Upon the filing of any partial settlement by the executor under a will, or the administrator of the estate of a deceased person, in the court in which such estate is pending, such executor or administrator may pray for a reduction in the amount of his or her bond as a fiduciary, and thereupon the court must set a day for the hearing of such partial settlement and must cause notices to be issued to all parties in interest as is now provided by law for final settlements of such estates. And on the day set for hearing the court may fix the amount to which the bond shall be reduced, which shall be determined as now provided by law for such bonds.