Exhibit 4.1

TRANCHE A-4 TERM LOAN

JOINDER AGREEMENT NO. 3

JOINDER AGREEMENT NO. 3, dated as of May 22, 2013 (this “Agreement”), by and among Bank of America, N.A. (the “Tranche A-4 Funding Loan Lender”), each Tranche A-4 Converting Loan Lender (as defined below), HCA INC., a Delaware corporation (the “Parent Borrower”) and BANK OF AMERICA, N. A., as Administrative Agent and as Collateral Agent.

RECITALS:

WHEREAS, reference is hereby made to the Amended and Restated Credit Agreement, dated as of May 4, 2011 (as amended, restated, supplemented or otherwise modified from time to time, the “Credit Agreement”), among the Parent Borrower, HCA UK Capital Limited (the “European Subsidiary Borrower” and, collectively with the Parent Borrower, the “Borrowers”), the Lenders party thereto, Bank of America, N. A., as Administrative Agent, Swingline Lender and Letter of Credit Issuer and the other parties named therein (capitalized terms used but not defined herein having the meaning provided in the Credit Agreement);

WHEREAS, subject to the terms and conditions of the Credit Agreement, the Borrowers may establish New Term Loan Commitments by, among other things, entering into one or more Joinder Agreements with New Term Loan Lenders;

WHEREAS, the Parent Borrower desires to establish a series of New Term Loans pursuant to this Agreement which shall be titled the “Tranche A-4 Term Loans;”

WHEREAS, the Tranche A-4 Term Loans constitute Ratio First Lien Indebtedness under the Credit Agreement; and

WHEREAS, Merrill Lynch, Pierce, Fenner & Smith Incorporated, J.P. Morgan Securities LLC, Citigroup Global Markets Inc., Deutsche Bank Securities Inc., Wells Fargo Securities LLC and Barclays Bank PLC are acting as joint lead arrangers and joint bookrunners for the Tranche A-4 Term Loans.

NOW, THEREFORE, in consideration of the premises and agreements, provisions and covenants herein contained, the parties hereto agree as follows:

The Tranche A-4 Funding Loan Lender hereby agrees to commit to provide its New Term Loan Commitment with respect to the Tranche A-4 Term Loans (its “Tranche A-4 Term Loan Commitment”), as set forth on Schedule A annexed hereto, on the terms and subject to the conditions set forth below. Each Tranche A-3 Term Loan Lender that has executed a counterpart of this Agreement in its capacity as such (each a “Tranche A-4 Converting Loan Lender” and together with the Tranche A-4 Funding Loan Lender, the “Tranche A-4 Loan Lenders”), hereby agrees to have the entire aggregate principal amount of its Tranche A-3 Term Loans (as to such Tranche A-4 Converting Loan Lender, its “Converted Tranche A-3 Term Loans”) converted to Tranche A-4 Term Loans, on the terms and subject to the conditions set forth below.

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Each Tranche A-4 Loan Lender (i) confirms that it has received a copy of the Credit Agreement and the other Credit Documents and the exhibits thereto, together with copies of the financial statements referred to therein and such other documents and information as it has deemed appropriate to make its own credit analysis and decision to enter into this Agreement; (ii) agrees that it will, independently and without reliance upon the Administrative Agent or any other Tranche A-4 Loan Lender or any other Lender or Agent and based on such documents and information as it shall deem appropriate at the time, continue to make its own credit decisions in taking or not taking action under the Credit Agreement; (iii) appoints and authorizes the Administrative Agent to take such action as agent on its behalf and to exercise such powers under the Credit Agreement and the other Credit Documents as are delegated to the Administrative Agent by the terms thereof, together with such powers as are reasonably incidental thereto; and (iv) agrees that it will perform in accordance with their terms all of the obligations which by the terms of the Credit Agreement are required to be performed by it as a Tranche A-4 Loan Lender.

Each Tranche A-4 Loan Lender hereby agrees to make its respective Commitment on the following terms and conditions:

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Notwithstanding the foregoing, the Parent Borrower shall repay all outstanding Tranche A-4 Term Loans on February 2, 2016 (or, if such day is not a Business Day, the next preceding Business Day) (the “Tranche A-4 Term Loan Maturity Date”).

For purposes of the foregoing:

“Repricing Transaction” shall mean the repayment, refinancing or replacement of all or a portion of the Tranche A-4 Term Loans with proceeds from the incurrence by any Credit Party of any long-term bank debt financing incurred for the primary purpose of repaying, refinancing, or replacing the Tranche A-4 Term Loans having an effective interest cost or weighted average yield (excluding any arrangement or commitment fees in connection therewith) that is less than the effective interest rate for or weighted average yield of the Tranche A-4 Term Loans, including, without limitation, as may be effected through any amendment to this Agreement relating to the interest rate for, or weighted average yield of, the Tranche A-4 Term Loans; provided that such prepayment premium shall not be payable if the prepayment or refinancing is made in connection with a Change of Control.

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Loan Lender agrees to make to the Parent Borrower a Tranche A-4 Term Loan in an aggregate principal amount equal to its Tranche A-4 Term Loan Commitment and (ii) each Converted Tranche A-3 Term Loan of each Tranche A-4 Converting Loan Lender shall be converted into a Tranche A-4 Term Loan of such Lender effective as of the Tranche A-4 Effective Date in a principal amount equal to the principal amount of such Lender’s Converted Tranche A-3 Term Loan immediately prior to such conversion. The Tranche A-4 Term Loan Commitment shall be automatically and permanently reduced to $0 upon the making of the Tranche A-4 Funding Loan Lender pursuant to this Section 6.

(a) The Administrative Agent shall have received executed counterparts hereof from the Parent Borrower, the Tranche A-4 Funding Loan Lender, each Tranche A-4 Converting Loan Lender and the Administrative Agent;

(b) receipt by the Administrative Agent from the Parent Borrower of an opinion of counsel from Simpson Thacher & Bartlett LLP reasonably acceptable to the Administrative Agent covering such matters as are required pursuant to Section 2.14 of the Credit Agreement.

(c) The Administrative Agent shall have received a completed “Life-of-Loan” Federal Emergency Management Agency standard flood hazard determination with respect to each improved Mortgaged Property (together with a notice about special flood hazard area status and flood disaster assistance duly executed by the applicable Credit

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Party relating thereto) and, with respect to any Mortgaged Property on which any “building” (as defined in the Flood Insurance Laws) is located in a special flood hazard area, evidence of flood insurance as and to the extent required under Section 9.3 of the Credit Agreement; and

(d) The Administrative Agent shall have received an Officers’ Certificate of the Parent Borrower setting forth the calculations (in reasonable detail) demonstrating compliance with (i) the financial test described in Section 10.8 of the Credit Agreement and (ii) the ratio set forth in the definition of “Ratio First Lien Indebtedness” in the Credit Agreement.

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IN WITNESS WHEREOF, each of the undersigned has caused its duly authorized officer to execute and deliver this Agreement as of the date set forth above.

[Signature Page to Tranche A-4 Joinder Agreement]

[Signature Page to Tranche A-4 Joinder Agreement]

[Signature Page to Tranche A-4 Joinder Agreement]

[Signature Page to Tranche A-4 Joinder Agreement]

SCHEDULE II