Is purchasing a house through Zaytuna Islamic Bank, which buys the house and sells it with a 5.4% profit margin and a 20% down payment, permissible or forbidden (halal or haram)?

If the bank first genuinely purchases the house after a prior promise from you to buy it, and then sells it to you at an agreed-upon increase, then this transaction (murabaha to the one who promises to purchase) is permissible. The bank must take possession of the commodity first, and there is no objection to the client paying an upfront portion and paying the rest in installments, or bearing the registration costs.