If the usufructuary of a usufruct established mortis causa advances funds to discharge an estate debt charged to the property subject to the usufruct, the naked owner shall reimburse the usufructuary, without interest, at the termination of the usufruct, but only to the extent of the principal of the debt he has discharged and for any interest he has paid that had accrued on the debt before the commencement of the usufruct.
La. C.C. § 589