribaa (interest and usury) buys a house for the customer is a method which involves Ribaa, as in reality it is not a question of sale, but it is a loan with interest; we have already clarified this in Fataawa 86960 and 87403.
Therefore, if a Muslim does not find an institution or a body which sells houses according to religious requirements, then it is not permissible for him to indulge in a transaction which involves Ribaa.
A transaction with the description mentioned in the question, which states that there will be an increase in installments in return for the delay in payments, is a forbidden contract as it includes an invalid condition (i.e. which is forbidden in religion), so it is forbidden to engage in this kind of contract.
Allaah Knows best.