R.I. Gen. Laws § 24-12-16: Repayment of excess deposits.

Whenever from time to time the authority has satisfied the court that the amount deposited with the court is greater than is amply sufficient to satisfy the claims of all persons interested in the land, the court may order that the amount of any excess including any interest or increment on any sums so deposited shall be repaid to the authority. Whenever the authority has satisfied the court that the claims of all persons interested in the land taken have been satisfied, the unexpended balance including any interest or increment on any sums so deposited shall be paid immediately to the authority.