Whenever any deposit is made in a bank by a person which in form is in trust for another, but no other or further notice of the existence and terms of a legal and valid trust is given in writing to the bank, in the event of the death of the trustee, the deposit or any part thereof, may be paid to the person for whom the deposit was made, together with the dividends or interest thereon, whether or not such person is a minor.
SDCL 51A-10-4