<PAGE>   1
                                                                    EXHIBIT 10.4


                     BANCO SANTANDER CENTRAL HISPANO, S.A.

                                                                   April 3, 2000

MetLife, Inc.
1 Madison Avenue
New York, New York 10010

                              Standstill Agreement

Ladies and Gentlemen:

            Pursuant to a Stock Purchase Agreement, dated April 3, 2000, among
MetLife, Inc., a Delaware corporation (the "Company"), Metropolitan Life
Insurance Company, a life insurance company organized under the laws of New York
("MetLife"), and Banco Santander Central Hispano, S.A., a Spanish corporation
(together with all of its current and fixture affiliates, "Purchaser") (the
"Stock Purchase Agreement"), the Company has agreed to sell to Purchaser or its
permitted assignees, and Purchaser has agreed to purchase from the Company, the
Shares (as defined in the Stock Purchase Agreement). For purposes of this
Agreement, "affiliate" shall mean a person or entity that directly or indirectly
through one or more intermediaries, controls, is controlled by, or is under
common control with, another person or entity.

            Purchaser and the Company are entering into this Agreement to define
the future relationship between Purchaser and the Company and in consideration
of the mutual covenants contained herein.

            1. Restrictions on Transfers; Registration Rights.

            (a) Restrictions on Transfers. Purchaser agrees that, prior to the
first anniversary of the Closing (as defined in the Stock Purchase Agreement),
it will not, directly or indirectly, sell, transfer or otherwise dispose of any
interest in the Shares, provided that Purchaser may transfer Shares (i) to any
affiliate (as defined in Rule 144

<PAGE>   2

of the Securities Act of 1933, as amended (the "Securities Act")) of Purchaser
that enters into a standstill agreement with the Company containing terms and
conditions substantially equivalent to those in this Agreement, or (ii) pursuant
to any tender offer or exchange offer which is recommended by the Board of
Directors of the Company. After the first anniversary of the Closing and for the
remaining term of this Agreement, Purchaser may sell, transfer or otherwise
dispose of any interest in the Shares, provided that (x) such sale, unless it is
made in a registered public offering or pursuant to a tender or exchange offer
to the Company's stockholders, is not knowingly made to any person or "group"
(within the meaning of Section 13(d)(3) of the Securities Exchange Act of 1934,
as amended (the "1934 Act")) acquiring all of Purchaser's Shares in the
acquisition or that would, after giving effect to its acquisition of such
Shares, beneficially own or have the right to acquire more than 4.9% of the
Voting Securities (as defined below) then outstanding, unless such person or
group has entered into a standstill agreement with the Company containing terms
and conditions substantially equivalent to those in this Agreement (it being
understood that Purchaser has no duty to inquire as to the beneficial ownership
of any such person or group when Purchaser sells the Shares in a transaction on
the New York Stock Exchange or any other exchange on which the Shares are listed
at the time), and (y)(i) such sale is pursuant to an effective registration
statement under the Securities Act, (ii) such sale is made after the termination
of sale restrictions pursuant to Rule 144 of the Securities Act or any successor
to such rule or, (iii) Purchaser shall have delivered to the Company an opinion
of counsel, which opinion and counsel shall be reasonably satisfactory to the
Company, to the effect that such sale is exempt from the provisions of Section 5
of the Securities Act.

            For purposes of this Agreement, the term "Voting Securities" shall
mean securities of the Company, including the Shares, with the power to vote
with respect to the election of directors generally, including any securities
that are convertible or exchangeable for Voting Securities, it being understood
that the number of Voting Securities outstanding as of any time of determination
shall be determined as though all such securities, whether or not in the money,
had been converted or exchanged, in accordance with their terms, into or for
Voting Securities immediately prior to the time of determination.

            (b) Registration Rights.

            (i) Required Registration. (A) At any time after the first
anniversary of the Closing, Purchaser shall have the right, by written notice
(the "Registration Notice") to the Company, to require the Company to use
reasonable efforts to register (the "Required Registration") under the
Securities Act all or any portion of the Shares then owned by Purchaser (the
"Registrable Securities"), and the Company shall be


                                       2
<PAGE>   3

obligated to register such Registrable Securities. Purchaser shall not be
entitled to exercise more than one such right in any 12 month period or more
than a total of five such rights during the term of this Agreement.
Notwithstanding the foregoing, if, in addition to the Registrable Securities,
the Required Registration is to include shares to be offered by the Company for
its own account, shares of Trust Beneficiaries (as defined in the Plan of
Reorganization, dated September 28, 1999, as amended, of MetLife (the "Plan"))
having registration rights pursuant to Section 3.3(c)(v) of the Plan or shares
of others persons with registration rights, and the Board of Directors of the
Company believes, based on advice of a nationally recognized investment banking
firm selected by the Company, that including all such shares would be likely to
have an adverse effect upon the price, timing or distribution of the shares
included in the Required Registration, then only such number of shares, if any,
as the Board shall determine can be included without adversely affecting the
offering shall be included in the Required Registration, and the shares to be
included in the Required Registration will be allocated in the following
priority: (w) all shares owned by such Trust Beneficiaries shall be included
first, (x) all shares of Purchaser and Credit Suisse First Boston, a Swiss
corporation (through its Guernsey Branch), and Winterthur Life, a Swiss
corporation (together with all of their current and future affiliates, the
"Other Private Placement Purchaser") shall be included second, in proportion, as
nearly as practicable, to the total number of shares of Common Stock proposed to
be offered by each of Purchaser and the Other Private Placement Purchaser at the
time of filing of the registration statement for the registration, (y) all
shares of Common Stock of any other persons with registration rights shall be
included third, in proportion, as nearly as practicable, to the total number of
shares of Common Stock proposed to be offered by each of them at the time of the
filing of the registration statement, and (z) all shares of the Company shall be
included last. Purchaser may elect that the offering of Registrable Securities
pursuant to this Section 1(b)(i) be in the form of an underwritten public
offering, in which case Purchaser shall select the managing underwriters and any
additional investment bankers and managers to be used in connection with the
offering, provided that such managing underwriters and additional investment
bankers and managers must be reasonably satisfactory to the Company. In the
event Purchaser is not able to include all of the Shares Purchaser wishes to
include in any Required Registration due to the limitation described in the
immediately preceding sentence, Purchaser shall have the right to one additional
Required Registration with respect to such Shares subject to the limitations set
forth in this Section 1(b)(i).

            (B) Upon receipt of such Registration Notice, the Company will, as
promptly as practicable, prepare and file with the Securities and Exchange
Commission (the "SEC") and use its reasonable efforts to cause to become
effective promptly, and in any event within 90 days from its receipt of the
Registration Notice, a


                                       3
<PAGE>   4

registration statement under the Securities Act with respect to the number of
Registrable Securities specified in the Registration Notice, and will use its
reasonable efforts to cause such registration statement to remain effective for
such period of time as shall be required to complete the distribution of
Registrable Securities contemplated thereby, but not for more than 120 days from
the effective date thereof, provided that the Company shall be entitled to defer
any such filing for a period of up to 180 days from the date of Purchaser's
Registration Notice if the Company shall furnish Purchaser a certificate signed
by its Chairman, President and Chief Executive Officer, Chief Financial Officer
or Vice-Chairman stating that the filing of a registration statement at such
time would be detrimental to the Company due to the pendency of a material
acquisition or financing or for other reasonable cause.

            (C) The Company will use its reasonable efforts to cause to be filed
as soon as practicable following the first anniversary of the Closing, and in
any event within 90 days thereafter, a shelf registration statement on Form S-3
(or any successor form) providing for the sale by Purchaser of all of the
Registrable Securities and to have such shelf registration statement declared
effective by the SEC. The Company will use its reasonable efforts to keep the
shelf registration statement continuously effective until the third anniversary
of the Closing or such shorter period that will terminate when all of the
Registrable Securities covered by the shelf registration statement have been
sold pursuant to the shelf registration statement. After the shelf registration
statement has been declared effective, Purchaser will have the right to request,
subject to paragraph (A), an unlimited number of sales pursuant to prospectuses
or prospectus supplements under such shelf registration statement (such requests
will be in writing and given at least ten business days prior to the proposed
disposition and will state the number of shares of Registrable Securities to be
disposed of and the intended method of disposition of such shares by Purchaser),
provided, however, that the Company shall be entitled to defer any such sale for
a period of up to 180 days from the date of the Purchaser's written request
therefor if the Company shall furnish Purchaser a certificate signed by its
Chairman, President and Chief Executive Officer, Chief Financial Officer or
Vice-Chairman stating that an offering at such time would be detrimental to the
Company due to the pendency of a material acquisition or financing or for other
reasonable cause, and provided further that the Company will not be required to
permit sales pursuant to this paragraph (a) more than twice in each calendar
year and (b) unless Purchaser proposes to dispose of outstanding Registrable
Securities whose anticipated aggregate offering price exceeds $50,000,000.
Notwithstanding anything to the contrary herein, an underwritten public offering
by Purchaser under such Form S-3 shall be deemed to be a Required Registration
and subject to the limitations set forth in paragraph (A) on the number of such
Required Registrations per year and in total. Upon receipt of Purchaser's
written request specified above, the Company will use its reasonable efforts to
prepare and file


                                       4
<PAGE>   5

with the SEC, prior to the date that the offering by Purchaser was proposed to
be commenced, a supplement or post-effective amendment to the shelf registration
statement or the related prospectus or any document incorporated therein by
reference or file any other required document so that, as thereafter delivered
to the purchasers of the Registrable Securities, such prospectus does not
contain any untrue statement of a material fact necessary to make the statements
therein, in light of the circumstances under which they were made, not
misleading.

            (D) The Company will, if requested, prior to filing a registration
statement or prospectus or any amendment or supplement thereto, furnish to
Purchaser and each underwriter, if any, of the Registrable Securities covered by
such registration statement copies of such registration statement as proposed to
be filed, and thereafter furnish to Purchaser and underwriter, if any, such
number of copies of such registration statement, each amendment or supplement
thereto (in each case including all exhibits thereto and documents incorporated
by reference therein), the prospectus included in such registration statement
(including each preliminary prospectus) and such other documents as Purchaser or
underwriter may reasonably request in order to facilitate the disposition of the
Registrable Securities owned by Purchaser.

            (E) After the filing of the registration statement, the Company will
promptly notify Purchaser of any stop order issued or threatened by the
Commission and take all reasonable actions required to prevent the entry of such
stop order or to remove it if entered.

            (F) The Company will use its reasonable efforts to register or
qualify the Registrable Securities under such other securities or blue sky laws
of such jurisdictions in the United States as any selling purchaser reasonably
(in light of such purchaser's intended plan of distribution) requests and cause
such Registrable Securities to be registered with or approved by such other
governmental agencies or authorities as may be necessary by virtue of the
business and operations of the Company and do any and all other acts and things
reasonably requested by Purchaser to enable Purchaser to consummate the
disposition of the Registrable Securities owned by Purchaser, provided that the
Company will not be required to qualify generally to do business in any
jurisdiction where it would not otherwise be required to qualify but for this
Section 1(b)(i)(F), subject itself to taxation in any such jurisdiction or
consent to general service of process in any such jurisdiction.

            (G) The Company will promptly notify Purchaser, at any time up to
150 days after the effectiveness of the registration statement therefor, or, in
the case of an offering under a registration statement on Form S-3 pursuant to
paragraph (C), 150 days after the written notice from Purchaser requesting such
offering pursuant to


                                       5
<PAGE>   6

paragraph (C), when a prospectus relating to an offering of Registrable
Securities pursuant to this Section 1(b) is required to be delivered under the
Securities Act, of the occurrence of an event requiring the preparation of a
supplement or amendment to such prospectus so that, as thereafter delivered to
Purchaser, such prospectus will not contain an untrue statement of a material
fact or omit to state any material fact required to be stated therein or
necessary to make the statements therein not misleading and promptly make
available to Purchaser any such supplement or amendment.

            (H) The Company will enter into customary agreements, including an
underwriting agreement that includes representations and warranties, covenants
and indemnification and contribution provisions, to the extent applicable,
substantially identical to those contained in the underwriting agreements for
the Company's initial public offering, and take such other actions as are
reasonably requested by Purchaser in order to facilitate the disposition of such
Registrable Securities.

            (I) The Company will make available for inspection by any Purchaser,
any underwriter participating in any disposition pursuant to such registration
statement and any attorney, accountant or other professional retained by any
Purchaser or underwriter (collectively, the "Inspectors"), all financial and
other records, pertinent corporate documents and properties of the Company
(collectively, the "Records") as shall be reasonably necessary to enable them to
exercise their due diligence responsibility under the Securities Act, and cause
the Company's officers, directors and employees to supply all information
reasonably requested by any Inspectors in connection with such registration
statement, subject to reasonable arrangements to ensure that privileges are
maintained. Records which the Company determines, in good faith, to be
confidential and which it notifies the Inspectors are confidential shall not be
disclosed by the Inspectors unless the disclosure of such Records is necessary
to avoid or correct a misstatement or omission in such registration statement or
the release of such Records is ordered pursuant to a subpoena or other order
from a court of competent jurisdiction. Purchaser agrees that information
obtained by it as a result of such inspections shall be deemed confidential and
shall not be used by it for any reason other than such due diligence purposes
unless and until such is made generally available to the public. Purchaser
further agrees that it will, upon learning that disclosure of such Records is
sought in a court of competent jurisdiction, give notice to the Company and
allow the Company, at its expense, to undertake appropriate action to prevent
disclosure of the Records deemed confidential.

            (J) The Company will furnish to each selling Purchaser and to each
underwriter, if any, a signed counterpart, addressed to such selling Purchaser
or underwriter, of an opinion or opinions of counsel to the Company and a
comfort letter


                                        6
<PAGE>   7

or comfort letters from the Company's independent public accountants, each, to
the extent applicable, in substantially identical form as those delivered in
connection with the Company's initial public offering or otherwise in customary
form and covering such matters of the type customarily covered by opinions or
comfort letters, as the case may be, as the Purchaser or the managing
underwriter therefore reasonably requests.

            (K) The Company will otherwise use its reasonable efforts to comply
with all applicable rules and regulations of the Securities Exchange Commission,
and make available to its security holders, as soon as reasonably practicable,
an earnings statement covering a period of 12 months that begins within three
months after the effective date of the registration statement, which earnings
statement shall satisfy the provisions of Section 11(a) of the Securities Act.

            (L) The Company will use its reasonable efforts to cause all such
Registrable Securities to be listed on each securities exchange on which similar
securities issued by the Company are then listed.

            (M) The Company shall make its senior management available for any
road show recommended by the underwriters in connection with not more than one
demand registration each year, and not more than five demand registrations in
total, in each case including any registration effected pursuant to a Form S-3.

            (N) Anything in this Agreement to the contrary notwithstanding, the
Company shall not be obligated to file a registration statement pursuant to this
Section 1(b) with respect to any Voting Securities or to include among the
securities covered by a registration statement any Voting Securities requested
to be so included pursuant to this Section 1(b) unless the Purchaser shall have,
on request of the Company, promptly furnished to the Company in writing all
information (x) with respect to Purchaser, such Voting Securities owned by
Purchaser and requested to be so included and the transaction or transactions
which Purchaser contemplates and (y) which any law, rule or regulation requires
to be disclosed therein. Purchaser shall promptly furnish to the Company all
information required to be disclosed in order to correct any misstatement or
omission of a material fact contained in any registration statement or
prospectus, or any amendment or supplement thereto, or any preliminary
prospectus, based upon any information previously supplied by Purchaser to the
Company.

            (O) Purchaser agrees by acquisition of Registrable Securities, if so
required by the managing underwriter, not to sell, make any short sale of, loan,
grant any option for the purchase of, effect any public sale or distribution of
or otherwise dispose of any securities of the Company of the same class of the
Registrable


                                       7
<PAGE>   8

Securities, during the 15 days prior to and the 90 days after any underwritten
registration pursuant to this Section 1(b) has become effective (or such shorter
period as may be required by the underwriter), except as part of such
underwritten registration. Notwithstanding the foregoing sentence, Purchaser
shall be entitled during the foregoing period to sell securities in a private
sale.

            (ii) Incidental Registration Rights. In addition to the provisions
contained in Section 1(b)(i), if the Company shall at any time after the first
anniversary of the Closing seek to register under the Securities Act for sale to
the public in an underwritten offering any Voting Securities either for its own
account or for the account of any one or more securityholders (other than a
registration relating to Voting Securities issued or granted pursuant to any
employee or director stock-based plan or in connection with an acquisition by
the Company), and if the form of registration statement proposed to be used may
be used for the registration of Registrable Securities, on each such occasion as
it shall furnish Purchaser with prior written notice thereof promptly, but in
any event less than 10 business days from the initial filing date. At the
written request of Purchaser, given within 5 days after the receipt of such
notice, to register any of Purchaser's Registrable Securities, the Company will
cause such Registrable Securities, for which registration shall have been
requested, to be included in such registration statement so as to permit the
sale or other disposition by Purchaser as part of such underwritten public
offering (an "Incidental Registration"). Notwithstanding the foregoing, if, in
addition to the Registrable Securities, the Incidental Registration is to
include shares to be offered by the Company for its own account, shares of Trust
Beneficiaries having registration rights pursuant to Section 3.3(c)(v) of the
Plan or shares of others persons with registration rights, and the Board of
Directors of the Company believes, based on advice of a nationally recognized
investment banking firm selected by the Company, that including all such shares
would be likely to have an adverse effect upon the price, timing or distribution
of the shares included in the Incidental Registration, then only such number of
shares, if any, as the Board shall determine can be included without adversely
affecting the offering shall be included in the offering, and the shares to be
included in the Incidental Registration will be allocated in the following
priority: (x) all shares of the Company and such Trust Beneficiaries shall be
included first, (y) all shares of Purchaser and the Other Private Placement
Purchaser shall be included second, in proportion, as nearly as practicable, to
the total number of shares of Common Stock proposed to be offered by each of
Purchaser and the Other Private Placement Purchaser at the time of filing of the
registration statement for the registration, and (z) all shares if Common Stock
of any other persons with registration rights shall be included third, in
proportion, as nearly as practicable, to the total number of shares of Common
Stock proposed to be offered by each of them at the time of the filing of the
registration statement


                                       8
<PAGE>   9

            (iii) Purchaser Obligation to Furnish Information. It shall be a
condition precedent to the obligations of the Company to take any action
pursuant to this Section 1(b) with respect to the Registrable Securities that
Purchaser shall furnish to the Company such information regarding itself and the
intended method of disposition of the Registrable Securities as shall be
required to effect the registration of such Registrable Securities under the
Securities Act.

            (c) Expenses. All expenses incurred by the Company in complying with
Section 1(b), including any registration and filing fees, fees and expenses of
compliance with securities or blue sky laws of the United States (including
reasonable fees and disbursements of counsel in connection with blue sky
qualifications of the Registrable Securities), printing expenses, fees and
disbursements of counsel and independent public accountants for the Company,
fees of the National Association of Securities Dealers, Inc., listing or
quotation fees, internal expenses (including all salaries and expenses of its
officers and employees performing legal and accounting duties), fees of transfer
agents and registrars, and the fees and expenses of counsel and accountants for
Purchaser shall be borne by the Company. Purchaser shall be responsible for all
underwriting fees, discounts or commissions and transfer taxes, with respect to
Registrable Securities.

            (d) Rule 144. The Company will file any reports required to be filed
by it under the Securities Act and the 1934 Act and will take such further
action as Purchaser may reasonably request, all to the extent required from time
to time to enable Purchaser to sell Registrable Securities without registration
under the Securities Act within the limitation of the exemptions provided by (i)
Rule 144 under the Securities Act, as such Rule may be amended from time to
time, or (ii) any similar rule or regulation hereafter adopted by the SEC. Upon
the request of Purchaser, the Company will deliver to Purchaser a written
statement as to whether it has complied with such requirements.

            2. Standstill Provisions. Purchaser agrees that, during the term of
this Agreement, without the Company's prior written consent, Purchaser will not:

            (a) acquire, announce an intention to acquire, offer or propose to
      acquire, or agree to acquire, directly or indirectly, by purchase or
      otherwise, beneficial ownership of any Voting Securities, or direct or
      indirect rights to options to acquire (through purchase, exchange,
      conversion or otherwise) any Voting Securities, if, immediately after any
      such acquisition, Purchaser would beneficially own, in the aggregate,
      Voting Securities representing (x) more than 4.9% of the outstanding
      Voting Securities, or (y) more than 5.0% of the outstanding Voting
      Securities, provided that approval beneficially to own such percentage of
      Voting


                                       9
<PAGE>   10

      Securities is obtained from the New York Superintendent of Insurance prior
      to such increase to 5%, except in each case for any increase resulting
      from transactions in the ordinary course of the business of Purchaser as
      underwriter, broker/dealer, investment manager or investment adviser or
      from ordinary trading activities, unless such transactions were made with
      the purpose of changing or influencing the control of the Company;

            (b) seek representation on the Board of Directors of the Company or
      the removal of any Company Directors or a change in the composition or
      size of the Board;

            (c) make any statement or proposal, whether written or oral, to the
      Board of Directors of the Company, or to any director, officer or agent of
      the Company, or make any public announcement or proposal whatsoever with
      respect to a merger or other business combination, sale or transfer of
      assets, recapitalization, dividend, share repurchase, liquidation or other
      extraordinary corporate transaction with the Company or any other
      transaction which could result in a change of control, solicit or
      encourage any other person to make any such statement or proposal, or take
      any action which might require the Company to make a public announcement
      regarding the possibility of any transaction referred to in this paragraph
      (c) or similar transaction, or advise, assist or encourage any other
      persons in connection with the foregoing, except in the ordinary course of
      its investment banking activities as financial advisor;

            (d) make, or in any way participate, directly or indirectly, in any
      "solicitation" of "proxies" (as such terms are defined in Rule 14a-1 under
      the 1934 Act) to vote any Voting Securities, seek to advise, encourage or
      influence any person or entity with respect to the voting of any Voting
      Securities, initiate or propose any shareholder proposal or induce or
      attempt to induce any other person to initiate any shareholder proposal,
      or execute any written consent with respect to the Company, except in the
      ordinary course of its investment banking activities as financial advisor;

            (e) deposit any Voting Securities into a voting trust or subject any
      Voting Securities to any arrangement or agreement with respect to the
      voting of any Voting Securities other than this Agreement;

            (f) form, join or in any way participate in a "group" (within the
      meaning of Section 13(d)(3) of the 1934 Act) with respect to any Voting
      Securities, other than a group which Purchaser is a member of as of the
      date hereof;


                                       10
<PAGE>   11

            (g) otherwise act, alone or in concert with others, to seek to
      exercise any control or influence over the management, Board of Directors
      or policies of the Company;

            (h) make a public request to the Company (or its directors,
      officers, shareholders, employees or agents) to take any action in respect
      of the foregoing matters; or

            (i) disclose any intention, plan or arrangement inconsistent with
      the foregoing.

            Purchaser shall not, individually or acting in concert with the
Other Private Placement Purchaser, direct or cause the direction, or attempt to
direct or cause the direction of, the management or policies of any of the
Company, MetLife and any of their affiliates that are controlled insurers, or
otherwise exercise, or attempt to exercise, control over such companies or such
affiliates, whether directly or indirectly.

            3. Specific Performance. Each of Purchaser and the Company
acknowledges that the other party would not have an adequate remedy at law for
money damages if any of the covenants or agreements of the other party in this
Agreement were not performed in accordance with its terms and therefore agrees
that the other party shall be entitled to specific enforcement of such covenants
or agreements and to injunctive and other equitable relief in addition to any
other remedy to which it may be entitled, at law or in equity.

            4. Legend. Each of the Company and Purchaser agrees that the
certificates for the Shares shall bear the following legend thereon, which
legend shall remain until the earliest of (a) the date the securities
represented by such certificates are transferred in accordance with the
provisions of this Agreement or (b) the termination of this Agreement pursuant
to Section 9(a) or (c) or the termination of this Agreement (other than Sections
1(b), (c) and (d)) pursuant to Section 9(b), or as otherwise agreed among the
Company, MetLife and Purchaser:

            THESE SECURITIES WERE SOLD IN A PRIVATE PLACEMENT, WITHOUT
            REGISTRATION UNDER THE SECURITIES ACT OF 1933, AND MAY BE OFFERED OR
            SOLD ONLY IF REGISTERED UNDER THE SECURITIES ACT OF 1933 OR IF AN
            EXEMPTION FROM REGISTRATION IS AVAILABLE. THESE SECURITIES ARE
            SUBJECT TO THE PROVISIONS OF A STANDSTILL AGREEMENT DATED APRIL 3,
            2000, BY AND BETWEEN THE ISSUER AND BANCO SANTANDER CENTRAL HISPANO,
            S.A., AND MAY NOT


                                       11
<PAGE>   12

            BE SOLD OR TRANSFERRED EXCEPT IN ACCORDANCE THEREWITH.

            5. Entire Agreement. The Stock Purchase Agreement and this Agreement
contain the entire understandings of the parties with respect to the subject
matter of such agreements. This Agreement may not be amended or any provision
waived except by a writing signed, in the case of an amendment, by each party
hereto and, in the case of a waiver, by the party against whom the waiver is to
be effective. No failure or delay by any party in exercising any right, power or
privilege hereunder shall operate as a waiver thereof unless the other party is
materially prejudiced thereby, nor shall any single or partial exercise thereof
preclude any other or further exercise thereof or the exercise of any other
right, power or privilege. The rights and remedies herein provided shall be
cumulative and not exclusive of any rights and remedies provided by law. At any
time from and including the date of this Agreement until the second anniversary
of the IPO, Purchaser and the Company shall not amend, directly or indirectly,
any provision of this Agreement without the prior approval of the New York
Superintendent of Insurance (the "Superintendent"). At any time from and
including the second anniversary of the IPO (as defined in the Stock Purchase
Agreement) until the end of the term of this Agreement, the Company shall notify
the New York Insurance Department (the "Department") of any amendment, direct or
indirect, to any provision, and the termination, of this Agreement. This
Agreement is not assignable by either of the parties without the prior written
consent of the other, except that (i) prior to Closing this Agreement may be
assigned by a Purchaser to any subsidiary of Purchaser, substantially all of the
Capital Stock of which is directly or indirectly owned by Purchaser, that is a
Qualified Institutional Buyer (as that term is defined in Rule 144A under the
Securities Act of 1933) or an accredited investor (as such term is defined under
Regulation D of the Act), provided that such assignee enters into an assumption
agreement reasonably satisfactory to the Company, and (ii) after Closing this
Agreement may be assigned by a Purchaser to one or more of its affiliates to
whom Shares are properly transferred in accordance with this Agreement, provided
that, no assignment pursuant to clause (i) or (ii) will relieve Purchaser of its
obligations hereunder. This Agreement shall be binding upon and inure to the
benefit of the parties hereto and their respective successors and permitted
assigns and upon transferees of Voting Securities who are affiliates or
associates of Purchaser.

            6. Severability. If any terms, provision or restriction of this
Agreement is held by a court of competent jurisdiction to be invalid, void or
unenforceable, the remainder of the terms, provisions and restrictions of this
Agreement shall remain in full force and effect, unless such action would
substantially impair the benefits to either party of the remaining provisions of
this Agreement.


                                       12
<PAGE>   13

            7. Notices. Any notices and other communications required to be
given pursuant to this Agreement shall be deemed to have been duly given or made
as of the date delivered or mailed if delivered personally, mailed by registered
or certified mail (postage prepaid, return receipt requested), or delivered by
facsimile or by telex, as follows:

                If to the Company:

                        MetLife, Inc.
                        1 Madison Avenue
                        New York, New York 10010-3690
                        Attention: General Counsel
                        Telecopier: (212) 679-4523

                with copies to:

                        Debevoise & Plimpton
                        875 Third Avenue
                        New York, New York 10022
                        Attention: James C. Scoville, Esq.
                        Telecopier: (212) 909-6836

                If to Purchaser:

                        Banco Santander Central Hispano, S.A.
                        45 East 53rd Street
                        New York, NY 10022
                        Attention: Gonzalo de Las Heras
                                   Executive Vice President
                        Telecopier: (212) 350-3443

                with a copy to:

                        Davis Polk & Wardwell
                        450 Lexington Avenue
                        New York, NY 10017
                        Attention: Nicholas Kronfeld, Esq.
                        Telecopier: (212) 450-3950

            Purchaser shall notify the Company, and the Company shall notify the
Department, of (a) any transfer of the Shares prior to the first anniversary of
the


                                       13
<PAGE>   14

Closing or any transfer thereafter requiring the entering into of a standstill
agreement pursuant to clause (x) of the proviso to the second sentence of
Section 1(a) and (b) any registration pursuant to Section 1(b). The Company
shall notify the Department of any consent requested or granted pursuant to
Section 2.

            8. Effectiveness of Agreement. This Agreement shall become effective
only upon the execution and delivery of this Agreement by the parties hereto and
the occurrence of the Closing under the Stock Purchase Agreement.

            9. Termination. This Agreement shall terminate upon the occurrence
of any of the following:

            (a) the written agreement of the Company and Purchaser to terminate
      this Agreement, provided that any termination prior to the second
      anniversary of the Closing shall not be effective without the approval of
      the Superintendent;

            (b) the fifth anniversary of the date of the Closing, except for
      Sections 1(b), (c) and (d), which shall continue in effect indefinitely
      until terminated by any other provision of this Section 9; or

            (c) Purchaser shall cease to own Voting Securities other than any
      Voting Securities acquired in the ordinary course of business of Purchaser
      as underwriter, broker-dealer, investment manager or investment adviser
      (unless such transactions were made with the purpose or with the effect of
      changing or influencing the control of the Company).

            10. Expenses. Except as otherwise provided herein, all costs and
expenses incurred in connection with this Agreement shall be paid by the party
incurring such cost or expense.

            11. Governing Law, etc. This Agreement shall be governed by and
construed in accordance with the laws of the State of New York, without regard
to the conflict of law provisions thereof. This Agreement may be executed in one
or more counterparts, which together will constitute a single agreement.

            12. Jurisdiction. Except as otherwise expressly provided in this
Agreement, the parties hereto agree that any suit, action or proceeding seeking
to enforce any provision of, or based on any matter arising out of or in
connection with, this Agreement or the transactions contemplated hereby shall be
brought in the United States District Court for the Southern District of New
York or, if such court shall not have jurisdiction over such suit, any New
York State court sitting in New York City,


                                       14
<PAGE>   15

so long as such courts shall have subject matter jurisdiction over such suit,
action or proceeding, and that any cause of action arising out of this Agreement
shall be deemed to have arisen from a transaction of business in the State of
New York, and each of the parties hereby irrevocably consents only with respect
to such suits, actions or proceedings to the jurisdiction of such courts (and of
the appropriate appellate courts therefrom) in any such suit, action or
proceeding and irrevocably waives, to the fullest extent permitted by law, any
objection that it may now or hereafter have to the laying of the venue of any
such suit, action or proceeding in any such court or that any such suit, action
or proceeding which is brought in any such court has been brought in an
inconvenient forum. Without limiting the foregoing, each party agrees that
service of process on such party by hand delivery as provided in Section 7 shall
be deemed effective service of process on such party.

            13. Waiver of Jury Trial. Each of the parties hereto irrevocably
waives any and all right to trial by jury in any legal proceeding arising out of
or related to this Agreement or the transactions contemplated hereby.

            14. Captions. The captions herein are included for convenience of
reference only and shall be ignored in the construction or interpretation
hereof.


                                       15
<PAGE>   16

            If you are in agreement with the foregoing, please sign the
accompanying copy of this letter and return it to the Company, whereupon this
letter shall be a binding agreement between you and the Company.


                                     Very truly yours,

                                     PURCHASER


                                     By: /s/ Gonzalo de las Heras
                                         -------------------------------
                                         Name:
                                         Title:


Accepted and agreed as of
the date first written above:

METLIFE, INC.

BY: /s/ William J. Wheeler
    -----------------------------
    Name:
    Title: