<PAGE>
                                                                  EXHIBIT 4(f)57

                                                                  EXECUTION COPY

                                                                 (COMERICA LOGO)

                                  July 29, 2005

Credit Acceptance Corporation
Suite 3000
25505 West Twelve Mile Road
Southfield, Michigan 48034

     Re: Extension, Waiver and Amendment under Third Amended and Restated
         Credit Acceptance Corporation Credit Agreement dated as of June 9,
         2004, as amended by First Amendment dated as of December 10, 2004
         ("Credit Agreement") by and among Credit Acceptance Corporation
         ("Company"), the Lenders which are parties thereto from time to time
         (each a "Bank" and collectively, the, "Banks"), and Comerica Bank as
         Administrative Agent for the Banks (in such capacity, "Agent")

Ladies and Gentlemen:

     Reference is made to the Credit Agreement and to the Extension, Waiver and
Amendment dated April 30, 2005 ("April Waiver") and the Extension, Waiver and
Amendment dated May 31, 2005 ("May Waiver" and collectively with the April
Waiver, the "Prior Waivers"), each as issued by the Agent under the Credit
Agreement. Except as defined to the contrary herein, capitalized terms used in
this Extension, Waiver and Amendment shall have the meanings given them in the
Credit Agreement, and if not defined therein, then as defined in the May Waiver.

     You had previously indicated that, until certain accounting issues were
resolved with the Company's auditors (such issues, as outlined in the Company's
March 10, 2005 and April 11, 2005 press releases, referred to herein as the
"Accounting Issues"), the Company would be unable to complete its audited
financial statements for the fiscal year ending December 31, 2004 and to deliver
those financial statements to the Banks as required under Section 7.3(b) of the
Credit Agreement or to file the Company's Form 10-K and Form 10-Q reports ("SEC
Reports") with the federal Securities and Exchange Commission as required under
Section 7.3(f) of the Credit Agreement and under applicable law. Under the Prior
Waivers, Agent and the Banks, among other things, extended the applicable time
periods for such deliveries to July 31, 2005 and waived the defaults under the
Credit Agreement resulting from the Company's failure to file its SEC Reports,
as set forth therein.

<PAGE>

Credit Acceptance Corporation
July 28,2005
Page 2


     In the releases issued by the Company on June 24 and June 30, 2005 and in
your July 8, 2005 request letter ("July Request Letter"), you have advised that,
after discussions with the SEC's Office of the Chief Accountant, the decision
has been made to change the Company's method of accounting for its business to
that of a servicer of loans generated by automobile dealers and lender to those
dealers, rather than, an originator of consumer loans and that, as a result of
this decision, the Company will be required to restate its previously reported
financial results. You have also advised, in those releases, that the Company
has dismissed Deloitte & Touche LLP as the Company's independent registered
public accounting firm as of June 24, 2005 and that you have selected Grant
Thornton LLP as your new auditing firm.

     As noted in your July Request Letter, while you believe this to be an
aggressive timetable, you expect that completion of the Company's restatement of
previously reported financial results ("Restatement") and the audit of the
Restatement by your new auditors (the "Audited Restatement") can occur by early
December 2005. As a result, you have asked for a further extension of the
required time period for delivery of the Company's audited financial statements
and filing of the Company's required SEC Reports and a further extension of the
related waivers at least through December 15, 2005. You have indicated that such
an extension would not only allow for completion of the audited financial
statements and filing of the required SEC Reports, but would also provide time
for the Company to determine whether additional waivers of other provisions of
the Credit Agreement will be necessary as a result of the new accounting
methodology. You have also indicated, in your July Request Letter, that the
Company intends during the waiver period to cooperate fully with Agent in the
Agent's performance of a third party field audit of the Collateral consistent
with a scope of services to be determined by and reasonably satisfactory to the
Agent ("Field Audit"), with completion of the Field Audit targeted by the Agent
for September 30, 2005. Furthermore, you have asked that we confirm, under
Section 7.3(b) of the Credit Agreement, that the appointment of Grant Thornton
LLP as your new independent registered public accounting firm is satisfactory.

     The Company represents and warrants to Agent and the Banks, as a continuing
representation and warranty until the Indebtedness under the Credit Agreement
has been repaid and discharged in full and no commitment to extend any credit
thereunder remains outstanding, that except as disclosed on Schedule 1 hereto
("Scheduled Waivers") it has obtained (directly or through a Subsidiary, as
applicable) all of the waivers, extensions and/or amendments ("Other Waivers")
in respect of (i) all agreements for borrowed money, (ii) all Permitted
Securitizations and (iii) all other contractual obligations, the occurrence of a
default under which could reasonably be expected to have a Material Adverse
Effect, in each case, to address the Accounting Issues and the completion of the
Audited Restatement so as to eliminate or continue to postpone the occurrence
thereunder of any event of default or other event or consequence which could
reasonably be expected to have a Material Adverse Effect as a result of the
Audited Restatement (and in the case of the Company's existing warehouse
securitization, an extension or continuation of the postponement of the Take-Out
provision contained therein).

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Credit Acceptance Corporation
July 28, 2005
Page 3


     Based on the approval of the requisite Banks (attached to this letter), the
Agent hereby confirms the following matters:

1.   The Banks extend (i) the time for delivery of the Company's audited
     financial statements under Section 7.3(b) of the Credit Agreement and the
     time for filing of the Company's Form 10-K, under Section 7.3(f) of the
     Credit Agreement, in each case for its fiscal year ending December 31,
     2004, from July 31, 2005 (as currently required thereunder) to December 15,
     2005 and (ii) the time for filing the Company's Form 10-Q under Section
     7.3(f) of the Credit Agreement (for its fiscal quarters ending March 31,
     2005, June 30, 2005 and September 30, 2005) to December 15, 2005 (such
     required Form 10-K and 10-Q filings being referred to herein as the
     "Required SEC Filings").

2.   The Banks waive any Default or Event of Default due to the Company's
     failure to make its Required SEC Filings arising or that may arise under
     any provision of the Credit Agreement or any of the other Loan Documents
     requiring the Company to make its Required SEC Filings on a timely basis,
     such waiver to be given retroactive effect to March 31, 2005 (in the case
     of its Form 10-K) and the applicable statutorily required filing dates (in
     the case of its Form 10-Q), provided that the extensions and waivers under
     paragraphs 1 and 2 of this letter ("Extensions and Waivers") shall expire,
     unless otherwise extended by the Majority Banks, on the earlier to occur of
     (i) December 15, 2005 and (ii) the date on which the Agent, at the
     direction or with the concurrence of the Majority Banks, terminates this
     Waiver by written notice to the Company ("Waiver Expiration Date") due
     either to (w) the Company's failure to obtain a Scheduled Waiver or upon
     any of the Other Waivers ceasing to be effective, unless replaced with a
     comparable Other Waiver or (x) the Company's failure to exercise its
     reasonable best efforts to cooperate fully with the performance of the
     Field Audit or the results of the Field Audit demonstrate any fact or
     circumstance which could reasonably be expected to have a Material Adverse
     Effect, as determined by the Majority Banks (in their reasonable
     discretion); provided that, if the Company completes the Audited
     Restatement and delivers and/or files the applicable audited financial
     statements and Required SEC Filings on a basis consistent with the Audited
     Restatement prior to the Waiver Expiration Date, the Extensions and Waivers
     shall become permanent, so long as the comparable extensions and waivers in
     the Other Waivers also become permanent. The Company agrees to notify the
     Agent and Banks in writing promptly upon becoming aware that any of the
     Other Waivers has ceased to be effective and shall deliver to the Agent,
     promptly following receipt thereof, a copy of any Scheduled Waiver or any
     replacement of an Other Waiver. In the event the Extensions and Waivers
     cease to be effective with respect to any of the matters described above,
     (y) this Extension, Waiver and Amendment shall satisfy any requirement that
     written notice of such defaults be provided to the Company pursuant to the
     terms of the Credit Agreement or the other Loan Documents before any
     remedies may be exercised in respect thereof and (z) any grace periods
     applicable to such defaults pursuant to the terms of the Credit Agreement
     and other Loan Documents shall be deemed to have commenced on April 30,
     2005 (with respect to the Company's Form

<PAGE>

Credit Acceptance Corporation
July 28, 2005
Page 4


     10-K) and on the applicable filing date required under Section 7.3(f) of
     the Credit Agreement (with respect to the Company's Form 10-Q), regardless
     of this Extension, Waiver and Amendment

3.   Until the Waiver Expiration Date, and notwithstanding Sections 7.2, 13.1 or
     any other provision of the Credit Agreement, (a) the Company shall not be
     required, to the extent of the Accounting Issues, (i) to prepare its
     financial statements, projections and similar financial information on a
     basis consistent with GAAP or (ii) to make any representation or warranty
     thereunder (or under any Request for Advance or similar document or
     instrument delivered pursuant to the Credit Agreement) that such financial
     statements, projections or similar financial information has been prepared
     on a basis consistent with GAAP, and (b) any misrepresentation, Default or
     Event of Default resulting from the Company's failure prior to the date
     hereof, to the extent of the Accounting Issues, to report on a basis
     consistent with GAAP is hereby Waived. The Company agrees and acknowledges
     that it shall continue to be obligated (without limitation) to deliver the
     financial reports and other information required (without limitation) under
     Section 7.3(C) of the Credit Agreement, certified by the chief financial
     officer of the Company on the same basis (until the Waiver Expiration Date)
     as set forth in condition (a) of the Prior Waivers.

4.   The appointment of Grant Thornton LLP as the Company's independent
     registered public accounting firm is satisfactory under Section 7.3(b) of
     the Credit Agreement.

5.   The Banks agree with the Company that Section 7.3(f) of the Credit
     Agreement is amended to add the following to the end of said Section:

          "and, promptly following the completion and delivery thereof to the
          Company's auditors, the internally prepared Restatement of its prior
          financial statements, prepared on the basis of the new accounting
          methodology described in the Company's June 24 and June 30, 2O05 press
          releases and the July Request Letter delivered to the Agent in
          connection with the Extension, Waiver and Amendment under the Credit
          Agreement issued by Agent on July 29, 2005."

     This Extension, Waiver and Amendment shall become effective, according to
the terms and as of the date hereof (except where given retroactive effect
hereunder), upon satisfaction by the Company of the following conditions:

     (a)  Agent shall have received (i) counterpart originals of this Extension,
          Waiver and Amendment, in each case duly executed and delivered by the
          Company and its Subsidiaries, as applicable, and the Majority Banks,
          in form satisfactory to Agent

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Credit Acceptance Corporation
July 28, 2005
Page 5


          and (ii) duly executed copies of the Other Waivers, other than the
          Scheduled Waivers, if any, and

     (b)  Agent shall have received from a responsible senior officer of the
          Company a certification (i) that all necessary actions have been taken
          by the Company to authorize execution and delivery of this Extension,
          Waiver and Amendment, and that no consents or other authorizations of
          any third parties are required in connection therewith; and (ii) that,
          after giving effect to this Extension, Waiver and Amendment, no
          Default or Event of Default has occurred and is continuing on the
          proposed effective date of this Extension, Waiver and Amendment.

     The Company ratifies and confirms, as of the date hereof after giving
effect to the waivers and amendments contained herein, each of the
representations and warranties set forth in Sections 6.1 through 6.18,
inclusive, of the Credit Agreement and acknowledges that such representations
and warranties are and shall remain continuing representations and warranties
until the Indebtedness under the Credit Agreement has been repaid and discharged
in full and no commitment to extend any credit thereunder remains outstanding.

     This Extension, Waiver and Amendment shall be governed by Michigan law and
is limited to the specific matters described above and shall not be deemed to be
a waiver of or consent to any other matter, including without limitation any
failure to comply with any provision of the Credit Agreement or any other Loan
Document or to comply with any financial covenant or any other reporting period,
or to amend or alter in any respect the terms and conditions of the Credit
Agreement (including without limitation all conditions for Advances) or to
constitute a waiver or release by the Banks or the Agent of any right, remedy,
Default or Event of Default under the Credit Agreement or any other Loan
Documents, except as specifically set forth above. Furthermore, this Extension,
Waiver and Amendment shall not affect in any manner whatsoever any rights or
remedies of the Banks with respect to any other non-compliance by the Company or
any Guarantor with the Credit Agreement or the other Loan Documents (including,
without limitation, any non-compliance demonstrated by the Field Audit),
whether in the nature of a Default or an Event of Default, and whether now in
existence or subsequently arising.

<PAGE>

Credit Acceptance Corporation
July 28, 2005
Page 6


     By signing and returning a counterpart of this letter to the Agent, the
Company acknowledges its acceptance of the terms of this letter.

                                        Very truly yours,

                                        COMERICA BANK, as Agent and as
                                        Collateral Agent


                                        By: /s/ Harve Light
                                            ------------------------------------
                                        Its: Vice President

Acknowledged and Agreed
on the 29th day of July, 2005

CREDIT ACCEPTANCE CORPORATION


By: /s/ Douglas W. Busk
    ---------------------------------
Its: Treasurer
<PAGE>

                      REAFFIRMATION OF OTHER LOAN DOCUMENTS

     Each of the undersigned hereby acknowledges that it is a party to the
Domestic Guaranty, certain of the Collateral Documents and/or certain of the
other Loan Documents, as the case may be, (collectively, the "Other Loan
Documents") and that it has received and reviewed a copy of the foregoing
Extension, Waiver and Amendment ("July 2005 Waiver") to which this
Reaffirmation, is attached. Each of the undersigned parties hereby ratifies and
confirms such party's obligations under the Other Loan Documents to which it is
a party, and agrees that such Other Loan Documents remain in full force and
effect according to their respective terms after giving effect to the July 2005
Waiver, subject to no setoff, defense or counterclaim. Each of the undersigned
parties confirms that this Reaffirmation is not required by the terms of the
Other Loan Documents to which it is a party and need not be obtained in
connection with this or any prior or future amendments, waivers or extensions of
or under the Credit Agreement. Capitalized terms not otherwise defined herein
will have the meanings given then in the Credit Agreement,

     Dated as of July 29, 2005.

                                        AUTO FUNDING AMERICA OF NEVADA, INC.
                                        BUYERS VEHICLE PROTECTION PLAN, INC,
                                        CAC LEASING, INC.
                                        CREDIT ACCEPTANCE CORPORATION OF NEVADA,
                                        INC.
                                        CREDIT ACCEPTANCE CORPORATION OF SOUTH
                                        DAKOTA, INC
                                        VEHICLE REMARKET1NG SERVICES, INC
                                        CAC (TCI), LTD.
                                        CAC REINSURANCE, LTD.


                                        By: /s/ Douglas W. Busk
                                            ------------------------------------
                                        Its: Treasurer

               [REAFFIRMATION TO EXTENSION, WAIVER AND AMENDMENT]

<PAGE>

                         EXTENSION, WAIVER AND AMENDMENT

     The undersigned Bank, by signing below, approves the matters described in
paragraphs 1 through 5 of this letter, and authorizes the Agent to execute and
deliver the foregoing Extension, Waiver and Amendment, in the form to which this
Authorization is attached.

                                        Comerica Bank
                                        [Bank]


                                        By: /s/ Harve Light
                                            ------------------------------------
                                        Its: Vice President
                                        Date: July 29,2005

            [BANK SIGNATURE PAGE TO EXTENSION, WAIVER AND AMENDMENT]

<PAGE>

                         EXTENSION, WAIVER AND AMENDMENT

     The undersigned Bank, by signing below, approves the matters described in
paragraphs 1 through 4 of this letter, and authorizes the Agent to execute and
deliver the foregoing Extension, Waiver and Amendment, in the form to which this
Authorization is attached.


                                        /s/ Mary P Riggins
                                        ----------------------------------------
                                        Bank of America N.A.
                                        By: Mary Pat Riggins
                                        Its: Senior Vice President
                                        Date: July 27, 2005

<PAGE>

                        EXTENSION, WAIVER AND AMENDMENT

     The undersigned Bank, by signing below, approves the matters described in
paragraphs I through 4 of this letter, and authorizes the Agent to execute and
deliver the foregoing Extension, Waiver and Amendment, in the form to which this
Authorization is attached.


                                        Harris N.A.
                                        [Bank]


                                        By: /s/ Paul Rubrich
                                            ------------------------------------
                                        Its: Vice President
                                        Date: July 25th,2005

            [BANK SIGNATURE PAGE TO EXTENSION, WAIVER AND AMENDMENT]

<PAGE>

                         EXTENSION, WAIVER AND AMENDMENT

     The undersigned Bank, by signing below, approves the matters described in
paragraphs 1 through 5 of this letter, and authorizes the Agent to execute and
deliver the foregoing Extension, Waiver and Amendment, in the form to which this
Authorization is attached.

                                        FIFTH THIRD BANK


                                        By: /s/ (ILLEGIBLE)
                                            ------------------------------------
                                        Its: Vice President
                                        Date: July 29, 2005

            [BANK SIGNATURE PAGE TO EXTENSION, WAIVER AND AMENDMENT]

<PAGE>
                         EXTENSION, WAIVER AND AMENDMENT

     The undersigned Bank, by signing below, approves the matters described in
paragraphs 1 through 5 of this letter, and authorizes the Agent to execute and
deliver the foregoing Extension, Waiver and Amendment, in the form to which this
Authorization is attached.

                                        National City Bank of the Midwest
                                        [Bank]


                                        By: /s/ Michael Kell
                                            ------------------------------------
                                        Its: Vice President
                                        Date: July 29, 2005

            [BANK SIGNATURE PAGE TO EXTENSION, WAIVER AND AMENDMENT]

<PAGE>

                         EXTENSION, WAIVER AND AMENDMENT

     The undersigned Bank, by signing below, approves the matters described in
paragraphs 1 through 5 of this letter, and authorizes the Agent to execute and
deliver the foregoing Extension, Waiver and Amendment, in the form to which this
Authorization is attached.

                                        LASALLE BANK NATIONAL ASSOCIATION


                                        By: /s/ David H. Sherer
                                            ------------------------------------
                                            David H. Sherer
                                        Its: Senior Vice President
                                        Date: July 29, 2005

            [BANK SIGNATURE PAGE TO EXTENSION, WAIVER AND AMENDMENT]