<PAGE>

                                                            Exhibit 10.15
                                                            -------------

                            FIRST AMERICAN BANCORP
                     NON-QUALIFIED STOCK OPTION AGREEMENT


    This Agreement is made between First American Bancorp (the "Company") and
Dan M. David (the "Optionee").

                             W I T N E S S E T H:

  1.  GRANT OF OPTION.  The Company hereby grants to the Optionee, subject to
the terms and conditions set forth in this Agreement, the right and option (the
"Option") to purchase from the Company all or any part of an aggregate of 20,000
shares of common stock ($.01 par value) of the Company (the "Stock") at the
purchase price of $14.00 per share.  The Option shall not be treated as an
incentive stock option as defined in Section 422 of the Internal Revenue Code of
1986, as amended.

  2.  TERMS AND CONDITIONS.  It is understood and agreed that the Option
evidenced hereby is subject to the following terms and conditions:

     (a)  Expiration Date.  The Option shall expire ten (10) years after the
          ---------------
effective date hereof (the "Expiration Date").  After the Expiration Date,
the parties shall have no further rights or obligations hereunder.

     (b)  Exercise of Option.  Subject to the terms and conditions of this
          ------------------
Agreement regarding the exercisability of the Option, the Option may be
exercised in whole or in part in accordance with the following vesting schedule:
<TABLE>
<CAPTION>

                                           The Option shall be
                                         Exercisable With Respect
   On or After                         to the Following Cumulative
   This Date                                Number of Shares
  ------------                         ---------------------------
<S>                                             <C>
 March 7, 1997                                     2,000
 March 7, 1998                                     2,000
 March 7, 1999                                     2,000
 March 7, 2000                                     2,000
 March 7, 2001                                     2,000
 March 7, 2002                                     2,000
 March 7, 2003                                     2,000
 March 7, 2004                                     2,000
 March 7, 2005                                     2,000
 March 7, 2006                                     2,000

</TABLE>

                                       1
<PAGE>

  Any exercise shall be accompanied by a written notice to the Company
specifying the number of shares purchased.  Notation of any partial exercise
shall be made by the Company on Schedule 1 hereto.

            (c)  Payment of Purchase Price Upon Exercise. At the time of any
                 ---------------------------------------
exercise, the purchase price of the shares as to which the Option shall be
exercised shall be paid in full to the Company in cash.

            (d)  Termination of Employment. Except as provided in Section 2(f)
                 -------------------------
below (concerning the effect of Optionee's death), if Optionee ceases to be
employed by the Company or any of its subsidiaries as defined in Section 424(f)
or Section 424(g) of the Internal Revenue Code of 1986, as amended (the
"Subsidiaries"), the Option shall terminate immediately; provided, however, that
if Optionee's cessation of employment with the Company and its Subsidiaries is
due to his retirement with the consent of the Company or any of its
Subsidiaries, the Optionee may, at any time within three months after such
cessation of employment, exercise the Option to the extent that he was entitled
to exercise the Option on the date of cessation of employment, but in no event
shall the Option be exercisable for more than ten (10) years from the effective
date hereof. Except as otherwise provided in this Agreement, the Board of
Directors or the Committee may cancel the Option during the three month period
referred to in this paragraph, if the Optionee engages in employment or other
activities which are contrary, in the opinion of the Board or the Committee, to
the best interests of the Company or any of its Subsidiaries. The Board or the
Committee shall determine in each case whether a termination of employment shall
be considered a retirement with the consent of the Company or a Subsidiary, and,
subject to applicable law, whether a leave of absence shall constitute a
termination of employment. Any such determination of the Board or the Committee
shall be final and conclusive.

            (e)  Exercise Upon Death. If the Optionee dies while employed by the
                 -------------------
Company or any of its Subsidiaries, or within three months after having retired
with the consent of the Company or any of its Subsidiaries, and without having
fully exercised the Option, the executors or administrators, or legatees or
heirs, of his estate shall have the right to exercise the Option to the extent
that such deceased Optionee was entitled to exercise the Option on the date of
his death; provided, however, that in no event shall the Option be exercisable
more than ten (10) years from the effective date hereof.

            (f)  Non-Transferability. The Option shall not be transferable other
                 -------------------
than by will or by the laws of descent and distribution. During the lifetime of
Optionee, the Option shall be exercisable only by the Optionee or Optionee's
guardian or authorized representative.

            (g)  No Rights as Shareholder. Optionee shall have no rights as a
                 ------------------------
shareholder with respect to any shares of Stock subject to the Option prior
to the date of issuance to him of a certificate or certificates for such
shares.

                                       2
<PAGE>

            (h)  No Right to Continued Employment. The Option shall not confer
                 --------------------------------
upon Optionee any right with respect to continuance of employment with
the Company or any subsidiary or affiliate thereof, nor shall it
interfere in any way with the right of Optionee's employer to
terminate Optionee's employment at any time.

            (i)  Compliance with Laws and Regulations. The Option and the
                 ------------------------------------
obligation of the Company to sell and deliver shares hereunder shall be subject
to all applicable federal and state laws, rules and regulations and to such
approvals by any government or regulatory agency as may be required. Moreover,
the Option may not be exercised if such exercise, or the receipt of shares of
Stock pursuant thereto, would be contrary to applicable law. By accepting this
Option, the Optionee represents and agrees for himself or herself and his or her
transferees by will or the laws of descent and distribution that, unless a
registration statement under the Securities Act of 1933 is in effect as to
shares purchased upon any exercise of this Option, (i) any and all shares so
purchased shall be acquired for his or her personal account and not with a view
to or for sale in connection with any distribution, and (ii) each notice of the
exercise of any portion of this Option shall be accompanied by a representation
and warranty in writing, signed by the person entitled to exercise the same,
that the shares are being so acquired in good faith for his personal account and
not with a view to or for sale in connection with any distribution.

  3.  STOCK CERTIFICATES.  Each certificate for shares of Stock issued upon
exercise of this Option will bear an appropriate legend with respect to the
restrictions on transfer, sale or pledge of such Stock and will require, among
other things, before any transfer of shares is permitted by the Company that the
Company receive an opinion of counsel, in form and from counsel satisfactory to
the Company and its counsel, to the effect that such transfer, sale or pledge
has been registered under all applicable federal and state securities laws or
that an exemption therefrom is available with respect to such proposed transfer,
sale or pledge.

  4.  CHANGE IN STOCK.  The aggregate number of shares subject to the Option,
and the price per share shall all be proportionately adjusted for any increase
or decrease in the number of issued shares of Stock subsequent to the effective
date of this Agreement resulting from (1) a subdivision or consolidation of
shares or any other capital adjustment, (2) the payment of a stock dividend, or
(3) other increase or decrease in the shares effected without receipt of
consideration by the Company.

  5.  MERGER OF CHANGE IN CONTROL.  If there is a merger or a change in control
transaction or series of transactions, then the shares subject to the Option
which are not vested, as set forth in Section 2(b) above, shall become vested
and may be exercised; provided, however, in no event shall an Option be
exercised more than ten (10) years from the date it was granted.  For the
purposes of this Agreement, "change in control" shall mean the acquisition of
the power to direct, or cause the direction of, the management and policies of
the Company by any person or entity or any group thereof not previously
possessing such power, acting alone or in conjunction with others, whether
through the ownership of Stock, by contract or otherwise.

                                       3
<PAGE>

  6.  PAYMENT OF TAXES.  Optionee shall, no later than the date as of which the
value of any portion of the Option first becomes includable in the Optionee's
gross income for federal income tax purposes, pay to the Company, or make other
arrangements satisfactory to the Board regarding payment of, any federal, state,
local or FICA taxes of any kind required by law to be withheld with respect to
the Option.  The obligations of the Company under the Option shall be
conditioned on such payment or arrangements, and the Company, where applicable,
and its subsidiaries and affiliates shall, to the extent permitted by law, have
the right to deduct such taxes from the payment of any kind otherwise due to the
Optionee.

  7.  NOTICES.  Any notice hereunder to the Company shall be in writing and
addressed to the President of the Company, 251 Johnston Street, S.E., Decatur,
Alabama  35601, subject to the right of the Company to designate at any time
hereafter in writing some other address.

  8.  COUNTERPARTS.  This Agreement has been executed in two counterparts each
of which shall constitute one and the same instrument.

  9.  GOVERNING LAW.  This Agreement shall be governed by and construed in
accordance with the laws of the State of Alabama (without regard to applicable
Alabama principles of conflicts of laws).

  10.  EFFECTIVE DATE.  The Option is granted effective as of March 7,1997.



                                                FIRST AMERICAN BANCORP



                                                By:/s/ Jon H. Moores
                                                    -----------------
                                                       Jon H. Moores
                                                       Its:  Secretary


                                                OPTIONEE



                                               /s/ Dan M. David
                                               ----------------
                                                     Dan M. David

                                       4
<PAGE>

                                  SCHEDULE 1

                       NOTATIONS AS TO PARTIAL EXERCISE


<TABLE>
<CAPTION>
               Number of           Balance
Date of        Purchased          of Shares      Authorized      Notation
Exercise        Shares            on Option       Signature       Date
-----------   -----------         ---------      ----------      --------
<S>           <C>                 <C>            <C>             <C>



</TABLE>

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