Whenever a fiduciary, as defined in §35-2-102, is required by law to execute a bond for assets placed with a financial institution in the form of a bank, trust company or savings and loan association, and the fiduciary agrees with the institution not to withdraw the principal of the assets, the bond required of the fiduciary shall be for the amount of the interest. No bond adjustment is necessary if the principal, or a portion of the principal, is withdrawn with court approval. The authorization for elimination of bond on the principal so deposited with the financial institution shall not apply unless the agreement by the fiduciary with the institution is approved by the court charged with administering the funds or the estate of the minor, and unless the agreement is filed in and enforced by the court.