Financial Guaranty Insurance Policy Endorsement No. 1 Effective

Exhibit 4.4

1221 Avenue of the Americas

New York, New York 10020

Telephone: (212) 478-3400

FINANCIAL GUARANTY

INSURANCE POLICY

XL Capital Assurance Inc. (“XLCA”), a New York stock insurance company, in consideration of the payment of the premium, hereby unconditionally and irrevocably guarantees to the Trustee for the benefit of the Owners of the Insured Obligations, full and complete payment by the Obligor of Scheduled Payments in respect of the Insured Obligation, subject only to the terms of this Policy (which includes the Endorsement(s) attached hereto).

XLCA will pay the Insured Amount to the Trustee upon the presentation of a Payment Notice to XLCA on the later of (a) one (1) Business Day following receipt by XLCA of a Payment Notice or (b) the Business Day on which Scheduled Payments are due for payment. XLCA shall be subrogated to the Owners’ rights to payment on the Insured Obligations to the extent of any payment by XLCA hereunder. The obligations of XLCA with respect to a Scheduled Payment will be discharged to the extent funds to pay such Scheduled Payment are deposited in the account specified in the Payment Notice, whether such funds are properly applied by the Trustee or claimed by an Owner.

In addition, in the event that any Scheduled Payment which has become due for payment and which is made to an Owner by or on behalf of the Trustee is recovered or is recoverable from the Owner pursuant to a final order of a court of competent jurisdiction in an Insolvency Proceeding that such payment constitutes an avoidable preference to such Owner within the meaning of any applicable bankruptcy law, XLCA unconditionally and irrevocably guarantees payment of the amount of such recovery (in accordance with Endorsement No. 1 hereto).

This Policy sets forth in full the undertaking of XLCA and shall not be cancelled or revoked by XLCA for any reason, including failure to receive payment of any premium due hereunder or under the Insurance Agreement, and may not be further endorsed or modified without the written consent of XLCA. The premium on this Policy is not refundable for any reason. This Policy does not insure against loss of any prepayment or other acceleration payment which at any time may become due in respect of any Insured Obligation, other than at the sole option of XLCA, nor against any risk other than Nonpayment and Avoided Payment, including any shortfalls, if any, attributable to the liability of the Obligor for taxes or withholding taxes if any, including interest and penalties in respect of such liability.

THIS POLICY IS NOT COVERED BY THE PROPERTY/CASUALTY INSURANCE SECURITY FUND SPECIFIED IN ARTICLE 76 OF THE NEW YORK INSURANCE LAW.

Any capitalized terms not defined herein shall have the meaning given such terms in the Endorsement attached hereto and forming a part hereof, or in the Insurance Agreement referenced therein. In witness whereof, XLCA has caused this Policy to be executed as of the Effective Date.

Financial Guaranty Insurance Policy Endorsement No. 1 Effective

Date February 3, 2005, Attached to and forming

part of Financial Guaranty Insurance

Policy No. CA01587A

Capitalized terms used herein and not otherwise defined herein or in the Policy shall have the meanings assigned to them in the Insurance Agreement, the Sale and Servicing Agreement or the Indenture as in effect on the date of execution of this Policy without giving effect to any subsequent amendment or modification thereto unless such amendment or modification has been approved in writing by XLCA.

As used herein the term “Business Day” means any day other than Saturday or Sunday on which commercial banking institutions in New York, New York, Minneapolis, Minnesota and the State in which the executive offices of the Servicer are located are generally open for banking business.

As used herein the term “Insolvency Proceeding” means the commencement, after the date hereof, of any bankruptcy, insolvency, readjustment of debt, reorganization, marshalling of assets and liabilities or similar proceedings by or against any Person, the commencement, after the date hereof, of any proceedings by or against any Person for the winding up or liquidation of its affairs, or the consent, after the date hereof, to the appointment of a trustee, conservator, receiver or liquidator in any bankruptcy, insolvency, readjustment of debt, reorganization, marshalling of assets and liabilities or similar proceedings of or relating to any Person.

As used herein the term “Insurance Agreement” means the Insurance Agreement, dated as of January 27, 2005, by and among XLCA, the Obligor, AmeriCredit, the Servicer, the Custodian, the Seller, the Trustee, the Trust Collateral Agent, the Collateral Agent and the Backup Servicer,

As used herein the term “Insured Amount” means, that portion of the Scheduled Payments that shall become due for payment but shall be unpaid by reason of Nonpayment.

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As used herein the term “Nonpayment” means, with respect to any Distribution Date, the failure of the Trustee to receive, in full, in accordance with the terms of the Indenture that Scheduled Payment that is due for payment with respect to such date.

As used herein the term “Owner” means the registered owner of any Insured Obligation as indicated in the registration books maintained by or on behalf of the Obligor for such purpose or, if the Insured Obligation is in bearer form, the holder of the Insured Obligation.

As used herein, the term “Person” means an individual, a partnership, a limited liability company, a joint venture, a corporation, a trust, an unincorporated organization, and a government or any department or agency thereof.

As used herein the term “Scheduled Payment” means for any Distribution Date, the excess, if any (without duplication) of (i) the Noteholders’ Interest Distributable Amount plus the Noteholders’ Parity Deficit Amount plus, if such Distribution Date is the Final Scheduled Distribution Date for any Class of Notes, the Outstanding Amount of such Class of Notes over (ii) the amount actually deposited into the Note Distribution Account on or with respect to such Distribution Date for application to the amounts described in the foregoing clause (i), in accordance with the original terms of the Insured Obligations and the Indenture when issued and without regard to any subsequent amendment or modification of the Insured Obligations or the Indenture that has not been consented to in writing by XLCA. Notwithstanding the foregoing, “Scheduled Payments” shall in no event include payments which become due on an accelerated basis as a result of (a) any default by the Obligor, (b) the occurrence of an Event of Default under the Indenture, (c) mandatory or optional redemption, in whole or in part, or (d) any other cause, unless XLCA elects, in its sole discretion, to pay such amounts in whole or in part (in which event Scheduled Payments shall include such accelerated payments as, when, and to the extent so elected by XLCA). In the event that it does not make such election, Scheduled Payments shall include payments due in accordance with the original scheduled terms without regard to any acceleration. In addition, “Scheduled Payment” shall not include, nor shall coverage be provided under the Policy in respect of, (i) any make whole, redemption or call premium payable in respect of the Insured Obligations, (ii) any amounts due in respect of the Insured Obligations attributable to any increase in interest rate, penalty or other sum payable by the Obligor by reason of any default or event of default in respect of the Insured Obligations, or by reason of any deterioration of the creditworthiness of the Obligor or (iii) any taxes, withholding or other charge imposed by any governmental authority due in connection with the payment of any Scheduled Payment to any holder of an Insured Obligation.

As used herein the term “Term of this Policy” means the period from and including the Effective Date to and including the first date on which (i) all Scheduled Payments have been paid that are required to be paid by the Obligor under the Indenture; and (ii) any period during which any Scheduled Payment could have been avoided in whole or in part as a preference payment under applicable bankruptcy, insolvency, receivership or similar law has expired; provided, however, that if any proceedings

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requisite to avoidance as a preference payment have been commenced prior to the occurrence of (i) and (ii) above, and the Owners are ultimately required to return any Avoided Payment (as defined below) as a result of such proceeding pursuant to a final and nonappealable order in resolution of any such proceeding (whether or not such order is entered before or after the occurrence of (i) and (ii) above), then the Term of the Policy shall terminate on the date on which XLCA has made all payments required to be made under the terms of this Policy in respect of all such Avoided Payments.

To make a claim under the Policy, the Trustee shall deliver to XLCA a Payment Notice in the form of Exhibit A hereto (a “Payment Notice”), appropriately completed and executed by the Trustee. A Payment Notice under this Policy may be presented to XLCA by (i) delivery of the original Payment Notice to XLCA at its address set forth below, or (ii) facsimile transmission of the original Payment Notice to XLCA at its facsimile number set forth below. If presentation is made by facsimile transmission, the Trustee shall (x) simultaneously confirm transmission by telephone to XLCA at its telephone number set forth below, and (y) as soon as reasonably practicable, deliver the original Payment Notice to XLCA at its address set forth below. Any Payment Notice received by XLCA after 10:00 a.m., New York City time, on a Business Day, or on any day that is not a Business Day, will be deemed to be received by XLCA at 9:00 a.m., New York City time, on the next succeeding Business Day. XLCA shall make payments due in respect of Insured Amounts no later than 2:00 p.m. New York City time to the Trustee upon the presentation of a Payment Notice to XLCA on the later of (a) one (1) Business Day following receipt by XLCA of a Payment Notice or (b) the Business Day on which Scheduled Payments are due for payment.

Subject to the foregoing, if the payment of any amount with respect to the Scheduled Payment is voided (a “Preference Event”) as a result of an Insolvency Proceeding and as a result of such Preference Event, the Owner is required to return such voided payment, or any portion of such voided payment, made in respect of the Insured Obligation (an “Avoided Payment”), XLCA will pay an amount equal to such Avoided Payment, as and when such payment would otherwise be due pursuant to the Indenture without regard to acceleration or prepayment, and upon payment of such Avoided Payment and receipt by XLCA from the Trustee on behalf of such Owner of (x) a certified copy of a final order of a court exercising jurisdiction in such Insolvency Proceeding to the effect that the Owner or the Trustee on behalf of the Owner is required to return any such payment or portion thereof because such payment was voided under applicable law, with respect to which order the appeal period has expired without an appeal having been filed (the “Final Order”), (y) an assignment, substantially in the form attached hereto as Exhibit B, properly completed and executed by such Owner irrevocably assigning to XLCA all rights and claims of such Owner relating to or arising under such Avoided Payment, and (z) a Payment Notice in the form of Exhibit A hereto appropriately completed and executed by the Trustee.

XLCA shall make payments due in respect of Avoided Payments no later than 2:00 p.m. New York City time on the Business Day following XLCA’s receipt of the documents required under clauses (x) through (z) of the preceding paragraph. Any such documents received by XLCA after 10:00 a.m. New York City time on any Business Day

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or on any day that is not a Business Day shall be deemed to have been received by XLCA at 9:00 a.m., New York City time, on the next succeeding Business Day. All payments made by XLCA hereunder on account of any Avoided Payment shall be disbursed to the receiver, conservator, debtor-in-possession or trustee in bankruptcy named in the Final Order and not to any Holder directly (unless a Holder previously paid such amount to the receiver, conservator, debtor-in-possession or trustee in bankruptcy named in the Final Order, in which case such payment shall be disbursed to the Trustee for distribution to such Holder upon proof of such payment reasonably satisfactory to XLCA).

XLCA hereby waives and agrees not to assert any and all rights to require the Trustee to make demand on or to proceed against any person, party or security prior to the Trustee demanding payment under this Policy.

No defenses, set-offs and counterclaims of any kind available to XLCA so as to deny payment of any amount due in respect of this Policy will be valid and XLCA hereby waives and agrees not to assert any and all such defenses (including without limitation, defense of fraud in the inducement or fact or any other circumstances which would have the effect of discharging a surety in law or in equity), set-offs and counterclaims, including, without limitation, any such rights acquired by subrogation, assignment or otherwise. Upon any payment hereunder, in furtherance and not in limitation of XLCA’s equitable right of subrogation and XLCA’s rights under the Insurance Agreement, XLCA will be subrogated to the rights of the Owner in respect of which such payment was made to receive any and all amounts due in respect of the obligations in respect of which XLCA has made a payment hereunder. Any rights of subrogation acquired by XLCA as a result of any payment made under this Policy shall, in all respects, be subordinate and junior in right of payment to the prior indefeasible payment in full of any amounts due the Owner on account of payments due under the Insured Obligation.

This Policy is neither transferable nor assignable, in whole or in part, except to a successor trustee duly appointed and qualified under the Indenture. All Payment Notices and other notices, presentations, transmissions, deliveries and communications made by the Trustee to XLCA with respect to this Policy shall specifically refer to the number of this Policy and shall be made to XLCA at:

XL Capital Assurance Inc.

1221 Avenue of the Americas

New York, New York 10020

Attention: Surveillance

Telephone: (212) 478-3400

Facsimile: (212) 478-3597

or such other address, telephone number or facsimile number as XLCA may designate to the Trustee in writing from time to time. Each such Payment Notice and other notice, presentation, transmission, delivery and communication shall be effective only upon actual receipt by XLCA.

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The obligations of XLCA under this Policy are irrevocable, primary, absolute and unconditional, subject to satisfaction of the conditions for making a claim under the Policy, and neither the failure of any Person to perform any covenant or obligation in favor of XLCA (or otherwise), nor the failure or omission to make a demand permitted hereunder, nor the failure of any assignment or grant of any security interest, nor the commencement of any Insolvency Proceeding by or against the Obligor, the Seller, the Servicer, the Trustee or any other person shall in any way affect or limit XLCA’s obligations under this Policy. If a successful action or proceeding to enforce this Policy is brought by the Trustee, the Trustee shall be entitled to recover from XLCA costs and expenses reasonably incurred, including, without limitation, reasonable fees and expenses of counsel.

This Policy and the obligations of XLCA hereunder shall terminate on the expiration of the Term of this Policy. This Policy shall be returned to XLCA by the Trustee upon the expiration of the Term of this Policy.

The foregoing notwithstanding, if an Insolvency Proceeding is existing by or against the Obligor, the Seller or the Servicer during the one year and one day period set forth in clauses (ii) or (iii) of the definition of “Term of this Policy” above, then this Policy and XLCA’s obligations hereunder shall terminate on (and the “Termination Date” shall be) the later of (i) the date of the conclusion or dismissal of such Insolvency Proceeding without continuing jurisdiction by the court in such Insolvency Proceeding, and (ii) the date on which XLCA has made all payments required to be made under the terms of this Policy in respect of Avoided Payments.

The Property/Casualty Insurance Security Fund specified in Article 76 of the New York Insurance Law does not cover this Policy. The Florida Insurance Guaranty Association created under Part II of Chapter 631 of the Florida Insurance Code does not cover this Policy. In the event that XLCA were to become insolvent, the California Insurance Guaranty Association, established pursuant to Article 14.2 of Chapter 1 of Part 2 of Division 1 of the California Insurance Code excludes from coverage any claims arising under this Policy.

THIS POLICY SHALL BE CONSTRUED, AND THE OBLIGATIONS, RIGHTS AND REMEDIES OF THE PARTIES HEREUNDER SHALL BE DETERMINED, IN ACCORDANCE WITH THE LAWS OF THE STATE OF NEW YORK, WITHOUT REGARD TO CONFLICT OF LAWS PRINCIPLES THAT WOULD REQUIRE THE APPLICATION OF THE LAWS OF ANY OTHER JURISDICTION.

In the event any term or provision of the form of this Policy is inconsistent with the provision of this Endorsement, the provision of this Endorsement shall take precedence and be binding.

[Remainder of Page Intentionally Left Blank]

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IN WITNESS WHEREOF, XL Capital Assurance Inc. has caused this Endorsement to the Policy to be executed on the Effective Date.

Policy No. CA01587A

Exhibit A to Financial Guaranty Policy No. CA01587A

XL Capital Assurance Inc.

1221 Avenue of the Americas

New York, New York 10020

Attention: Surveillance

PAYMENT NOTICE

UNDER FINANCIAL GUARANTY POLICY NO. CA01587A

[ Identify Trustee] as Trustee (the “Trustee”), hereby certifies to XL Capital Assurance Inc. (“XLCA”) with reference to that certain Financial Guaranty Policy, No. CA01587A, dated February 3, 2005 (the “Policy”), issued by XLCA in favor of the Trustee on behalf of the Owner under the Indenture    , as follows:

1. The Trustee is the trustee under the Indenture and the beneficiary on behalf of each Owner of the Policy.

2. Trustee is entitled to make a demand under the Policy pursuant to the Sale and Servicing Agreement.

3. This notice relates to the [insert date] [Distribution Date]. The amount demanded is to be paid in immediately available funds to the [Specify Account] at [Identify Financial Institution Holding Account] account number [             ] which is the “Note Distribution Account.”

[For a Payment Notice in respect of Insured Amounts other than Avoided Payment, use paragraph 4.]

4. The Trustee demands payment of $             which is an amount equal to [Describe calculation of the Insured Amount under Policy].

[For a Payment Notice in respect of an Avoided Payment use the following paragraphs [4] or [5].]

[4.] or [5.] The Trustee hereby represents and warrants, based upon information available to it, that (i) the amount entitled to be drawn under the Policy on the date hereof in respect of Avoided Payments is the amount paid or to be paid simultaneously with such draw on the Policy, by the Owner on account of a Preference Event [$            ] (the “Avoided Payment Amount”), (ii) the Owner with respect to which the drawing is being made under the Policy has paid or simultaneously with such

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draw on the Policy will pay such Avoided Payment Amount, and (iii) the documents required by the Policy to be delivered in connection with such Avoided Payment and Avoided Payment Amount have previously been presented to XLCA or are attached hereto.

[6] The Trustee agrees that, following payment of funds by XLCA, it shall use reasonable efforts to procure (a) that such amounts are applied directly to the payment of any Insured Amount which is due for payment; (b) that such funds are not applied for any other purpose; and (c) the maintenance of accurate record of such payments in respect of the Insured Obligation and the corresponding claim on the Policy and the proceeds thereof.

[7] The Trustee, on behalf of itself and the Owners, hereby assigns to XLCA all rights and claims (including rights of actions and claims in respect of securities laws violations or otherwise) of the Trustee and the Owners with respect to the Insured Obligation to the extent of any payments under the Policy. The foregoing assignment is in addition to, and not in limitation of, rights of subrogation otherwise available to XLCA in respect of such payments. The Trustee shall take such action and deliver such instruments as may be reasonably required by XLCA to effectuate the purposes of the provisions of this Clause 7.

[8] The Trustee, on behalf of itself and the Owners, hereby appoints XLCA as agent and attorney-in-fact for the Trustee and the Owners in any legal proceeding in respect of the Insured Obligation. The Trustee, on behalf of itself and the Owners, thereby (and without limiting the generality of the preceding sentence) agrees that XLCA may at any time during the continuation of any proceeding by or against any debtor with respect to which a Preference Claim (as defined below) or other claim with respect to the Insured Obligation is asserted under any Insolvency Proceeding, direct all matters relating to such Insolvency Proceeding, including, without limitation, (a) all matters relating to any claim in connection with a Insolvency Proceeding seeking the avoidance as a preferential transfer of any payment made with respect to the obligations (a “Preference Claim”), (b) the direction of any appeal of any order relating to any Preference Claim and (c) the posting of any surety, supersedes or performance bond pending any such appeal. In addition, the Trustee, on behalf of itself and the Owners, hereby agrees that XLCA shall be subrogated to, and the Trustee, on behalf of itself and the Owners, hereby delegates and assigns, to the fullest extent permitted by law, the rights of the Trustee and the Owners in the conduct of any Insolvency Proceeding, including, without limitation, all rights of any party to an adversary proceeding or action with respect to any court order issued in connection with any such Insolvency Proceeding.

Capitalized terms used herein and not otherwise defined herein shall have the meanings assigned to them in the Policy or the Indenture.

IN WITNESS WHEREOF, this notice has been executed this              day of             ,             .

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Any Person Who Knowingly And With Intent To Defraud Any Insurance Company Or Other Person Files An Application For Insurance Or Statement Of Claim Containing Any Materially False Information, Or Conceals For The Purpose Of Misleading Information Concerning Any Fact Material Thereof, Commits A Fraudulent Insurance Act, Which Is A Crime, And Shall Also Be Subject To A Civil Penalty Not To Exceed Five Thousand Dollars And The Stated Value Of The Claim For Each Such Violation

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Exhibit B to Financial Guaranty Insurance Policy, No. CA01587A

Form of Assignment

Reference is made to the Financial Guaranty Insurance Policy No. CA01587A, dated February 3, 2005 (together with the Endorsement attached thereto, the “Policy”) issued by XL Capital Assurance Inc. (“XLCA”) relating to the Class [[]] Notes issued by AmeriCredit Automobile Receivables Trust 2005-A-X pursuant to that certain Indenture dated February 3, 2005. Unless otherwise defined herein, capitalized terms used in this Assignment shall have the meanings assigned thereto in the Policy as incorporated by reference therein. In connection with the Avoided Payment of [$             ] paid by the undersigned (the “Owner”) on [            ] and the payment by XLCA in respect of such Avoided Payment pursuant to the Policy, the Owner hereby irrevocably and unconditionally, without recourse, representation or warranty (except as provided below), sells, assigns, transfers, conveys and delivers all of such Owner’s rights, title and interest in and to any rights or claims, whether accrued, contingent or otherwise, which the Owner now has or may hereafter acquire, against any person relating to, arising out of or in connection with such Avoided Payment. The Owner represents and warrants that such claims and rights are free and clear of any lien or encumbrance created or incurred by such Owner.¹