To what extent does the loan offered by Al Rajhi Bank, which involves the bank purchasing air conditioners from Al-Babtain Company and selling them to me on an installment basis with an annual addition of 2.5% and administrative fees, and then my appointing Al-Babtain Company to sell them, conform to Islamic Sharia?

The criterion is realities and actions, not papers. If the bank purchases the air conditioners and they become its property, it is permissible to keep them in the seller’s warehouses, provided they are distinguished from what has not been sold. Then the bank sells them to the customer. It is permissible for the customer to authorize the company to sell his goods to another buyer for a known commission. However, the customer should take possession of the air conditioners and sell them himself to avoid the suspicion of an unreal sale or collusion between the company and the bank in repurchasing them, as this carries the suspicion of circumvention.