Document:

<PAGE>

                                                                   Exhibit 10.1

                           FIRST AMENDMENT TO SECOND
                      AMENDED AND RESTATED LOAN AGREEMENT
                      -----------------------------------

                                 (And Waiver)

     THIS DOCUMENT is entered into as of December 28, 1999, but effective as of
September 30, 1999, between MATRIX FINANCIAL SERVICES CORPORATION, an Arizona
corporation ("Borrower"), those Lenders signing on the signature page below, and
BANK ONE, TEXAS, N.A., as Administrative Agent for Lenders (in that capacity
"Administrative Agent").

     Borrower, Lenders, and Administrative Agent have entered into the Second
Amended and Restated Loan Agreement (as renewed, extended, amended, or restated,
the "Loan Agreement") dated as of July 30, 1999, providing for loans to
Borrower.  Borrower has requested and, upon the following terms and conditions,
Administrative Agent and Determining Lenders have agreed, to certain amendments
described in Paragraph 2 below and certain waivers described in Paragraph 3
below.

     Accordingly, for adequate and sufficient consideration, Borrower,
Determining Lenders, and Administrative Agent agree as follows:

     1.   TERMS AND REFERENCES.  Unless otherwise stated in this document (A)
terms defined in the Loan Agreement have the same meanings when used in this
document and (B) all references to "Sections," "Schedules," and "Exhibits" are
to the Loan Agreement's sections, schedules, and exhibits.

     2.   AMENDMENTS.
          ----------

     (A)  Section 1.1 is amended to add the following definition in alphabetical
order with the other definitions in that section:

               Minimum Servicing Portfolio means, at any time, the sum of (a)
          the Servicing Portfolio plus (b) the total unpaid principal amount of
          Mortgage Loans serviced (under a subservicing agreement) by Borrower
          for a fee, the servicing rights to which are owned by Matrix Capital
          Bank.

     (B)  Section 9.1(b) is entirely amended as follows:

               (b)  The Companies' Adjusted-Net Worth may never be less than
          $27,000,000.

     (C)  Section 9.6 is entirely amended as follows:

               9.6  Minimum Servicing Portfolio.  (a) The Minimum Servicing
          Portfolio may never be less than $4,250,000,000, (b) the Servicing
          Portfolio may never be less than $3,000,000,000, and (c)  Agency
          servicing must represent a minimum of 65% of the total Servicing
          Portfolio.

     (D)  Item 16 on Schedule 5 is deleted as a condition precedent to any
extensions of credit under the Loan Agreement.

                                                                First Amendment
                                                                ---------------
<PAGE>

     (E)  Exhibit D-6 is entirely amended in the form of  (and all references in
the Loan Agreement to that exhibit are changed to) the attached Amended Exhibit
D-6.

     3.   WAIVER.  Upon Borrower's request, Determining Lenders waive any
          ------
Potential Default or Default that may exist solely as a result of:

     (A)  The Companies' failure to maintain the minimum Adjusted-Net Worth for
the periods ending May 31, 1999, through September 30, 1999, as required by
Section 9.1(b)(ii); and

     (B)  Borrower's failure to maintain at least $4,000,000,000 of Servicing
Portfolio for the periods ending May 31, 1999, through September 30, 1999, as
required by Section 9.6.

Except as expressly stated, this paragraph is not a waiver of existing or future
Potential Defaults or Defaults or a waiver of Administrative Agent's or any
Lender's Rights to insist upon compliance by all other relevant parties with
each Loan Document.

     4.   CONDITIONS PRECEDENT.  Notwithstanding any contrary provision, the
          --------------------
foregoing paragraphs in this document are not effective unless and until (A) the
representations and warranties in this document are true and correct and (B)
Administrative Agent receives (1) counterparts of this document executed by
Borrower, Guarantor, and Determining Lenders, and (2) a $9,999 amendment fee to
be shared equally by Lenders.

     5.   RATIFICATIONS.  To induce Administrative Agent and Lenders to enter
          -------------
into this document, Borrower (A) ratifies and confirms all provisions of the
Loan Documents as amended by this document, (B) ratifies and confirms that all
guaranties, assurances, and Liens granted, conveyed, or assigned to
Administrative Agent and Lenders under the Loan Documents (as they may have been
renewed, extended, and amended) are not released, reduced, or otherwise
adversely affected by this document and continue to guarantee, assure, and
secure full payment and performance of the present and future Obligation, and
(C) agrees to perform those acts and duly authorize, execute, acknowledge,
deliver, file, and record those additional documents, and certificates as
Administrative Agent or any Lender may request in order to create, perfect,
preserve, and protect those guaranties, assurances, and Liens.

     6.   REPRESENTATIONS.  To induce Administrative Agent and Lenders to enter
          ---------------
into this document, Borrower represents and warrants to Administrative Agent and
Lenders that as of the date of this document (A) Borrower has all requisite
authority and power to execute, deliver, and perform its obligations under this
document, which execution, delivery, and performance have been duly authorized
by all necessary corporate action, require no action by or filing with any
Tribunal, do not violate its corporate charter or bylaws, or (except where not a
Material-Adverse Event) violate any Law applicable to it or any material
agreement to which it or its assets are bound, (B) upon execution and delivery
by all parties to it, this document will constitute Borrower's legal and binding
obligation, enforceable against it in accordance with their respective terms
except as that enforceability may be limited by Debtor Laws and general
principles of equity, (C) all other representations and warranties in the Loan
Documents are true and correct in all material respects except to the extent
that (1) any of them speak to a different specific date or (2) the facts on
which any of them were based have been changed by transactions contemplated or
permitted by the Loan Agreement, and (D) no Material-Adverse Event, Default, or
Potential Default exists.

     7.   EXPENSES.  Borrower shall pay all costs, fees, and expenses paid or
          --------
incurred by Administrative Agent incident to this document, including, without
limitation, the reasonable fees and

                                       2                        First Amendment
                                                                ---------------
<PAGE>

expenses of Administrative Agent's special counsel in connection with the
negotiation, preparation, delivery, and execution of this document and any
related documents.

     8.   MISCELLANEOUS.  All references in the Loan Documents to the "Loan
Agreement" refer to the Loan Agreement as amended by this document. This
document is a "Loan Document" referred to in the Loan Agreement; therefore, the
provisions relating to Loan Documents in Sections 1 and 12 are incorporated in
this document by reference. Except as specifically amended and modified in this
document, the Loan Agreement is unchanged and continues in full force and
effect. This document may be executed in any number of counterparts with the
same effect as if all signatories had signed the same document. All counterparts
must be construed together to constitute one and the same instrument. This
document binds and inures to each of the undersigned and their respective
successors and permitted assigns, subject to Section 12.12. This document and
the other Loan Documents represent the final agreement between the parties and
may not be contradicted by evidence of prior, contemporaneous, or subsequent
oral agreements by the parties. There are no unwritten oral agreements between
the parties.

                    Remainder of page intentionally blank.
                            Signature page follows.

                                       3                        First Amendment
                                                                ---------------
<PAGE>

     EXECUTED as of the date first stated in this First Amendment to Second
Amended and Restated Loan Agreement.

MATRIX FINANCIAL SERVICES           BANK ONE, TEXAS, N.A., as Administrative
CORPORATION, as Borrower            Agent, as a Lender, and as Bank One

By   /s/ George R. Bender           By   /s/ Carol L. Whitley
     -----------------------------       --------------------------------------
     George R. Bender, President         Carol L. Whitley, Vice President

U.S. BANK NATIONAL ASSOCIATION,     RESIDENTIAL FUNDING CORPORATION,
formerly Colorado National Bank,    as a Lender
as a Lender

By   /s/ Mark A. Bagley             By   /s/ Mitchell K. Nomura
     -----------------------------       --------------------------------------
     Mark A. Bagley, Vice President      Mitchell K. Nomura, Director

                             CONSENT AND AGREEMENT
                             ---------------------

     To induce Administrative Agent and Lenders to enter into this document, the
undersigned (a) consents and agrees to this document's execution and delivery,
(b) ratifies and confirms that all guaranties, assurances, Liens, and
subordinations granted, conveyed, or assigned to Administrative Agent and
Lenders under the Loan Documents (as they may have been renewed, extended, and
amended) are not released, diminished, impaired, reduced, or otherwise adversely
affected by this document and continue to guarantee, assure, secure, and
subordinate other debt to the full payment and performance of all present and
future Obligation, (c) agrees to perform those acts and duly authorize, execute,
acknowledge, deliver, file, and record those additional guaranties, assignments,
security agreements, deeds of trust, mortgages, and other agreements, documents,
instruments, and certificates as Administrative Agent or any Lender may
reasonably deem necessary or appropriate in order to create, perfect, preserve,
and protect those guaranties, assurances, Liens, and subordinations, (d)
represents and warrants to Administrative Agent and Lenders that (i) the value
of the consideration received and to be received by the undersigned in respect
of those guaranties, assurances, Liens, and subordinations are reasonably worth
at least as much as the related liability and obligation, (ii) that liability
and obligation may reasonably be expected to directly or indirectly benefit the
undersigned, and (iii) the undersigned is -- and after giving effect to those
guaranties, assurances, Liens, subordinations, and the Loan Documents, in light
of all existing facts and circumstances (including, without limitation,
collateral for and other obligors in respect of the Obligation and various
components of it and various rights of subrogation and contribution), the
undersigned will be -- Solvent, and (e) waives notice of acceptance of this
consent and agreement, which consent and agreement binds the undersigned and its
successors and permitted assigns and inures to Administrative Agent, each
Lender, and their successors and permitted assigns.

                                            MATRIX BANCORP, INC., as Guarantor

                                            By   /s/ Guy A. Gibson
                                                 ------------------------------
                                                 Guy A. Gibson, President

                                Signature Page<PAGE>

                                                                   Exhibit 10.2

                      NINTH AMENDMENT TO CREDIT AGREEMENT
                      -----------------------------------

     THIS DOCUMENT is entered into as of June 30, 2000, between MATRIX BANCORP,
INC., a Colorado corporation formerly named Matrix Capital Corporation
("Borrower"), the Lenders described below, and U.S. Bank National Association,
as Agent for Lenders.

     Borrower, Lenders, and Agent are party to the Credit Agreement (as renewed,
extended, and amended, the "Credit Agreement") dated as of March 12, 1997,
providing for a $10,000,000 Term Loan and a Revolving Facility of up to
$10,000,000.  Borrower, Lenders, and Agent have agreed, upon the following terms
and conditions, to amend the Credit Agreement as further described herein.

1.  TERMS AND REFERENCES.  Unless otherwise stated in this document terms
    --------------------
defined in the Credit Agreement have the same meanings when used in this
document.

2.  AMENDMENT.  The definition of "Stated-Termination Date" in Section 1.1 of
    ---------
the Credit Agreement is amended to read as follows:

               "'Stated-Termination Date'  means the earlier of either (a)
                 ------------------------
          September 30, 2000, or (b) 30 days after the date on which at least
          90% of the total Commitments for the Revolving Facility have been
          funded under Section 2.2."

3.  CONDITIONS PRECEDENT.  Notwithstanding any contrary provision, the foregoing
    --------------------
paragraphs in this document are not effective unless and until (A) the
representations and warranties in this document are true and correct, and (B)
Agent receives counterparts of this document executed by Agent, Lenders,
Borrower, and each other Company named on the signature pages of this document.

4.  RATIFICATIONS.  To induce Agent and Lenders to enter into this document,
    -------------
Borrower (A) ratifies and confirms all provisions of the Loan Documents as
amended by this document, (B) ratifies and confirms that all guaranties,
assurances, and Liens granted, conveyed, or assigned to Agent and Lenders under
the Loan Documents (as they may have been renewed, extended, and amended) are
not released, reduced, or otherwise adversely affected by this document and
continue to guarantee, assure, and secure full payment and performance of the
present and future Obligation, and (C) agrees to perform those acts and duly
authorize, execute, acknowledge, deliver, file, and record those additional
agreements, and certificates as Agent or any Lender may request in order to
create, perfect, preserve, and protect those guaranties, assurances, and Liens.

5.  REPRESENTATIONS.  To induce Agent and Lenders to enter into this document,
    ---------------
Borrower represents and warrants to Agent and Lenders that as of the date of
this document (A) each Company has all requisite authority and power to execute,
deliver, and perform its obligations under this document, which execution,
delivery, and performance have been duly authorized by all necessary corporate
action, require no action by or filing with any Tribunal, do not violate
corporate charter or bylaws or (except where not a Material-Adverse Event)
violate any Law applicable to it or any material agreement to which it or its
assets are bound, (B) upon execution and delivery by all parties to it, this
document will constitute each Company's legal and binding obligation,
enforceable against it in accordance with this document's terms except as that
enforceability may be limited by Debtor Laws and general principles of equity,
(C) all other representations and warranties in the Loan Documents are true and
correct in all material respects except to the extent that (1) any of them speak
to a different specific date or (2) the facts on which
<PAGE>

any of them were based have been changed by transactions contemplated or
permitted by the Credit Agreement, and (D) no Material-Adverse Event, Default,
or Potential Default exists.

6.  EXPENSES.  Borrower shall, subject to a contrary written agreement between
    --------
Agent and Borrower, pay all costs, fees, and expenses paid or incurred by Agent
incident to this document, including, without limitation, the reasonable fees
and expenses of Agent's counsel in connection with the negotiation, preparation,
delivery, and execution of this document and any related agreements.

7.  MISCELLANEOUS.  All references in the Loan Documents to the "Credit
    -------------
Agreement" refer to the Credit Agreement as amended by this document.  This
document is a "Loan Document" referred to in the Credit Agreement; therefore,
the provisions relating to Loan Documents in Sections 1 and 12 are incorporated
in this document by reference.  Except as specifically amended and modified in
this document, the Credit Agreement is unchanged and continues in full force and
effect.  This document may be executed in any number of counterparts with the
same effect as if all signatories had signed the same document.  All
counterparts must be construed together to constitute one and the same
instrument.  This document binds and inures to each of the undersigned and their
respective successors and permitted assigns, subject to Section 12.12.  This
document and the other Loan Documents represent the final agreement between the
parties in respect of the matters covered by the Loan Documents and may not be
contradicted by evidence of prior, contemporaneous, or subsequent oral
agreements by the parties.  There are no unwritten oral agreements between the
parties.

     EXECUTED as of the date first stated in this Sixth Amendment to Credit
Agreement.

MATRIX BANCORP, INC. (formerly Matrix    BANK ONE, TEXAS, N.A., as a Lender
Capital Corporation) as Borrower

By:       /s/ David W. Kloos             By:       /s/ Carol L. Whitley
   ----------------------------------        ---------------------------------

Title:    S.V.P.                         Title:    Vice President
      -------------------------------          -------------------------------

U.S. BANK NATIONAL ASSOCIATION,          RESIDENTIAL FUNDING CORPORATION,
as Agent and as a Lender                 as a Lender

By:       /s/ Mark A. Bagley             By:       /s/ Mitchell K. Nomura
   ----------------------------------       ----------------------------------

Title:    Vice President                 Title:    Director
      -------------------------------          -------------------------------

                                       2
<PAGE>

                             CONSENT AND AGREEMENT
                             ---------------------

     To induce Agent and Lenders to enter into this document, the undersigned
jointly and severally (a) consent and agree to this document's execution and
delivery, (b) ratify and confirm that all guaranties, assurances, Liens, and
subordinations granted, conveyed, or assigned to Agent or any Lender under the
Loan Documents (as they may have been renewed, extended, and amended) are not
released, diminished, impaired, reduced, or otherwise adversely affected by this
document and continue to guarantee, assure, secure, and subordinate other debt
to the full payment and performance of all present and future Obligation, (c)
agree to perform those acts and duly authorize, execute, acknowledge, deliver,
file, and record those additional guaranties, assignments, security agreements,
deeds of trust, mortgages, and other agreements, agreements, instruments, and
certificates as Agent or any Lender may reasonably deem necessary or appropriate
in order to create, perfect, preserve, and protect those guaranties, assurances,
Liens, and subordinations, (d) represent and warrant to Agent and Lenders that
(i) the value of the consideration received and to be received by the
undersigned in respect of those guaranties, assurances, Liens, and
subordinations are reasonably worth at least as much as the related liability
and obligation, (ii) that liability and obligation may reasonably be expected to
directly or indirectly benefit the undersigned, and (iii) each undersigned is --
and after giving effect to those guaranties, assurances, Liens, subordinations,
and the Loan Documents, in light of all existing facts and circumstances
(including, without limitation, collateral for and other obligors in respect of
the Obligation and various components of it and various rights of subrogation
and contribution), each undersigned will be -- Solvent, and (e) waive notice of
acceptance of this consent and agreement, which consent and agreement binds the
undersigned and their successors and permitted assigns and inures to Agent and
Lenders and their respective successors and permitted assigns.

MATRIX FINANCIAL SERVICES                UNITED CAPITAL MARKETS, INC.
CORPORATION

By:       /s/ George R. Bender           By:       /s/ Austin Tilghman
   ----------------------------------       ----------------------------------

Title:    President                      Title:    President
      -------------------------------          -------------------------------

MATRIX FUNDING CORPORATION               UNITED FINANCIAL, INC.

By:       /s/ David W. Kloos             By:       /s/ Carl de Rozario
   ----------------------------------       ----------------------------------

Title:    Vice President                 Title:    President
      -------------------------------          -------------------------------

UNITED SPECIAL SERVICES, INC.            VINTAGE DELAWARE HOLDINGS, INC.

By:       /s/ Linda Preston              By:       /s/ David W. Kloos
   ----------------------------------       ----------------------------------

Title:    C.E.O.                         Title:    President
      -------------------------------          -------------------------------

FIRST MATRIX INVESTMENT SERVICES CORP.   THE VINTAGE GROUP, INC.

By:       /s/ Paul E. Skretny            By:       /s/ Paul E. Skretny
   ----------------------------------       ----------------------------------

Title:    Chairman of the Board          Title:    Chief Executive Officer
      -------------------------------          -------------------------------

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