Is it permissible to sell an apartment with a down payment requested in installments over 15 months, with an increase in the total amount due to the extended period, knowing that this is considered an installment sale?

There is no objection to increasing the deferred price over the immediate price, and this is not usury (riba). This is because selling on credit or by installment differs from usury. Allah permitted selling due to need and forbade usury because the increase in usury is solely due to the deferment. Whereas, in selling on credit or by installment, the item sold is a commodity, and this is a form of leniency in selling because the buyer received a commodity, not money, and did not give an increase of the same kind as what he received.