The Secretary of Finance shall pay to each hospital qualified under § 7201 of this title such amount shown to be due to it as shall be approved by the Department of Health and Social Services at such rate per day as shall be determined by the Budget Director at the Budget Director's discretion for each person receiving such medical or surgical care and attention. No money shall be paid to any hospital for any month until the amount due to all the hospitals for the preceding month has been fully determined and paid.