What is the alternative to a loan, and where is the Muslim treasury (Bayt al-Mal) that lends without interest?

Usurious loans are forbidden and are considered grave sins. The Islamic alternative is a benevolent loan (Qard Hasan (definition)). If that is not available, the Shariah-compliant alternatives are Murabaha for the one who commands the purchase, or Tawaruq. In Murabaha, the bank buys a commodity requested by the client, then sells it to him at a known profit, after the bank has acquired ownership and possession of it. As for Tawaruq, it is when a person in need of cash buys a commodity on credit, then sells it for cash to a third party for less than what he bought it for.