<PAGE>   1
                                                                    EXHIBIT 10.2


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                WILMINGTON TRUST COMPANY, AS OWNER TRUSTEE OF THE
             HOUSEHOLD PRIVATE LABEL CREDIT CARD MASTER NOTE TRUST I

                                     Issuer

                                       and

                          HOUSEHOLD FINANCE CORPORATION

                                  Administrator




                            ADMINISTRATION AGREEMENT

                            Dated as of June 12, 2001



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<PAGE>   2
                                Table of Contents
<Table>
<Caption>
                                                                                                 Page
                                                                                                 ----
<S>          <C>                                                                                 <C>
SECTION 1.   DUTIES OF ADMINISTRATOR...............................................................2


SECTION 2.   RECORDS...............................................................................6


SECTION 3.   COMPENSATION..........................................................................6


SECTION 4.   ADDITIONAL INFORMATION TO BE FURNISHED TO ISSUER......................................6


SECTION 5.   INDEPENDENCE OF ADMINISTRATOR.........................................................6


SECTION 6.   NO JOINT VENTURE......................................................................7


SECTION 7.   OTHER ACTIVITIES OF ADMINISTRATOR.....................................................7


SECTION 8.   TERM OF AGREEMENT; RESIGNATION AND REMOVAL OF ADMINISTRATOR...........................7


SECTION 9.   ACTION UPON TERMINATION, RESIGNATION OR REMOVAL.......................................8


SECTION 10.  NOTICES...............................................................................8


SECTION 11.  AMENDMENTS............................................................................9


SECTION 12.  SUCCESSORS AND ASSIGNS...............................................................10


SECTION 13.  GOVERNING LAW........................................................................10


SECTION 14.  HEADINGS.............................................................................10


SECTION 15.  COUNTERPARTS.........................................................................10


SECTION 16.  SEVERABILITY.........................................................................11


SECTION 17.  NOT APPLICABLE TO HOUSEHOLD FINANCE CORPORATION IN OTHER CAPACITIES..................11
</Table>


                                       i
<PAGE>   3


<Table>
<Caption>
                                                                                                 Page
                                                                                                 ----
<S>          <C>                                                                                 <C>
SECTION 18.  LIMITATION OF LIABILITY OF OWNER TRUSTEE.............................................11

SECTION 19.  THIRD-PARTY BENEFICIARY..............................................................11

SECTION 20.  NONPETITION COVENANTS................................................................11

SECTION 21.  SUCCESSOR ADMINISTRATOR..............................................................11

EXHIBIT A - FORM OF POWER OF ATTORNEY
</Table>

                                       ii

<PAGE>   4


                  ADMINISTRATION AGREEMENT dated as of June 12, 2001 (the
"Administration Agreement"), between WILMINGTON TRUST COMPANY, not in its
individual capacity but solely as Owner Trustee, on behalf of the HOUSEHOLD
PRIVATE LABEL CREDIT CARD MASTER NOTE TRUST I, a common law trust organized and
existing under the laws of the State of Delaware (herein, the "Issuer"), and
HOUSEHOLD FINANCE CORPORATION, a Delaware corporation ("Household Finance
Corporation"), as administrator (herein, the "Administrator").

                                  WITNESSETH:

                  WHEREAS the Issuer was formed pursuant to a trust agreement
dated as of June 12, 2001 (the "Trust Agreement"), between HRSI Funding, Inc. II
and Wilmington Trust Company, as owner trustee (the "Owner Trustee");

                  WHEREAS the Issuer has entered into a Master Indenture, dated
as of the Closing Date (as amended, modified or supplemented from time to time
in accordance with the provisions thereof, the "Indenture"), between the Issuer
and U.S. Bank National Association, a national banking association, as indenture
trustee (the "Indenture Trustee") to provide for the issuance of its asset
backed notes (the "Notes");

                  WHEREAS the Issuer has entered into certain agreements in
connection with the issuance of the Notes and of the beneficial ownership
interest of the Issuer, including (i) a Transfer and Servicing Agreement, dated
as of the Closing Date (as amended, modified or supplemented from time to time
in accordance with the provisions thereof, the "Transfer and Servicing
Agreement"), among HRSI Funding, Inc. II, as Transferor (the "Transferor"),
Household Finance Corporation, as Servicer (in such capacity, the "Servicer"),
and the Issuer, and (ii) the Indenture (the Transfer and Servicing Agreement,
the Trust Agreement and the Indenture being hereinafter referred to collectively
as the "Related Agreements") (capitalized terms used herein and not defined
herein shall have the meanings assigned to such terms in the Transfer and
Servicing Agreement, or if not defined therein, in the Indenture);

                  WHEREAS pursuant to the Related Agreements, the Issuer and the
Owner Trustee are required to perform certain duties in connection with (a) the
Notes and the collateral therefor pledged pursuant to the Indenture (the
"Collateral") and (b) the beneficial ownership interest in the Issuer (the
holder of such interest being referred to herein as the "Owner");

                  WHEREAS the Issuer and the Owner Trustee desire to have the
Administrator perform certain of the duties of the Issuer and the Owner Trustee
referred to in the preceding clause, and to provide such additional services
consistent with the terms of this Agreement and the Related Agreements as the
Issuer and the Owner Trustee may from time to time request;

                  WHEREAS the Administrator has the capacity to provide the
services required hereby and is willing to perform such services for the Issuer
and the Owner Trustee on the terms set forth herein;


<PAGE>   5


                  NOW, THEREFORE, in consideration of the mutual covenants
contained herein, and other good and valuable consideration, the receipt and
adequacy of which are hereby acknowledged, the parties agree as follows:

                  Section 1. Duties of Administrator.

                  (a) Duties with Respect to the Related Agreements.

                  (i) The Administrator shall consult with the Owner Trustee
         regarding the duties of the Issuer and the Owner Trustee under the
         Related Agreements. The Administrator shall monitor the performance of
         the Issuer and shall advise the Owner Trustee when action is necessary
         to comply with the Issuer's or the Owner Trustee's duties under the
         Related Agreements. The Administrator shall prepare for execution by
         the Issuer or the Owner Trustee or shall cause the preparation by other
         appropriate persons of all such documents, reports, filings,
         instruments, certificates and opinions as it shall be the duty of the
         Issuer or the Owner Trustee to prepare, file or deliver pursuant to any
         Related Agreement. In furtherance of the foregoing, the Administrator
         shall take all appropriate action that it is the duty of the Issuer or
         the Owner Trustee to take pursuant to the Indenture including, without
         limitation, such of the foregoing as are required with respect to the
         following matters under the Indenture (references are to sections of
         the Indenture):

                           (1) the preparation of or obtaining of the documents
                  and instruments required for authentication of the Notes, if
                  any, and delivery of the same to the Indenture Trustee
                  (Section 2.03);

                           (2) the duty to cause the Note Register to be kept
                  and to give the Indenture Trustee notice of any appointment of
                  a new Registrar and the location, or change in location, of
                  the Note Register (Section 2.05);

                           (3) the furnishing of the Indenture Trustee, the
                  Servicer, any Noteholder or the Paying Agent with the names
                  and addresses of Noteholders after receipt of a written
                  request therefor from the Indenture Trustee, the Servicer, any
                  Noteholder or the Paying Agent, respectively (Section
                  2.09(a));

                           (4) the preparation, obtaining or filing of the
                  instruments, opinions and certificates and other documents
                  required for the release of collateral (Section 2.11);

                           (5) the duty to cause newly appointed Paying Agents,
                  if any, to deliver to the Indenture Trustee the instrument
                  specified in the Indenture regarding funds held in trust
                  (Section 3.03);

                           (6) the direction to Paying Agents to pay to the
                  Indenture Trustee all sums held in trust by such Paying Agents
                  (Section 3.03);


                                       2
<PAGE>   6

                           (7) the obtaining and preservation of the Issuer's
                  qualification to do business in each jurisdiction in which
                  such qualification is or shall be necessary to protect the
                  validity and enforceability of the Indenture, the Notes, the
                  Collateral and each other instrument and agreement (Section
                  3.04);

                           (8) the preparation of all supplements, amendments,
                  financing statements, continuation statements, if any,
                  instruments of further assurance and other instruments
                  necessary to protect the Collateral (Section 3.05);

                           (9) the obtaining of the Opinion of Counsel on the
                  Closing Date and the annual delivery of Opinions of Counsel as
                  to the Collateral, and the annual delivery of the Officers'
                  Certificate and certain other statements as to compliance with
                  the Indenture (Sections 3.06 and 3.09);

                           (10) the identification to the Indenture Trustee in
                  an Officer's Certificate of a Person with whom the Issuer has
                  contracted to perform its duties under the Indenture (Section
                  3.07(b));

                           (11) the delivery of notice to the Indenture Trustee
                  of the occurrence of any Servicer Default of which the Issuer
                  has knowledge and the action, if any, the Issuer is taking in
                  connection with such default (Section 3.07(d));

                           (12) the delivery to the Indenture Trustee, within
                  120 days after the end of each fiscal year of the Issuer of an
                  Officer's Certificate with respect to various matters relating
                  to compliance with the Indenture (Section 3.09);

                           (13) the preparation and obtaining of documents and
                  instruments required for the release of the Issuer from its
                  obligation under the Indenture (Section 3.10);

                           (14) the delivery of notice to the Indenture Trustee
                  of each Event of Default and each default by the Servicer or
                  the Transferor under the Transfer and Servicing Agreement
                  (Section 3.19);

                           (15) the monitoring of the Issuer's obligations as to
                  the satisfaction and discharge of the Indenture and the
                  preparation of an Officer's Certificate and the obtaining of
                  the Opinion of Counsel and the Independent Certificate
                  relating thereto (Section 4.01);

                           (16) the compliance with any written directive of the
                  Indenture Trustee with respect to the sale of the Collateral
                  in a commercially reasonable manner if an Event of Default
                  specified in clause (a) or (b) of Section 5.02 of the
                  Indenture shall have occurred and be continuing (Section
                  5.05);


                                       3
<PAGE>   7


                           (17) the preparation of any written instruments
                  required to confirm more fully the authority of any co-trustee
                  or separate trustee and any written instruments necessary in
                  connection with the resignation or removal of any co-trustee
                  or separate trustee (Sections 6.08 and 6.10);

                           (18) the preparation of an Issuer Request and
                  Officers' Certificate and the obtaining of an Opinion of
                  Counsel and Independent Certificates, if necessary, for the
                  release of the Collateral (Section 8.09);

                           (19) the preparation of Issuer Orders and the
                  obtaining of Opinions of Counsel with respect to the execution
                  of supplemental indentures and the mailing to the Noteholders
                  of notices with respect to such supplemental indentures
                  (Sections 10.01, 10.02 and 10.03);

                           (20) the execution of new Notes conforming to any
                  supplemental indenture (Section 10.06);

                           (21) the preparation of all Officers' Certificates,
                  Opinions of Counsel and Independent Certificates with respect
                  to any requests by the Issuer to the Indenture Trustee to take
                  any action under the Indenture (Section 12.01(a));

                           (22) the preparation and delivery of Officers'
                  Certificates and the obtaining of Independent Certificates, if
                  necessary, for the release of property from the lien of the
                  Indenture (Section 12.01(b));

                           (23) the notification of each Rating Agency of the
                  information required pursuant to Section 12.05 of the
                  Indenture (Section 12.05);

                           (24) the preparation and delivery to Noteholders and
                  the Indenture Trustee of any agreements with respect to
                  alternate payment and notice provisions (Section 12.06); and

                           (25) compliance with the administrative provisions of
                  the Transfer and Servicing Agreement.

                  (b) Additional Duties.

                  (i) In addition to the duties of the Administrator set forth
         above, the Administrator shall perform all duties and obligations of
         the Issuer under the Related Agreements and shall perform such
         calculations and shall prepare for execution by the Issuer and shall
         cause the preparation by other appropriate persons of all such
         documents, reports, filings, instruments, certificates and opinions as
         it shall be the duty of the Issuer or the Owner Trustee to prepare,
         file or deliver pursuant to the Related Agreements, and at the request
         of the Issuer shall take all appropriate action that it is the duty of
         the Issuer or the Owner Trustee to take pursuant to the Related
         Agreements. Subject to Sections 1(c)(ii) and 5 of this Agreement, and
         in accordance with the directions of the Issuer, the Administrator


                                       4
<PAGE>   8


         shall administer, perform or supervise the performance of such other
         activities in connection with the Collateral (including the Related
         Agreements) as are not covered by any of the foregoing provisions and
         as are expressly requested by the Owner Trustee and are reasonably
         within the capability of the Administrator.

                  (ii) The Administrator shall perform the duties of the
         Administrator specified in Section 9.02 of the Trust Agreement required
         to be performed in connection with the resignation or removal of the
         Owner Trustee, and any other duties expressly required to be performed
         by the Administrator under the Trust Agreement.

                  (iii) In carrying out the foregoing duties or any of its other
         obligations under this Agreement, the Administrator may enter into
         transactions with or otherwise deal with any of its Affiliates;
         provided, however, that the terms of any such transactions or dealings
         shall be in accordance with any directions received from the Issuer and
         shall be, in the Administrator's opinion, no less favorable to the
         Issuer than would be available from unaffiliated parties.

                  (iv) It is the intention of the parties hereto that the
         Administrator shall, and the Administrator hereby agrees to, prepare,
         file and deliver on behalf of the Issuer all such documents, reports,
         filings, instruments, certificates and opinions as it shall be the duty
         of the Issuer to prepare, file or deliver pursuant to the Related
         Agreements. In furtherance thereof, the Owner Trustee shall, on behalf
         of the Issuer, execute and deliver to the Administrator and its agents,
         and to each successor Administrator appointed pursuant to the terms
         hereof, one or more powers of attorney substantially in the form of
         Exhibit A hereto, appointing the Administrator the attorney-in-fact of
         the Issuer for the purpose of executing on behalf of the Issuer all
         such documents, reports, filings, instruments, certificates and
         opinions.

                  (c) Non-Ministerial Matters.

                  (i) With respect to matters that in the reasonable judgment of
         the Administrator are non-ministerial, the Administrator shall not take
         any action unless within a reasonable time before the taking of such
         action, the Administrator shall have notified the Transferor of the
         proposed action and the Transferor shall not have withheld consent or
         provided an alternative direction. For the purpose of the preceding
         sentence, "non-ministerial matters" shall include, without limitation:

                           (1) the amendment of or any supplement to the
                  Indenture;

                           (2) the initiation of any claim or lawsuit by the
                  Issuer and the compromise of any action, claim or lawsuit
                  brought by or against the Issuer (other than in connection
                  with the collection or enforcement of the Collateral);


                                       5
<PAGE>   9


                           (3) the amendment, change or modification of the
                  Related Agreements;

                           (4) the appointment of successor Registrars,
                  successor Paying Agents and successor Indenture Trustees
                  pursuant to the Indenture or the appointment of successor
                  Administrators, or the consent to the assignment by the
                  Registrar, Paying Agent or Indenture Trustee of its
                  obligations under the Indenture; and

                           (5) the removal of the Indenture Trustee.

                  (ii) Notwithstanding anything to the contrary in this
         Agreement, the Administrator shall not be obligated to, and shall not,
         (A) make any payments from its own funds to the Noteholders or the
         Owner under the Related Agreements, (B) sell the Collateral pursuant to
         Section 5.05 of the Indenture other than pursuant to a written
         directive of the Indenture Trustee or (C) take any other action that
         the Issuer directs the Administrator not to take on its behalf.

                  Section 2. Records. The Administrator shall maintain
appropriate books of account and records relating to services performed
hereunder, which books of account and records shall be accessible for inspection
by the Issuer, the Owner Trustee, the Indenture Trustee, the Servicer and the
Transferor at any time during normal business hours.

                  Section 3. Compensation. As compensation for the performance
of the Administrator's obligations under this Agreement, the Administrator shall
be entitled to the amount agreed from time to time with the Owner Trustee which
shall be payable in accordance with the applicable Indenture Supplement. The
Transferor shall be responsible for payment of the Administrator's fees (to the
extent not paid pursuant to the applicable Indenture Supplement) and shall
reimburse the Administrator for any of its liabilities and extra out-of-pocket
expenses related to its performance hereunder or under any Related Document
(including without limitation those expenses set forth in Section 1(a)(ii) of
this Agreement).

                  Section 4. Additional Information to be Furnished to Issuer.
The Administrator shall furnish to the Issuer from time to time such additional
information regarding the Collateral as the Issuer shall reasonably request.

                  Section 5. Independence of Administrator. For all purposes of
this Agreement, the Administrator shall be an independent contractor and shall
not be subject to the supervision of the Issuer or the Owner Trustee with
respect to the manner in which it accomplishes the performance of its
obligations hereunder. Unless expressly authorized by the Issuer, the
Administrator shall have no authority to act for or represent the Issuer or the
Owner Trustee in any way and shall not otherwise be deemed an agent of the
Issuer or the Owner Trustee.


                                       6
<PAGE>   10

                  Section 6. No Joint Venture. Nothing contained in this
Agreement shall (a) constitute the Administrator and either of the Issuer or the
Owner Trustee as members of any partnership, joint venture, association,
syndicate, unincorporated business or other separate entity, (b) be construed to
impose any liability as such on any of them or (c) be deemed to confer on any of
them any express, implied or apparent authority to incur any obligation or
liability on behalf of the others.

                  Section 7. Other Activities of Administrator. Nothing herein
shall prevent the Administrator or its affiliates from engaging in other
businesses or, in its sole discretion, from acting in a similar capacity as an
administrator for any other person or entity even though such person or entity
may engage in business activities similar to those of the Issuer, the Owner
Trustee or the Indenture Trustee.

                  Section 8. Term of Agreement; Resignation and Removal of
Administrator.

                  (a) This Agreement shall continue in force until the
termination of the Issuer, upon which event this Agreement shall automatically
terminate.

                  (b) Subject to Section 8(e) and (f), the Administrator may
resign its duties hereunder by providing the Issuer with at least 60 days prior
written notice.

                  (c) Subject to Section 8(e) and (f), the Issuer may remove the
Administrator without cause by providing the Administrator with at least 60 days
prior written notice.

                  (d) Subject to Section 8(e) and (f), at the sole option of the
Issuer, the Administrator may be removed immediately upon written notice of
termination from the Issuer to the Administrator if any of the following events
shall occur:

                  (i) the Administrator shall default in the performance of any
         of its duties under this Agreement and, after notice of such default,
         shall not cure such default within 30 days (or, if such default cannot
         be cured in such time, shall not give within 30 days such assurance of
         cure as shall be reasonably satisfactory to the Issuer);

                  (ii) a court having jurisdiction in the premises shall enter a
         decree or order for relief, and such decree or order shall not have
         been vacated within 60 days, in respect of the Administrator in any
         involuntary case under any applicable bankruptcy, insolvency or other
         similar law now or hereafter in effect or appoint a receiver,
         conservator, liquidator, assignee, custodian, trustee, sequestrator or
         similar official for the Administrator or any substantial part of its
         property or order the winding-up or liquidation of its affairs; or

                  (iii) the Administrator shall commence a voluntary case under
         any applicable bankruptcy, insolvency or other similar law now or
         hereafter in effect, shall consent to the entry of an order for relief
         in an involuntary case under any


                                       7
<PAGE>   11


         such law, or shall consent to the appointment of a receiver,
         conservator, liquidator, assignee, trustee, custodian, sequestrator or
         similar official for the Administrator or any substantial part of its
         property, shall consent to the taking of possession by any such
         official of any substantial part of its property, shall make any
         general assignment for the benefit of creditors, shall admit in writing
         its inability to pay its debts generally as they become due or shall
         fail generally to pay its debts as they become due.

                  The Administrator agrees that if any of the events specified
in clause (ii) or (iii) of this Section 8(d) shall occur, it shall give written
notice thereof to the Issuer and the Indenture Trustee within seven days after
the happening of such event.

                  (e) No resignation or removal of the Administrator pursuant to
this Section 8 shall be effective until (i) a successor Administrator shall have
been appointed by the Issuer and (ii) such successor Administrator shall have
agreed in writing to be bound by the terms of this Agreement in the same manner
as the Administrator is bound hereunder.

                  (f) The appointment of any successor Administrator shall be
effective only after satisfaction of the Rating Agency Condition with respect to
the proposed appointment.

                  Section 9. Action upon Termination, Resignation or Removal.
Promptly upon the effective date of termination of this Agreement pursuant to
Section 8(a) or the resignation or removal of the Administrator pursuant to
Section 8(b), (c) or (d) respectively, the Administrator shall be entitled to be
paid all fees and reimbursable expenses accruing to it to the date of such
termination, resignation or removal. The Administrator shall forthwith upon such
termination pursuant to Section 8(a) deliver to the Issuer all property and
documents of or relating to the Collateral then in the custody of the
Administrator. In the event of the resignation or removal of the Administrator
pursuant to Section 8(b), (c) or (d), respectively, the Administrator shall
cooperate with the Issuer and take all reasonable steps requested to assist the
Issuer in making an orderly transfer of the duties of the Administrator.

                  Section 10. Notices. Any notice, report or other communication
given hereunder shall be in writing and addressed as follows:

                  (a) if to the Issuer or the Owner Trustee, to

                  Household Private Label Credit Card Master Note Trust I
                  c/o Wilmington Trust Company
                  Rodney Square North
                  1100 North Market Street
                  Wilmington, DE 19890-0001
                  Telephone: 302-651-8856



                                       8
<PAGE>   12

                  (b) if to the Transferor, to

                  HRSI Funding, Inc. II
                  2700 Sanders Road
                  Prospect Heights, Illinois 60070
                  Telephone: 847-564-6223

                  (c) if to the Administrator, to

                  Household Finance Corporation
                  2700 Sanders Road
                  Prospect Heights, Illinois 60070
                  Telephone:  847-564-5000

                  (d) if to the Indenture Trustee, to

                  U.S. Bank National Association
                  111 East Wacker Drive
                  Chicago, Illinois 60601
                  Attention:  Corporate Trust Department
                  Telephone:  (312) 228-9400

or to such other address as any party shall have provided to the other parties
in writing. Any notice required to be in writing hereunder shall be deemed given
if such notice is mailed by certified mail, postage prepaid, or hand-delivered
to the address of such party as provided above, except that notices to the
Indenture Trustee are effective only upon receipt.

                  Section 11. Amendments. This Agreement may be amended from
time to time, by a written amendment duly executed and delivered by the Issuer,
the Administrator and the Transferor, with the written consent of the Owner
Trustee, without the consent of any of the Noteholders or the Owner, (i) to cure
any ambiguity, (ii) to correct or supplement any provisions herein which may be
inconsistent with any other provisions herein, (iii) to add any other provisions
with respect to matters or questions arising under this Agreement which shall
not be inconsistent with the provisions of this Agreement, (iv) to change,
modify, delete or add any other obligation of the Issuer and the Administrator;
provided, however, the Issuer and the Administrator shall have delivered to the
Indenture Trustee an Officer's Certificate, dated the date of any such action,
stating that each of the Issuer and the Administrator reasonably believes that
such action will not have an Adverse Effect, unless the Owner Trustee and the
Indenture Trustee shall consent thereto.

                  This Agreement may also be amended from time to time, by a
written amendment duly executed and delivered by the Issuer, the Administrator
and the Transferor, with the written consent of the Owner Trustee, the holders
of Notes evidencing not less than a majority in the Outstanding Amount of the
Notes and the Owner, for the purpose of adding any provisions to or changing in
any manner or eliminating any of the


                                       9
<PAGE>   13


provisions of this Agreement or modifying in any manner the rights of
Noteholders or the Owner; provided, however, that, without the consent of the
Holders of all of the Notes then outstanding, no such amendment shall (a)
increase or reduce in any manner the amount of, or accelerate or delay the
timing of, collections of payments on the Receivables or distributions that are
required to be made for the benefit of the Noteholders or (b) reduce the
aforesaid portion of the Outstanding Amount of the Notes, the Holders of which
are required to consent to any such amendment.

                  Prior to the execution of any such amendment or consent, the
Administrator shall furnish written notification of the substance of such
amendment or consent to each Rating Agency. Promptly after the execution of any
such amendment or consent, the Administrator shall furnish written notification
of the substance of such amendment or consent to the Indenture Trustee.

                  It shall not be necessary for the consent of Noteholders
pursuant to this Section 11 to approve the particular form of any proposed
amendment or consent, but it shall be sufficient if such consent shall approve
the substance thereof.

                  Section 12. Successors and Assigns. This Agreement may not be
assigned by the Administrator unless such assignment is previously consented to
in writing by the Issuer, the Transferor and the Owner Trustee and subject to
the satisfaction of the Rating Agency Condition in respect thereof. An
assignment with such consent and satisfaction, if accepted by the assignee,
shall bind the assignee hereunder in the same manner as the Administrator is
bound hereunder. Notwithstanding the foregoing, this Agreement may be assigned
by the Administrator without the consent of the Issuer, the Transferor, the
Owner Trustee or the Rating Agencies to a corporation or other organization that
is a successor (by merger, consolidation or purchase of assets) to the
Administrator, provided that such successor organization executes and delivers
to the Issuer, the Transferor and the Owner Trustee an agreement in which such
corporation or other organization agrees to be bound hereunder by the terms of
said assignment in the same manner as the Administrator is bound hereunder.
Subject to the foregoing, this Agreement shall bind any successors or assigns of
the parties hereto.

                  Section 13. GOVERNING LAW. THIS AGREEMENT SHALL BE CONSTRUED
IN ACCORDANCE WITH THE LAWS OF THE STATE OF NEW YORK, WITHOUT REFERENCE TO ITS
CONFLICT OF LAW PROVISIONS AND THE OBLIGATIONS, RIGHTS AND REMEDIES OF THE
PARTIES HEREUNDER SHALL BE DETERMINED IN ACCORDANCE WITH SUCH LAWS.

                  Section 14. Headings. The section headings hereof have been
inserted for convenience of reference only and shall not be construed to affect
the meaning, construction or effect of this Agreement.

                  Section 15. Counterparts. This Agreement may be executed in
counterparts, each of which when so executed shall together constitute but one
and the same agreement.


                                       10
<PAGE>   14


                  Section 16. Severability. Any provision of this Agreement that
is prohibited or unenforceable in any jurisdiction shall be ineffective to the
extent of such prohibition or unenforceability without invalidating the
remaining provisions hereof and any such prohibition or unenforceability in any
jurisdiction shall not invalidate or render unenforceable such provision in any
other jurisdiction.

                  Section 17. Not Applicable to Household Finance Corporation
in Other Capacities. Nothing in this Agreement shall affect any obligation
Household Finance Corporation may have in any other capacity.

                  Section 18. Limitation of Liability of Owner Trustee.
Notwithstanding anything contained herein to the contrary, this instrument has
been signed by Wilmington Trust Company not in its individual capacity but
solely in its capacity as Owner Trustee of the Issuer and in no event shall
Wilmington Trust Company in its individual capacity or any beneficial owner of
the Issuer have any liability for the representations, warranties, covenants,
agreements or other obligations of the Issuer hereunder, as to all of which
recourse shall be had solely to the assets of the Issuer. For all purposes of
this Agreement, in the performance of any duties or obligations of the Issuer
hereunder, the Owner Trustee shall be subject to, and entitled to the benefits
of, the terms and provisions of Articles IV, V, VI and VII of the Trust
Agreement.

                  Section 19. Third-Party Beneficiary. The Owner Trustee is a
third-party beneficiary to this Agreement and is entitled to the rights and
benefits hereunder and may enforce the provisions hereof as if it were a party
hereto.

                  Section 20. Nonpetition Covenants. Notwithstanding any prior
termination of this Agreement, the Administrator shall not at any time with
respect to the Issuer or the Transferor acquiesce, petition or otherwise invoke
or cause the Issuer or the Transferor to invoke the process of any court or
government authority for the purpose of commencing or sustaining a case against
the Issuer or the Transferor under any Federal or state bankruptcy, insolvency
or similar law or appointing a receiver, conservator, liquidator, assignee,
trustee, custodian, sequestrator or other similar official of the Issuer or the
Transferor or any substantial part of its property, or ordering the winding up
or liquidation of the affairs of the Issuer or the Transferor; provided,
however, that this Section 20 shall not operate to preclude any remedy described
in Article V of the Indenture.

                  Section 21. Successor Administrator. In the event of a
servicing transfer pursuant to Article V of the Transfer and Servicing
Agreement, the successor servicer under the Transfer and Servicing Agreement
shall, upon the date of such servicing transfer, become the successor
Administrator hereunder. "Administrator" shall mean initially Household Finance
Corporation and thereafter its permitted successor and assigns as provided in
Section 12 or any successor Administrator as provided in this Section 21.


                                       11
<PAGE>   15



                  IN WITNESS WHEREOF, the parties have caused this Agreement to
be duly executed and delivered as of the day and year first above written.

                                     WILMINGTON TRUST COMPANY,
                                     not in its individual capacity but solely
                                     as Owner Trustee on behalf of the
                                     HOUSEHOLD PRIVATE LABEL CREDIT
                                     CARD MASTER NOTE TRUST I



                                     By:  /s/ DONALD G. MACKELCAN
                                         --------------------------------------
                                         Name:  Donald G. Mackelcan
                                         Title: Vice President


                                     HOUSEHOLD FINANCE CORPORATION,
                                     as Administrator,




                                     By:  /s/ B. B. MOSS, JR.
                                         --------------------------------------
                                         Name:  B. B. Moss, Jr.
                                         Title: Vice President and Treasurer


ACKNOWLEDGED AND ACCEPTED:

By: HRSI Funding, Inc. II,
    Transferor




By:  /s/ S. H. SMITH
    --------------------------------------
    Name:  S. H. Smith
    Title: Vice President and Treasurer


<PAGE>   16


                                                                     EXHIBIT A
                                                    [Form of Power of Attorney]

                                POWER OF ATTORNEY

STATE OF DELAWARE     )
                      )
COUNTY OF             )

                  KNOW ALL MEN BY THESE PRESENTS, that Household Private Label
Credit Card Master Note Trust I, a Delaware common law trust ("Trust"), does
hereby make, constitute and appoint Household Finance Corporation, as
Administrator under the Administration Agreement (as defined below), and its
agents and attorneys, as Attorneys-in-Fact to execute on behalf of the Trust all
such documents, reports, filings, instruments, certificates and opinions as it
shall be the duty of the Trust to prepare, file or deliver pursuant to the
Related Agreements (as defined in the Administration Agreement), including,
without limitation, to appear for and represent the Trust in connection with the
preparation, filing and audit of federal, state and local tax returns pertaining
to the Trust, and with full power to perform any and all acts associated with
such returns and audits that the Trust could perform, including without
limitation, the right to distribute and receive confidential information, defend
and assert positions in response to audits, initiate and defend litigation, and
to execute waivers of restriction on assessments of deficiencies, consents to
the extension of any statutory or regulatory time limit, and settlements. For
the purpose of this Power of Attorney, the term "Administration Agreement" means
the Administration Agreement, dated as of June 12, 2001, between the Trust and
Household Finance Corporation, as Administrator and as such may be amended from
time to time.

                  This power of attorney is coupled with an interest and shall
survive and not be affected by the subsequent bankruptcy or dissolution of the
Trust.

                  All powers of attorney for this purpose heretofore filed or
executed by the Trust are hereby revoked.

                  EXECUTED this ____ day of __________, 2001


                                      WILMINGTON TRUST COMPANY,
                                      not in its individual capacity but solely
                                      as Owner Trustee on behalf of the
                                      HOUSEHOLD PRIVATE LABEL CREDIT
                                      CARD MASTER NOTE TRUST I




                                     By:
                                         --------------------------------------
                                         Name:
                                         Title: