Any corporation organized and operating as a trust company or as a bank authorized by law to do a trust business may deposit with the State Treasurer or elsewhere United States bonds, bonds, notes or debentures of any federal agency such as a federal land bank, banks for cooperatives, Farm Home Administration, Federal National Mortgage Association, etc., Alabama bonds, bonds of any city or county in the State of Alabama or mortgages which are first liens on real estate, worth in each case double the face of the mortgage, situated in this state, to an amount not less than $25,000.00, and may increase said deposit from time to time or reduce the same to an amount not less than $25,000.00, or may withdraw the deposit entirely, provided such trust companies or banks have made final settlement and accounted for all assets in their possession and under their control by reason of any appointment under this chapter. Immediately upon the appointment of any bank or trust company to act as guardian, administrator, executor, receiver or trustee or other fiduciary by the judge of any court in this state, under Section 5-11A-9, said judge shall certify such appointment under his seal of office to the State Treasurer, giving the name and amount of assets of the estate or cestui que trusts; and, upon receipt of said certificate, the State Treasurer shall charge against any deposit the liability under said appointment.