What is the ruling on subscribing to a state-affiliated housing association whose installments are paid to a usurious bank, especially if the subscriber did not own a house at the time of subscription but later bought one, and if it is impermissible, what should he do to expiate for that?

If the subscription to the state-affiliated housing association is for the purpose of purchasing a dwelling, and the association's installments are deposited in a usurious bank without there being a direct relationship with the bank, then there is no objection to it and no sin in it. This is because the matter is merely a referral from the seller (the association) to an agent for depositing the money.