Is zakat on money due in the month of Rabi' al-Awwal on the amount saved (principal and previous earnings), in addition to the expected rate of return up to this month, even if the new earnings have not been actually added to the account?

You are required to pay zakat (definition) on your share of the profit along with the capital when it materializes. You should pay zakat when the capital's hawl (one lunar year) is due (Rabi' al-Awwal), even if the profit has not yet been deposited into your account. However, if the profit does not appear or you are unable to ascertain its materialization, then pay zakat on the entire capital when its hawl is due, and defer the zakat on the unknown profit until its existence and amount are known, at which point you would pay its zakat.