I had occasion to address this for a member on Banking and Credit Cards:
(Deleted a great deal, but those are the relevant rules.)
Rule 1.090
(a) Computation. In computing any period of time prescribed or allowed by these rules, by order of court, or by any applicable statute, the day of the act, event, or default from which the designated period of time begins to run shall not be included. The last day of the period so computed shall be included unless it is a Saturday, Sunday, or legal holiday, in which event the period shall run until the end of the next day which is neither a Saturday, Sunday, or legal holiday. When the period of time prescribed or allowed is less than 7 days, intermediate Saturdays, Sundays, and legal holidays shall be excluded in the computation.
(e) Additional Time after Service by Mail. When a party has the right or is required to do some act or take some proceeding within a prescribed period after the service of a notice or other paper upon that party and the notice or paper is served upon that party by mail, 5 days shall be added to the prescribed period.
Rule 1.380
(a) Motion for Order Compelling Discovery. Upon reasonable notice to other parties and all persons affected, a party may apply for an order compelling discovery as follows:
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(2) Motion. If . . .a party in response to a request for inspection submitted under rule 1.350 fails to respond that inspection will be permitted as requested or fails to permit inspection as requested, or if a party in response to a request for examination of a person submitted under rule 1.360(a) objects to the examination, fails to respond that the examination will be permitted as requested, or fails to submit to or to produce a person in that party’s custody or legal control for examination, the discovering party may move for an order compelling an answer, or a designation or an order compelling inspection, or an order compelling an examination in accordance with the request.
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(4) Award of Expenses of Motion. If the motion is granted and after opportunity for hearing, the court shall require the party or deponent whose conduct necessitated the motion or the party or counsel advising the conduct to pay to the moving party the reasonable expenses incurred in obtaining the order that may include attorneys’ fees,
(b) Failure to Comply with Order.
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(2) If a party or an officer, director, or managing agent of a party or a person designated under rule 1.310(b)(6) or 1.320(a) to testify on behalf of a party fails to obey an order to provide or permit discovery, . . .the court in which the action is pending may make any of the following orders:
(A) An order that the matters regarding which the questions were asked or any other designated facts shall be taken to be established for the purposes of the action in accordance with the claim of the party obtaining the order.
(B) An order refusing to allow the disobedient party to support or oppose designated claims or defenses, or prohibiting that party from introducing designated matters in evidence.
(C) An order striking out pleadings or parts of them or staying further proceedings until the order is obeyed, or dismissing the action or proceeding or any part of it, or rendering a judgment by default against the disobedient party.
(D) Instead of any of the foregoing orders or in addition to them, an order treating as a contempt of court the failure to obey any orders except an order to submit to an examination made pursuant to rule 1.360(a)(1)(B) or subdivision (a)(2) of this rule.*****************************************************************
(d) Failure of Party to Attend at Own Deposition or Serve Answers to Interrogatories or Respond to
Request for Inspection. If a party or an officer, director, or managing agent of a party or a person designated under rule 1.310(b)(6) or 1.320(a) to testify on behalf of a party fails (1) to appear before the officer who is to take the deposition after being served with a proper notice, (2) to serve answers or objections to interrogatories submitted under rule 1.340 after proper service of the interrogatories, or (3) to serve a written response to a request for inspection submitted under rule 1.350 after proper service of the request, the court in which the action is pending may take any action authorized under paragraphs (A), (B), and (C) of subdivision (b)(2) of this rule. Any motion specifying a failure under clause (2) or (3) of this subdivision shall include a certification that the movant, in good faith, has conferred or attempted to confer with the party failing to answer or respond in an effort to obtain such answer or response without court action. Instead of any order or in addition to it, the court shall require the party failing to act to pay the reasonable expenses caused by the failure, which may include attorneys’ fees . . . .