D.C. Code § 24-201.04: Commutation of fine.

In all cases in the District of Columbia where a defendant is sent to jail or to the Workhouse in default of the payment of a fine he shall be released upon the payment of the balance of the fine due by him after crediting thereon as paid an amount equal to the proportion the time thus served by him in the Jail or Workhouse bears to the whole time he was to serve under the sentence.