What is the ruling on purchasing a house through an Islamic institution that buys the house and then sells it to the buyer for a fixed monthly payment over a specified period, with the buyer also paying an additional amount as processing fees and a 20% down payment of the house's value, and the final price of the house being higher than its original price?

It is permissible to purchase a house from the entity that owns it, as well as to pay a down payment and defer the remaining amount, paying it in installments. The additional sum paid for the transaction is permissible if it represents a profit for the seller. However, if the transaction concludes with a lease that ends in ownership, it is not permissible. But if it involves monthly installments after the house becomes the property of the buyer, then it is permissible. This transaction is a form of murabaha and there is no legal impediment to it, unless it is a lease-to-own arrangement, in which case it is not permissible.