All the books, papers, letters, and transactions pertaining to the office of State Treasurer shall be open to the inspection of a committee of the Legislature to examine and settle all accounts and to count all money. When the successor of any such treasurer shall be elected and qualified, the Auditor of Public Accounts shall examine and settle all accounts of such treasurer remaining unsettled and give him or her a certified statement showing the balance of money, securities, and effects for which he or she is accountable, and which have been delivered to his or her successor, and report the balance electronically to the Legislature.