On the determination by death or otherwise, of the estate or other thing, from or in respect of which any rent, hire or money, coming due at fixed periods, issues or is derived, or on the death of any person interested in such rent, hire or money, the person or the personal representative or assignee of the person who would have been entitled, but for such death or determination, to the rent, hire, or money coming due at any such period, shall have a proportion thereof, according to the time which shall have elapsed of the time for which such rent, hire, or other money was growing due, including the day of such death or determination, deducting a proportional part of the charges.