What is the ruling on purchasing a house from a bank through an installment system, where a fixed, unchangeable interest rate is added to the monthly installment, knowing that the questioner resides in America?

Installment sale is originally permissible, and there is no harm in increasing the price of a commodity sold on credit over its cash price, provided that the contract between the seller and the buyer is concluded at a specific, known price. So, if the bank genuinely owns the property and sells it at a specified price, the transaction is permissible, and the amount the bank earns in excess of the property's purchase price does not affect the validity of the contract.