PREMIUM LETTER May 10, 2006

Exhibit 10.4

PREMIUM LETTER

May 10, 2006

AmeriCredit Financial Services, Inc.

801 Cherry Street, Suite 3900

Fort Worth, TX 76102

AmeriCredit Automobile Receivables Trust 2006-R-M

c/o Wilmington Trust Company

Rodney Square North

1100 North Market Street

Wilmington, DE ###-###-####

Wells Fargo Bank, National Association

Sixth Street and Marquette Avenue

MAC N9311-161

Minneapolis, MN 55479

$1,200,000,000

AmeriCredit Automobile Receivables Trust 2006-R-M

Automobile Receivables Backed Notes

$448,000,000 Class A-1 Notes

$552,000,000 Class A-2 Notes

$200,000,000 Class A-3 Notes

Ladies and Gentlemen:

This letter (this “Premium Letter”) will confirm the agreement of AmeriCredit Financial Services, Inc. (“AmeriCredit”) AmeriCredit Automobile Receivables Trust 2006-R-M (the “Issuer”), Wells Fargo Bank, National Association (the “Trustee,” the “Trust Collateral Agent,” the “Collateral Agent,” and the “Backup Servicer”) and MBIA Insurance Corporation (“MBIA”) that the following nonrefundable payments and other obligations are to be made and undertaken in connection with, and subject to, the closing of the above-described transaction and in consideration of the issuance by MBIA of its Note Guaranty Insurance Policy No. 47966 (the “Policy”), in respect thereof. The Insurer Premium paid hereunder shall be nonrefundable for any reason whatsoever, including the lack of any payment under the Policy or any other circumstances relating to the $1,200,000,000 AmeriCredit Automobile Receivables Trust 2006-R-M Automobile Receivables Backed Notes $448,000,000 Class A-1 Notes, $552,000,000 Class A-2 Notes, $200,000,000 Class A-3 Notes, (the “MBIA-Insured Obligations”) or provision being made for payments of the MBIA-Insured Obligations prior to maturity.

The payments payable pursuant to the terms hereof shall constitute the “Premium” referred to in the Insurance Agreement dated as of May 10, 2006 (the “Insurance Agreement”) among MBIA, the Issuer, AmeriCredit, individually and as Servicer and Custodian, AFS SenSub Corp., as Seller, the Trustee, the Trust Collateral Agent, the Collateral Agent and the Backup

Servicer. The obligations of AmeriCredit and the Issuer hereunder constitute an obligation of AmeriCredit or the Issuer, as applicable, under the Insurance Agreement. Capitalized terms used but not otherwise defined herein shall have the meanings set forth in the Insurance Agreement or in the Sale and Servicing Agreement (as defined in the Insurance Agreement).

1. AmeriCredit shall pay or cause to be paid the following amounts on or before the Closing Date:

(a) Except as set forth in clauses (b), (c) and (d) below, all legal fees, disbursements and all other out of pocket expenses incurred by MBIA or agents of MBIA in connection with the issuance of the Policy, fees for the consent letter of MBIA’s accountants, and fees of MBIA’s auditors, if any. Such amounts shall be wired on the Closing Date to the MBIA account set forth below (or as otherwise directed by a third party upon presentation of its invoice);

(b) Legal fees and expenses of Kutak Rock LLP in an amount not to exceed $40,000.00 to be billed separately by Kutak Rock LLP, which shall paid by check or wire transfer on or about the Closing Date to Kutak Rock LLP pursuant to the instructions set forth on their statement; and

(c) Fees of Moody’s Investors Service Inc., Fitch Inc., and Standard & Poor’s Ratings Services (the “Rating Agencies”) to be billed directly by the Rating Agencies; and

(d) All costs and expenses of due diligence reviews performed by [Virgil Baker & Associates Inc.] in the amount of $13,886.87 which shall be paid within 30 days of presentation of an invoice therefore.

2. The Issuer shall pay pursuant to Section 5.7 of the Sale and Servicing Agreement, an Insurer Premium (the “Insurer Premium”) payable monthly in arrears in accordance with the wiring instructions for MBIA set forth below in the following amounts:

(a) On the June 2006 Distribution Date, in an amount equal to $126,666.67, which equals the 19 days of premium due from the Closing Date to but excluding the first Distribution Date at the Premium Percentage set forth below;

(b) Beginning on the July 2006 Distribution Date and on each Distribution Date thereafter, in an amount equal to 0.0167% (based upon a “Premium Percentage” of 0.20% per annum) times the outstanding principal amount of the MBIA-Insured Obligations (before taking into account any distributions on that date). The Insurer Premium for each Distribution Date shall be calculated on the basis of a 360-day year consisting of twelve 30-day months.

3. All Rating Agency fees and accountants’ fees incurred at any time by MBIA in connection with the Insurance Agreement and the transactions described in the Prospectus Supplement but excluding any Rating Agency Fees associated with the Revolving Period, shall be payable by AmeriCredit within 30 days of presentation of an invoice therefore.

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4. All reasonable costs and expenses (including those of legal counsel) incurred by MBIA in connection with any modification, waiver, amendment, revision or similar action of the Insurance Agreement, the Policies, and/or the Basic Documents and/or the enforcement against AmeriCredit, the Issuer, the Seller, the Trust Collateral Agent, the Back-up Servicer, the Trustee or the Servicer of MBIA’s rights under the Insurance Agreement, the Policy, and/or the Basic Documents, shall be payable by AmeriCredit within 30 days of presentation of an invoice therefore.

5. Unless another account is designated to you in writing, federal funds wire transfers to MBIA should be made with the following details specifically stated on the wire instructions:

MBIA wiring instructions:

Account Name: MBIA Insurance Corporation

Account Number: 910-2-721728

Bank: JPMorgan Chase Bank

4 Chase Metro Tech Center

Brooklyn, NY 11245

ABA Number: 021-000-021

Reference: Policy No. 47966

6. All fees and expenses due and payable to MBIA hereunder that are not paid on the date due, shall accrue interest at the Late Payment Rate, such interest to be calculated on the basis of a 360-day year for the actual number of days elapsed and shall be payable on demand.

7. The Trustee and the Trust Collateral Agent hereby acknowledges their obligations to pay the amounts set forth above from moneys of the Issuer pursuant to the terms of the Indenture or the Sale and Servicing Agreement.

8. This Premium Letter may be executed in counterparts by the parties hereto, and all such counterparts shall constitute one and the same instrument.

[REMAINDER OF PAGE INTENTIONALLY LEFT BLANK,

SIGNATURE PAGE FOLLOWS]

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AMERICREDIT AUTOMOBILE RECEIVABLES TRUST 2006-R-M, as Issuer

By: Wilmington Trust Company,

not in its individual capacity but solely as Owner Trustee