What is the ruling on purchasing a house through an interest-based bank that buys the house and then sells it to the client at an increased price, while keeping the house mortgaged until the full amount is paid, and is it permissible to live in it while it is mortgaged, and what is the ruling if the client becomes unable to pay after a period, knowing that this transaction is more expensive than a regular interest-based loan?

If the bank first buys the house and takes possession of it, then sells it to the client in installments, this is a permissible Murabaha sale. It is permissible for the bank to mortgage the house until the price is paid in full. In the event of the buyer's default, it is permissible to sell the mortgaged house, provided that the ruler undertakes the sale after granting the buyer a grace period. It is permissible for the buyer to reside in the mortgaged house. However, if the bank lends the client the price of the commodity with an increment, this is an usurious loan and is forbidden.