(a) If the account is a trust account and there is a written agreement signed by the trustee or trustees, on death of the trustee or the survivor of two or more trustees, any sums remaining on deposit belong to:
(1) the person or persons named as beneficiaries, if surviving; or
(2) the survivor of the persons named as beneficiaries if one or more beneficiaries die before the trustee.
(b) If two or more beneficiaries survive, no right of survivorship exists between the surviving beneficiaries unless the terms of the account or deposit agreement expressly provide for survivorship between those beneficiaries.