Is it permissible to take out a loan to buy a new house until the current house is sold, while renting out the current house and donating its rent until it is sold?

If your current home is sufficient for you, or if you can rent another house, then it is not permissible to take out a usurious loan to buy a new house. This is because necessity is determined by its extent, and taking a usurious loan without necessity is considered transgression and aggression. You can stay in your current home until it is sold, or rent another house and pay its rent from the rent of your own house.