Depositories, before entering upon the discharge of their duties, by their proper officers, shall execute bonds, with good and sufficient securities, to be fixed and approved by the Governor. The bonds shall be conditioned for the faithful performance of all such duties as shall be required of them by law and for a faithful accounting for the money or effects that may come into their hands during their continuance in office. The bonds shall be filed and recorded in the Governor's office and copies thereof, certified by one of the Governor's secretaries under the seal of the executive department, shall be received in evidence in lieu of the original in any of the courts; and the bonds shall have the same binding force and effect as public officers' bonds and, in case of default, shall be enforced in like manner. In determining the amount of the bond to be given by a depository under this Code section, the Governor shall fix the same as to make it not less than the amount of money to be entrusted to the depository; and in no case shall a larger amount of money be deposited in any depository than the amount of the bond; and the Governor, at any time, may require additional bond, if necessary, to cover fully the amount deposited or intended to be deposited in such bank. The board, in its discretion, may waive the requirement of such bond as to demand deposits in a depository.