<PAGE>
 
                                                                     Exhibit 4.3

                                                                     May 6, 1996


Health Management Associates, Inc.
5811 Pelican Bay Blvd., Suite 500
Naples, FL  33963

Attn:  Robert E. Farnham

Dear Mr. Farnham:

    This letter agreement (this "Agreement") documents the parties'
understandings relative to an extension of credit by FIRST UNION NATIONAL BANK
OF FLORIDA ("Bank"), a national banking association, to HEALTH MANAGEMENT
ASSOCIATES, INC. ("Borrower), a Delaware corporation.  Bank and Borrower agree
as follows:

    DEFINITIONS.  As used in this Agreement, the capitalized terms defined
    -----------                                                           
below have the respective meanings ascribed to them:

         "ADVANCE" means an advance to Borrower of proceeds of the Loan pursuant
          -------                                                               
to this Agreement, on any given Advance Date.

         "ADVANCE DATE" means the date as of which an Advance is made.
          ------------                                                

         "BUSINESS DAY" means a weekday on which commercial banks are open for
          ------------                                                        
business in Tampa, Florida.

         "COMMITMENT EXPIRATION" means November 1, 1996, or such earlier date
          ---------------------                                              
that Borrower terminates its cash management arrangements with Bank.

         "DEFAULT" has the meaning set forth in section 8.
          -------                                         

         "DEFAULT RATE" means the highest lawful rate of interest, under Florida
          ------------                                                          
law, per annum specified in any Note to apply after a default under such Note
or, if no such rate is specified, a rate equal to the lesser of (a) two (2)
percentage points above the contract rate on the Loan otherwise in effect from
time to time or (b) the highest rate of interest allowed by law.

         "GAAP" means Generally Accepted Accounting Principles as defined by the
          ----                                                                  
Financial Accounting Standards Board or its successor as in effect at the time
any calculation is required to be made under this Agreement or any financial
statement or report is prepared pursuant to it.

         "GOVERNMENTAL AUTHORITY" means any nation or government, any state or
          ----------------------                                              
other political subdivision thereof and any entity exercising executive,
legislative, judicial, regulatory or administrative functions pertaining to
government.


                                      53
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Health Management Associates, Inc.
May 6, 1996


         "LIABILITIES" means all current and future liabilities, obligations,
          -----------                                                        
and indebtedness (including interest thereon and any renewals, extensions, or
modifications) of Borrower owing to Bank pursuant to the Loan, the Note, this
Agreement, or the Loan Documents, whether now due or to become due, and whether
now existing or later created, advanced or contracted.

         "LOAN" means the loan or loans from Bank to Borrower described in
          ----                                                            
section 2 and evidenced by the Note.

         "LOAN COMMITMENT" means the obligation of Bank to make Advances with
          ---------------                                                    
respect to the Loan pursuant to section 2 of this Agreement.

         "LOAN DOCUMENTS" mean the Note, this Agreement, and all other documents
          --------------                                                        
and agreements necessary or appropriate to document and effectuate the Loan.

         "MASTER CREDIT FACILITY" means the credit facility established by
          ----------------------                                          
Borrower pursuant to the Fourth Amended and Restated Revolving Credit Agreement
dated December 1, 1994, and any amendments, renewals, and substitutions for that
facility.

         "MAXIMUM LOAN AMOUNT" means $10,000,000 or such other amount to which
          -------------------                                                 
Bank consents in writing from time to time.

         "NOTE" means the promissory note dated the same date at this Agreement,
          ----                                                                  
executed by Borrower in favor of Bank, in the face amount of the Maximum Loan
Amount, and any renewal, modification, extension, or consolidation of the Note.

         "PERMITTED LIENS" means
          ---------------       

         (a) Liens securing the Liabilities;

         (b) Liens securing Borrower's obligations under the Master Credit
Facility;

         (c) Liens for taxes and other statutory liens, landlord's liens, and
similar liens arising by operation of law, so long as the obligations secured
thereby are not past due or are being contested as permitted herein; and

         (d) such other Liens to which Bank consents in writing from time to
time.

         "PERSON" means any natural person, corporation, unin corporated
          ------                                                        
organization, trust, joint-stock company, joint venture, association, company,
limited or general partnership, 

                                       54
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Health Management Associates, Inc.
May 6, 1996

limited liability company, any government, or any agency or political
subdivision of any government.

         "PRIME RATE" means that index rate of interest per annum announced from
          ----------                                                            
time to time by Bank (or its successor) as its "Prime Rate" or "Prime Lending
Rate" (which rate shall not necessarily be the best or lowest rate for any
particular type of loan or for loans to any particular class or category of cus
tomer).  A change in the Prime Rate will become effective from the beginning of
the day on which such change is announced by Bank.

         "REQUIREMENT OF LAW" means, as to any Person, the ar ticles of
          ------------------                                           
incorporation and bylaws or other organizational or governing documents of the
person, and any law, treaty, rule, or regulation or determination of an
arbitrator or a court or other Governmental Authority in each case applicable to
or binding on the Person or any of its property or to which the Person or any of
its property is subject.

         "RESPONSIBLE OFFICER" means a financial officer of Borrower.
          -------------------                                        

         "SUBSIDIARY" means any corporation, partnership, or other Person in
          ----------                                                        
which Borrower, directly or indirectly, owns more than fifty percent (50%) of
the stock, capital, or income interests, or other beneficial interests, or which
is effectively controlled by Borrower.

   2.    LOAN.  Subject to the terms and conditions of this Agreement, Bank
         ----                                                              
shall make available to Borrower loans for short-term working capital in a total
principal amount not to exceed the Maximum Loan Amount (the "Loan").  The Loan
is to be used by Borrower solely to facilitate day-to-day cash management needs
in conjunction with services provided by Bank.  Borrower shall execute and
deliver to Bank the Note, which will evidence the outstanding principal balance
of the Loan, as it may change from time to time, and provide for accrual and
payment of interest and repayment in accordance with the terms of this
Agreement.  Advances under the Loan will be subject to the following terms:

         (a)  Borrower may borrow, repay, and reborrow from time to time from
the Loan for a period from the date of this Agreement to the earlier of the
Commitment Expiration or the termination of the Loan Commitment pursuant to
section 8 of this Agreement.

         (b)  The outstanding balance of the Loan may increase and decrease from
time to time, and Advances thereunder may be repaid and reborrowed, but the
total of Advances outstanding at any one time under the Loan shall never exceed
the Maximum Loan Amount.

                                       55
<PAGE>
 
Health Management Associates, Inc.
May 6, 1996

Borrower immediately shall pay to Bank any such excess. Bank may, in its
discretion, make or permit to remain outstanding Advances to Borrower under the
Loan in excess of the Maximum Loan Amount, which will become part of the Loan
and the indebtedness under the Note, bear interest as provided in the Note, be
payable upon demand, and be entitled to all rights and benefits under this
Agreement and under all other Loan Documents.

         (c) Borrower shall repay on the Commitment Expiration all Advances and
accrued interest under the Loan not previously repaid.

         (d) Borrower shall make all payments of interest and principal under
the Note without setoff or counterclaim, in immediately available funds, at
Bank's offices set forth in this Agreement, and in such coin or currency of the
United States of America that at the time of payment is legal tender for the
payment of public and private debt.

         (e) Borrower may prepay the principal balance of the Loan, in whole or
in part, at any time without premium or penalty.

     3.  COMPUTATION AND PAYMENT OF INTEREST.
         ----------------------------------- 

         (a) From the date of this Agreement to and including the Commitment
Expiration, the outstanding principal balance of the Loan shall bear interest
until paid in full at a rate per annum equal to the Prime Rate minus one-quarter
of one percent (1/4%).

         (b) Borrower shall pay interest monthly on the outstanding principal
balance of the Loan, on the last day of each month beginning on the first of
such days to occur after an Advance has been made.

         (c) All interest and fees under the Note or this Agreement will be
calculated on a 365-day year for the actual number of days elapsed in an
interest period (actual/365 method).

         (d) Any payments not made as and when due (whether at stated maturity,
by acceleration, or otherwise) shall bear interest at the Default Rate from the
date due until paid, payable on demand.

     4.  CONDITIONS PRECEDENT TO INITIAL ADVANCE.  In addition to any other
         ---------------------------------------                           
requirement set forth in this Agreement, Bank will not make the initial Advance
under the Loan unless and until the following conditions have been satisfied, in
the sole opinion of Bank and its counsel:

                                       56
<PAGE>
 
Health Management Associates, Inc.
May 6, 1996

         (a) Cash Management System.  Borrower has entered into the cash
             ----------------------                                     
management system with Bank contemplated by this Agreement.

         (b) Loan Documents.  Borrower and each other party to any Loan
             --------------                                            
Documents, as applicable, have executed and delivered this Agreement and the
Note.

         (c) Supporting Documents.  Borrower has delivered to Bank the following
             --------------------                                               
documents:

         (i)  A copy of the articles of incorporation and bylaws of Borrower and
      a good standing certif icate of Borrower, certified by the appropriate
      official of the State of Delaware; and

         (ii) An incumbency certificate and certified resolutions of the board
      of directors (or other appropriate persons) of Borrower authorizing the
      execution, delivery, and performance of the Loan Documents.

         (d) Opinion Letter.  Borrower has delivered to Bank a favorable opinion
             --------------                                                     
letter of Borrower's counsel in form and substance satisfactory to Bank and its
counsel.

         (e) Fees and Expenses.  Bank has received all amounts required to be
             -----------------                                               
paid by Borrower or another Person pursuant to the commitment letter delivered
by Bank to Borrower in connection with the Loan.

         (f) Additional Matters.  All corporate and other proceedings, and all
             ------------------                                               
documents, instruments, and other legal matters in connection with the
transactions contemplated by this Agreement and the Loan Documents, must be
satisfactory in form and substance to Bank, and Bank must have received any of
the documents, legal opinions, and other opinions pertaining to any aspect or
consequence of the transaction contemplated by this Agreement that it reasonably
requests.

     5.  CONDITIONS PRECEDENT TO EACH ADVANCE.  The following conditions, in
         ------------------------------------                               
addition to any other requirement set forth in this Agreement, must have been
satisfied or performed by each Advance Date, in the sole opinion of Bank and its
counsel:

         (a) Accuracy of Representations.  All representations and warranties
             ---------------------------                                     
made by Borrower in this Agreement or otherwise in writing in connection with
this Agreement are true and correct as if made on and as of the proposed Advance
Date, and at Bank's 

                                       57
<PAGE>
 
Health Management Associates, Inc.
May 6, 1996

request, Borrower has so certified in an Advance Request.

         (b) No Default.  No Default has occurred and is continuing, and
             ----------                                                 
Borrower has so certified in the Advance Request.

     6.  REPRESENTATIONS AND WARRANTIES.  Unless otherwise specified, the
         ------------------------------                                  
following representations and warranties will be deemed made as of the date of
this Agreement and as of the Advance Date of any Advance by Bank to Borrower.
Borrower represents and warrants to Bank as follows:

         (a) Financial Condition.  The financial statements of Borrower, copies
             -------------------                                               
of which have been furnished to Bank, are complete and correct and fairly
represent the financial condition of Borrower as of that date and the results of
its operations and its cash flow for the applicable fiscal year or interim
period then ended.  As of the date of its most recent balance sheet furnished by
Borrower to Bank and referenced above (the "Balance Sheet Date"), Borrower had
no other material liabilities or obligations (including contingent, indemnity,
or suretyship obligations, liabilities for taxes, long-term leases or unusual
forward or long-term commitments) not reflected in the balance sheet or in the
notes to it.  All financial statements of Borrower previously furnished to Bank
were prepared in accordance with GAAP applied on a consistent basis.  Since the
Balance Sheet Date, there has not been any material adverse change in the
financial condition of Borrower.


         (b) Corporate Organization and Authority; Compliance with Law.
             ---------------------------------------------------------  
Borrower (i) is a corporation duly organized and validly existing in good
standing under the laws of the juris diction of its incorporation and (ii) has
all requisite power and authority, and the legal right to own its assets and to
conduct its business as now conducted and to execute, deliver, and per form this
Agreement and the other Loan Documents, and to borrow under this Agreement.
Borrower further (x) is in compliance with all Requirements of Law applicable to
it, (y) possesses all governmental franchises, licenses, and permits that are
necessary to own or lease its assets and to carry on its business as now
conducted, and (z) is qualified to transact business as a foreign corporation or
organization in any jurisdiction in which such qualification is necessary.

         (c) Authorization and Validity of Agreements.  The execution, delivery,
             ----------------------------------------                           
and performance by Borrower of the Loan Documents and Borrower's borrowings
pursuant to this Agreement: (i) have been duly authorized by all requisite
action of Borrower; (ii) will not conflict with the articles of incorporation
or

                                       58
<PAGE>
 
Health Management Associates, Inc.
May 6, 1996

bylaws of Borrower; and (iii) will not require any registration with, or
consent or approval of, or other act by any Government Authority.  This
Agreement has been, and each other Loan Document to which it is a party will be,
duly executed and delivered to Bank on behalf of Borrower.  In addition, the
Note, this Agreement, and the other Loan Documents, when executed and delivered
to Bank, will be valid and legally binding obligations of Borrower enforceable
against Borrower in accordance with their terms.

         (d) No Legal Bar.  The execution, delivery, and perfor mance by
             ------------                                               
Borrower of this Agreement and the other Loan Documents, Borrower's borrowings
pursuant to this Agreement, and use of the loan proceeds, will not violate any
Requirement of Law applicable to Borrower or constitute a breach or violation
of, a default under, or require any consent under, any of its Contractual
Obligations.

         (e) No Material Litigation.  No litigation, investiga tion, or
             ----------------------                                    
proceeding of or before any arbitrator or Governmental Authority is pending or,
to the knowledge of Borrower, threatened by or against Borrower or against any
of its respective busi nesses, properties, or revenues (i) with respect to any
of the Loan Documents or any of the transactions contemplated by them, or (ii)
which could have a material adverse effect on the assets, business, operations,
property, or condition (financial or other) of Borrower.

         (f) No Default.  No Default or event that with notice or the passage of
             ----------                                                         
time or both would constitute a Default has oc curred and is continuing.
Borrower is not in default under or with respect to the Master Credit Facility
or any material Contractual Obligations.

         (g) Full Disclosure.  All information furnished by Borrower to Bank
             ---------------                                                
concerning Borrower, its financial condition, or otherwise for the purpose of
obtaining credit for the Borrower is, or will be at the time the same is
furnished, accurate and correct in all material respects.

         COVENANTS.  From the date of this Agreement and until payment in full
         ---------                                                            
of the Liabilities and formal termination of this Agreement, Borrower shall
comply fully with the following provisions:

         (a) Investigation of Borrower.  Borrower shall: (i) give agents and
             -------------------------                                      
representatives of Bank full and unrestricted access from time to time during
normal business hours to its 

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<PAGE>
 
Health Management Associates, Inc.
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business premises, offices, properties, books, records, and information; (ii)
permit agents and representatives of Bank to make such audit and examination
thereof, and conduct such other investigation, as they consider appropriate to
determine and verify its assets, business, operation, property, or condition
(financial or other) and to consummate the transactions con templated by this
Agreement; and (iii) furnish to Bank and its agents and representatives such
additional information with respect to its business and affairs as Bank or they
reasonably request from time to time. Borrower shall bear the costs of such
audits, reports, and inspections.

         (b) Conduct of Business.  Borrower shall (i) conduct and maintain its
             -------------------                                              
present business in the ordinary course; (ii) maintain itself at all times as a
corporation organized and validly existing in good standing under the laws of
its state of incorporation; and (iii) comply in all material respects with all
Requirements of Law and Contractual Obligations applicable to it and its
business and properties.

         (c) Use of Loan Proceeds.  Borrower shall use the pro ceeds of the Loan
             --------------------                                               
only to facilitate the cash management arrangement contemplated by this
Agreement and furnish to Bank all evidence that it may reasonably require with
respect to such use.

         (d) Notices.  Borrower promptly shall notify Bank of: (i) any Default,
             -------                                                           
(ii) a default in the performance of, or compli ance with, any Requirement of
Law or Contractual Obligation of Borrower that might reasonably be expected to
have a material adverse effect on Borrower; (iii) any litigation, dispute, or
proceeding that is pending or known by Borrower's officers to be threatened
against Borrower and that might involve a claim for damages or a request for
injunctive, enforcement, or other relief that, if granted, might reasonably be
expected to have a material adverse effect on Borrower; (iv) a change in either
the name or the principal place of business of Borrower or the office where its
books and records are kept; and (v) a material adverse change in the assets,
business, operations, property, or condition (financial or other) of Borrower.
Borrower shall provide with each notice pursuant to this section a statement of
a Responsible Officer setting forth details of the occurrence referred to in the
notice and stating what action Borrower proposes to take with respect to it.

         (e) Financial Statements and Periodic Reports. Borrower shall keep true
             -----------------------------------------                          
books, records, and accounts that com pletely, accurately, and fairly reflect
all dealings and transactions relating to its assets, business, and activities
and shall record 

                                      60
<PAGE>
 
Health Management Associates, Inc.
May 6, 1996


all transactions in such manner as is necessary to permit preparation of its
financial statements in accordance with GAAP applied on a Consistent Basis.
Borrower shall furnish to Bank:

              (i)  Quarterly Reports.  As soon as available and in any event
                   -----------------
within 45 days after the end of each calendar quarter, an income statement and a
balance sheet of Borrower prepared in accordance with GAAP applied on a
Consistent Basis as of the end of such month and year-to-date, each certified by
a Responsible Officer of Borrower as being true and accurate;

              (ii) Annual Reports.  Within 90 days after the end of each fiscal
                   --------------                                              
year, an income statement and a reconciliation of surplus statement of Borrower
for such year, and a balance sheet as of the end of such year, prepared in
accordance with GAAP applied on a Consistent Basis, certified without
qualification by Borrower's independent accountants.

    The financial statements required above shall be in consoli dated and, if
required by Bank, consolidating form for Borrower and all Subsidiaries required
by GAAP to be consolidated for financial reporting purposes.  In addition to the
financial statements required herein, Bank reserves the right to require from
time to time other or additional financial or other information concerning
Borrower.

         (f) Certificates; Other Information.  Borrower shall furnish to Bank:
             -------------------------------                                  

          (i)  concurrently with the delivery of the annual financial statements
referred to in section 6(e)(ii), a certifi cate from its independent accountants
stating that after reviewing the financial statements, the accountants do not
know of any Default by Borrower under this Agreement or the other Loan
Documents;

          (ii)  concurrently with the delivery of the annual and quarterly
financial statements referred to in section 7(e), a certificate from a
Responsible Officer (x) containing computa tions confirming Borrower's
compliance with the financial covenants in the Master Credit Facility, and (y)
stating that the officer does not know of any Default by Borrower under this
Agreement or the other Loan Documents; and

          (iii)  all other information regarding the affairs of Borrower that
Bank from time to time reasonably requests.

         (g) Payment of Debt, Taxes, and Other Obligations.  Bor rower shall (i)
             ---------------------------------------------                      
pay and perform all of its indebtedness and 

                                       61
<PAGE>
 
Health Management Associates, Inc.
May 6, 1996


obligations promptly and in accordance with normal terms; and (ii) pay and
discharge or cause to be paid and discharged promptly when due and payable and
before they are in default, all taxes, assessments, and other governmental
charges or levies imposed on it or its income, profits, property, or business,
and all lawful claims for labor, material and supplies, or other goods or
services which, if unpaid, might become a lien or charge on its properties.
However, any tax, assessment, charge, levy, or claim need not be paid if its
validity is being contested in good faith by appropriate proceedings and
Borrower has made ade quate reserves for it on its books in accordance with GAAP
applied on a consistent basis, provided that the aggregate of such contested
amounts does not at any time exceed $500,000.

         (h) Limitation on Liens.  Borrower shall not create or permit to exist
             -------------------                                               
any Liens on any of its property, except Per mitted Liens.

         (i) Margin Stock.  Borrower shall not use any proceeds of the Loan to
             ------------                                                     
purchase or carry any margin stock (within the meaning of Regulation U of the
Board of Governors of the Federal Reserve System) or extend credit to others for
the purpose of purchasing or carrying any margin stock.

         (j) Further Assurances.  Borrower shall take such fur ther action,
             ------------------                                            
execute such further agreements, and provide to Bank such further assurances as
may be reasonably requested to ensure compliance with the intent of this
Agreement and the other Loan Documents.

     8.  DEFAULT.  The occurrence of one or more of the following events
         -------                                                        
constitutes a Default under this Agreement and with respect to the other Loan
Documents:

         (a)  Nonpayment.  Borrower fails to pay any principal or interest on
              ----------                                                     
the Note when the same becomes due and payable in accordance with its terms or
fails to pay any other Liabilities when the same becomes due and payable; or

         (b)  Representation False.  Any representation or warranty made by
              --------------------                                         
Borrower or any other party to any Loan Document (other than Bank) herein or
therein or in any certificate or report furnished in connection herewith or
therewith shall prove to have been untrue or incorrect in any material respect
when made; or
 
         (c)  Other Covenants.  Borrower fails to observe or perform any
              ---------------                                           
agreement, covenant, or obligation contained in this Agreement or any other Loan
Document not provided for elsewhere in 

                                       62
<PAGE>
 
Health Management Associates, Inc.
May 6, 1996


this section 8 and such default is not cured within any grace period provided in
this Agreement or such other Loan Document; or

         (d)  Other Debts.  Borrower shall be in default under the Master Credit
              -----------                                                       
Facility or any material Contractual Obliga tion; or

         (e)  Voluntary Proceedings.  Borrower shall (i) voluntarily liquidate
              ---------------------                                           
or terminate operations or apply for or consent to the appointment of, or the
taking of possession by, a receiver, custodian, trustee or liquidator of such
Person or of all or of a substantial part of its assets, (ii) admit in writing
its inability, or be generally unable, to pay its debts as the debts become due,
(iii) make a general assignment for the benefit of its creditors, (iv) commence
a voluntary case under the feder al Bankruptcy Code (as now or hereafter in
effect), (v) file a petition seeking to take advantage of any other law relating
to bankruptcy, insolvency, reorganization, winding-up, or com position or
adjustment of debts, (vi) fail to controvert in a timely and appropriate manner,
or acquiesce in writing to, any petition filed against it in an involuntary case
under the Bankruptcy Code, or (vii) take any corporate action for the purpose of
effecting any of the foregoing; or

         (f) Judgments.  Judgments in excess of $100,000 in the aggregate shall
             ---------                                                         
be rendered against Borrower and shall remain undischarged, undismissed, and
unstayed for more than 30 days (except judgments validly covered by insurance)
or there shall occur any levy upon, or attachment, garnishment or other seizure
of, any material portion of the assets of Borrower, by reason of the issuance of
any tax levy, judicial attachment or garnishment or levy of execution; or

         (g) Material Adverse Change.  Borrower suffers a material adverse
             -----------------------                                      
change in its assets, business, operation, property, or condition (financial or
other), or any material loss, theft, damage, or destruction of the assets of
Borrower, which loss is not fully insured and which could have material adverse
effect on the business, operations, property, or condition (financial or other)
of Borrower; or

    If any Default occurs, Bank may, without notice to Borrower, at its option,
terminate the Loan Commitment and withhold further Advances to Borrower, and may
declare any or all Liabilities to be immediately due and payable (if not earlier
demanded), bring suit against Borrower to collect the Liabilities, exercise any
remedy available to Bank hereunder and take any action or exercise any remedy
provided herein or in any other Loan Document or under applicable law.  No
remedy shall be exclusive of other remedies or impair the right of Bank to
exercise any other remedies.

                                       63
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Health Management Associates, Inc.
May 6, 1996

     9.  EXPENSES.  Borrower shall pay on demand (i) all of Bank's costs and
         --------                                                           
expenses in connection with the negotiation, preparation, execution, delivery,
administration of, and any amendment, supplement, or modification to, the Note,
this Agreement, and the other Loan Documents including the reasonable fees and
out-of-pocket expenses of counsel for Bank with respect thereto and all
reasonable costs and expenses incurred in enforcing or preserving Bank's rights
under the foregoing documents (including all reasonable attorney's fees and
expenses) incurred in all matters of enforcement, negotiation, interpreta tion,
and collection, before, during, and after demand, suit, proceeding, trial,
appeal, and post-judgment collection efforts, and any bankruptcy,
reorganization, or similar proceeding (including efforts to obtain relief from
any stay) if Borrower or any other Person or entity liable for the Loan becomes
involved in any bankruptcy, reorganization, or similar proceeding, (ii) any and
all stamp and other taxes and fees payable or determined to be payable in
connection with the execution, delivery, filing, and recording of the Note, this
Agreement, and the other Loan Documents, and Borrower shall save Bank harmless
from and against any and all liabilities with respect to or resulting from any
delay in paying or omission by Borrower to pay such taxes and fees.  Bank's
legal fees in connection with preparation of this Agreement will not exceed
$5,000.  The agreements in this section will survive the repayment of the
Liabilities and the termination of this Agreement.

   10.   WAIVER AND MODIFICATION; REMEDIES CUMULATIVE.  A waiver, amendment,
         --------------------------------------------                       
discharge, extension, termination, or modification of this Agreement or the
other Loan Documents will be valid and effective only if it is in writing and
signed by all the parties to the agreement.  A written waiver by the Bank of a
Default under any provision of this Agreement or the other Loan Documents will
not operate as a waiver of either any other Default or a succeeding Default
under the same provision or as a waiver of the provision itself.  No delay or
course of dealing by the Bank will operate as a waiver of any right, power, or
remedy of the Bank, except to the extent manifested in writing by the Bank and
except when this Agreement or the other Loan Documents expressly requires a
right, power, or remedy to be exercised within a specified time.

   11.   NOTICES.  Every demand, consent, notice, or approval required or
         -------                                                         
permitted to be given by a party under this Agreement or the other Loan
Documents will be valid only if it is in writing (whether or not the applicable
provision of this Agreement or the other Loan Documents state that it must be in
writing) and delivered personally or by telecopy, commercial courier, or first
class, postage prepaid, United States mail (whether or not 

                                       64
<PAGE>
 
Health Management Associates, Inc.
May 6, 1996



certified or registered and regardless of whether a return receipt is requested
or received by the sender), and addressed by the sender as follows:

    (a)  If to Borrower:
         -------------- 

         Health Management Associates, Inc.
         5811 Pelican Bay Blvd., Suite 500
         Naples, FL  33963

         Attn:  Robert E. Farnham




    (b)  If to Bank:
         ---------- 

         First Union National Bank of Florida
         100 South Ashley Drive
         Tampa, Florida  33602
         Telecopy:   (813) 276-6526
 
         Attention:  Robert E. Hastings, Jr.
 
or to such other address as Bank or Borrower may designate by notice given to
the other parties in accordance with this section. A validly given demand,
consent, notice, or approval will be effective on its receipt. The Bank and
Borrower shall promptly notify each other of any change in their respective
mailing addresses that are listed in this Agreement.

   12. GOVERNING LAW.  The validity, construction, enforcement, and
       -------------                                               
interpretation of this Agreement will be governed by the laws of the State of
Florida and the federal laws of the United States of America, excluding the laws
of those jurisdiction pertaining to the resolution of conflicts of laws with
other jurisdictions.

   13. MISCELLANEOUS.  Time is of the essence with respect to the performance or
       -------------                                                            
satisfaction by Borrower of every term, condition, covenant, agreement, and
obligation under the Loan Documents.  The Loan Documents are not assignable by
Borrower, and any purported assignment will be invalid and unenforceable against
Bank.  This Agreement is binding on the respective heirs, assignees, successors,
and personal representatives of the parties to it and inures to the benefit of
Bank's assignees, successors, and legal representatives and any subsequent
holder of the Note.  If this Agreement calls for the approval or consent of
Bank, such 

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<PAGE>
 
Health Management Associates, Inc.
May 6, 1996

approval or consent may be given or withheld in the discretion of
Bank unless otherwise specified in this Agreement. The parties may execute each
Loan Document in counterparts.  Each executed counterpart will constitute an
original document, and all of them, together, will constitute the same
agreement.

      WAIVER OF JURY TRIAL.  BORROWER AND BANK WAIVE TRIAL BY JURY IN CONNECTION
      --------------------                                                      
WITH LITIGATION ARISING IN CONNECTION WITH THIS AGREEMENT.

                          ___________________________

    If this Agreement accurately states our understandings and agreements with
you, please so signify by signing in the space provided below for your signature
in the presence of a notary public, and have the notary contemporaneously sign
this Agreement in the space provided below.

                            Sincerely yours,

                            FIRST UNION NATIONAL
                              BANK OF FLORIDA



                            By:/s/ Jeffrey E. Noble
                               -------------------------
                               Jeffrey E. Noble
                               Vice President
 

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<PAGE>
 
Health Management Associates, Inc.
May 6, 1996

                            Accepted and Approved:

                            HEALTH MANAGEMENT ASSOCIATES,
                              INC.



                            By:/s/ Stephen M. Ray
                               ---------------------------
                               Name:_Stephen M.Ray________
                            Title:Senior Vice President - Finance
                                  -------------------------------

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