When there are proceeds of sale belonging to an unknown owner, or to a person without the state who has no representative within it, or when there are proceeds arising from the sale of property including the prior estate of a tenant for life or for years, which are paid into court or deposited with the court administrator, the same shall be invested in interest-bearing securities for the benefit of the persons entitled thereto. Except as in this chapter otherwise provided, such investment shall be made in the name of the court administrator and the court administrator’s successors in office, who shall hold the same for the use and benefit of the persons interested, subject to the order of the court. The court administrator shall receive the interest and principal as it becomes due, apply and invest the same as the court may direct, file in the court administrator’s office the securities taken, and keep an account of such investments and of the moneys received thereon and the disposition thereof, in a book kept for that purpose, which shall be open to inspection by all persons.