Is it permissible to build a house through an Islamic Murabaha system with a bank, where the bank sends a representative to purchase construction materials while the Murabaha rate remains fixed at 4% annually, and the beneficiary is responsible for the workers' wages?

If the bank buys construction materials and then sells them to you in installments with a known increase, this is permissible, provided the contract is free of late payment penalties, and that the increase is specified and known. However, if the bank gives you money to buy materials and then you return it to the bank with an increase, this is forbidden.