Exhibit 10.9

AMENDED AND RESTATED

DIRECT FINANCE AND SERVICES ADDENDUM

TO LETTER AGREEMENT

This Amended and Restated Direct Finance and Services Addendum to Letter Agreement (“Addendum”) is entered into by and among Aspen Technology, Inc. (“AspenTech”), Fleet Business Credit, LLC, formerly known as Sanwa Business Credit Corporation (“FBC”), Fleet Business Credit (UK) Limited (“FBC-UK”) and Fleet Business Credit (Deutschland) GmbH (“FBC-Germany”) effective as of December 30, 2004.  The terms of this Addendum are supplemental to the Letter Agreement (as defined below), and form a part of the Letter Agreement, which will remain in full force and effect except as provided in this Addendum.  This Addendum amends, restates, and replaces and supercedes the existing Direct Finance and Services Addendum to Letter Agreement, dated as of March 29, 1999 (the “Existing Direct Finance Addendum”).

WHEREAS, AspenTech and FBC are parties to that certain letter agreement dated as of March 25, 1992, as amended by a First Amendment dated as of March 3, 1994, a Second Amendment dated as of January 1, 1997, the Existing Direct Finance Addendum, a Third Amendment dated as of March 28, 2003 (the “Letter Agreement”); and

WHEREAS, AspenTech, FBC, FBC-UK and FBC-Germany are parties to an Accession Agreement dated September 30, 2002 and a Side Agreement dated April 22, 2003; and

WHEREAS, AspenTech and FBC wish to restate the provision of a method under which AspenTech, subject to the terms of the Letter Agreement as supplemented by this Addendum, may refer to FBC those customers which desire to finance their acquisition of AspenTech software and services, with financing documentation to be originated and compiled by AspenTech; and

WHEREAS, AspenTech and FBC also wish to provide for purchase financing and direct financing of services that are provided in conjunction with AspenTech software products; and

WHEREAS, FBC-UK and FBC-Germany wish to consent to the terms of this Addendum,

NOW THEREFORE, in consideration of the premises and for other good and valuable consideration the receipt of which is hereby acknowledged, AspenTech and FBC hereby agree as follows:

1.                                       Definitions.

(a)                                  Capitalized Terms.  Capitalized terms used in this Addendum will have the same meaning given under the Letter Agreement, as amended, except as provided in Section 1(c) below.

(b)                                 Additional Definitions.  The following terms will have the meanings given to them in this Section:

“Acquisition Cost” for any Software financed for an Obligor by FBC and covered by a Direct Finance Contract, means an amount equal to the amount (net of rebates and credits) which AspenTech charges for such Software, less the amount of any down payments or credits, and/or unpaid refinancing or “take-out” liabilities associated with such Software.

“Closing Date” has the meaning given in Section 2(f).

“Direct Finance Contract” means a non-cancelable full pay-out financing agreement arising out of the licensing and provision of Software, which is a direct agreement between the Obligor and FBC.  A Direct Finance Contract is a “Contract” under the Letter Agreement.

“Software Agreements” has the meaning given in Section 2(e).

(c)                                  Replacement Definitions.  The definition of “Software” provided under the Letter Agreement is replaced by the following definition:

“Software” means software products licensed by AspenTech under license agreements with Obligors and services, such as maintenance, support, consulting and special applications development, which are provided to by AspenTech to Obligors under the terms of such license agreements.

2.                                       Direct Finance Transactions.

(a)                                  Offers; Origination.  AspenTech may advise its prospective Obligors about direct financing opportunities under this Addendum.  FBC may in its sole discretion elect to finance or decline to finance an Obligor’s acquisition of AspenTech Software.

(b)                                 Financed Amount.  The amount to be financed for Software under direct financings will not exceed the actual license fee, service fee for and/or cost of such Software to the Obligor.

(c)                                  Limitations on Direct Finance Contracts.  Each Direct Finance Contract shall be in the form attached hereto as Exhibit A, except as specifically approved in writing by FBC.

(d)                                 Credit Acceptance.  FBC will in its sole discretion determine the acceptability of the Obligor’s credit under proposed transactions and will advise AspenTech of FBC’s credit determination.  If FBC does not approve the creditworthiness of an Obligor under a proposed transaction within thirty (30) business days, the proposed transaction will be deemed rejected.  Credit approvals by FBC shall be in writing and shall be valid for a period of ninety (90) days from their issuance unless a different time is specified in writing by FBC, and will be subject to

any terms specified by FBC in connection with the approval.  Credit approval may be revoked if FBC determines, in its sole discretion, that (i) a change has occurred in the structure of the proposed transaction from that represented by AspenTech to FBC at the time of its approval, (ii) there has occurred a material adverse change (as determined by FBC) in the creditworthiness or business condition of the Obligor, or (iii) any of the materials, information, statements and/or representations provided to FBC in connection with its credit review or approval are false, misleading or incomplete to any material extent. FBC will promptly notify AspenTech, in writing, of any revocation.

(e)                                  Conditions to Financing.  In the event FBC agrees to directly finance any AspenTech Software, all of the following conditions must be satisfied at or prior to the Closing Date with respect to such financing:

(1)                                  No material change shall have occurred to AspenTech’s business or financial status since the date of this Addendum which prevent AspenTech from meeting its obligations under the Letter Agreement, this Addendum or any Assignment and its obligations (if any) with respect to any Software covered by any Software Agreement;

(2)                                  This Addendum must be in full force and effect and shall not have expired, or been terminated or revoked;

(3)                                  AspenTech must not be in breach of any of its obligations under this Addendum.

(4)                                  FBC must have approved the credit of the and such approval shall not have been revoked;

(5)                                  AspenTech must have originated and compiled, and FBC must have received:

(i)                                     The original Direct Finance Contract, any schedules, riders and attachments thereto, all fully executed by the Obligor;

(ii)                                  Evidence that the software components of the Software covered or financed under the Direct Finance Contract have been shipped to, and that such software components have been accepted in accordance with and as defined by the terms and conditions of the Software Agreements;

(iii)                               A copy of any license or other agreements between AspenTech and the Obligor with respect to the Software, (“Software Agreements”), certified as true, accurate and correct by AspenTech; and

(iv)                              Such other guaranties, documents, instruments and agreements as required under FBC’s credit approval or as FBC may otherwise reasonably require.

(f)                                    Closing.  Except as otherwise mutually agreed to by AspenTech and FBC, each closing shall occur on a mutually agreed upon business day following the satisfaction of all of the conditions precedent to purchase set forth in Section 2(e) (the “Closing Date”).  On each Closing Date, FBC shall pay to AspenTech the aggregate Acquisition Cost for all Software being financed on such Closing Date.

(g)                                 No Assumption by FBC.  FBC shall not be deemed to have assumed any of AspenTech’s, any licensor’s, or any service provider’s obligations with respect to any Software.

3.                                       Warranties as to the Direct Finance Contracts.  AspenTech warrants that all of the following are true and correct with respect to all Software financed under this Addendum and the Direct Finance Contract and related agreements covering such Software.  These warranties will, for Direct Finance Contracts, supersede and replace the eligibility provisions of the Letter Agreement:

(a)                                  Bona Fide Transaction; Acceptance.  The Direct Finance Contract arises from a bona fide financing of the Software described in the Direct Finance Contract; as of the Closing Date, the software components of the Software have been shipped to, and accepted in accordance with and as defined by the terms and conditions of the Software Agreements, by the Obligor;

(b)                                 Software Complies With License and Laws.  The Software complies with the requirements of any applicable license or other agreement and any applicable laws and regulations and AspenTech has an unconditional, non-terminable right to license, relicense or sublicense the software components of the Software covered under the Direct Finance Contract for the full term of the Direct Finance Contract;

(c)                                  Counterparts.  All original counterparts of the Direct Finance Contract and any related agreements have been delivered to FBC as of the Closing Date, together with complete fully executed copies of all Software license agreements and other agreements entered into in connection with the Software and Direct Finance Contract; the Direct Finance Contract and related agreements accurately set forth the name of the Obligor, the Software financed under the Direct Finance Contract, and the term, Payments and other details of the related transaction;

(d)                                 Form of Direct Finance Contract.  Except as specifically approved in writing by FBC, the Direct Finance Contract is unaltered from the form attached hereto as Exhibit A;

(e)                                  Unimpaired Right to License Software.  AspenTech has good title to and an unimpaired fully paid right to license the Software for the full term of the Direct Finance Contract, subject only to the interest of the Obligor and the interest, if any, of the developer or third-party licensor of the Software to whom or which all license fees and/or royalties relating to the Software have been or will be fully paid on such a basis as to maintain, for the full term of the Direct Finance Contract, the Obligor’s license and Software rights with respect to sublicensed and re-licensed Software;

(f)                                    Authorization.  Each party to the Direct Finance Contract or any Obligor Guaranty has all the legal capacity, power and right required for it to enter into the Direct Finance Contract or Obligor Guaranty and any supplemental agreements, and to perform its obligations thereunder; and all such actions have received all corporate or governmental authorization required by any applicable charter, by-law, constitution, law, rule or regulation;

(g)                                 No Default.  As of the Closing Date, there existed no event of default, or event which with the passage of time or giving of notice, or both, would become an event of default under terms of the Direct Finance Contract or any license or other agreement covering the Software, and Aspen had no knowledge of any fact that may impair the Direct Finance Contract’s validity;

(h)                                 No Offsets, Etc.  There exist no setoffs, counterclaims or defenses on the part of any Obligor under the Direct Finance Contract or any Obligor Guaranty which arise out AspenTech’s acts or omissions or which are based upon any alleged breach by AspenTech of any warranty, representation or obligation under the Software Agreements.

(i)                                     Taxes.  All taxes, assessments, fines, fees and other liabilities relating to the Software and which have been assessed or accrued prior to our purchase have been paid when due, and all filings in respect of any such taxes, assessments, fines, fees and other liabilities have been timely made;

(j)                                     No Licensor or Provider Default.  Neither AspenTech, nor any developer, licensor or provider of the Software is in default of any of AspenTech’s or such developer’s, licensor’s or provider’s material obligations with respect to the Software or imposed by applicable law, rule or regulation with respect to the Direct Finance Contract and the related Software;

(k)                                  No Impairment.  Aspen has not amended or modified, directly or indirectly, any Direct Finance Contract, any Payments thereunder, or any related Obligor Guaranty; Aspen has not made any statements to any Obligor under the Direct Finance Contract which waive or alter the terms of the Direct Finance Contract or could have the effect of waiving or modifying the terms of the Direct Finance Contract.

(l)                                     Termination Right.  AspenTech acknowledges that FBC may provide under the Direct Finance Contract that the Obligor’s license and right to use and receive the Software financed under the Direct Finance Contract may be terminated by FBC or AspenTech (at FBC’s request) in the event of non-payment or breach of the Direct Finance Contract by the Obligor.

4.                                       Covenants.

Until the termination of this Addendum and for as long as any Direct Finance Contract remains outstanding, AspenTech will:

(a)                                  Performance of Obligations.  Maintain all rights to license Software financed under the Direct Finance Contracts for the full term of the Direct Finance Contracts and perform

or cause to be performed all of AspenTech’s or any developer’s, service provider’s or licensor’s obligations arising by contract or imposed by applicable law, rule or regulation with respect to the Software.

(b)                                 License Transfers to Successors, Etc.  AspenTech will permit Software to be transferred freely, at no additional charge, to any Obligor’s successor or to any purchaser of the business or assets of an Obligor, subject only to any site, term, user number and/or similar restrictions specified in the Software Agreements and such successor’s or purchaser’s agreement to be bound by any Software agreement that is effective against the Obligor.

(c)                                  License Transfer.  AspenTech agrees to any transfer and assignment of the Software license and related software support and maintenance from the Obligor to FBC and further agrees to any subsequent transfer and assignment of such Software License and related software support and maintenance from FBC to a third party, provided such transfer and assignment complies with the Export Administration Act.

(d)                                 FBC Authorized to Terminate, Transfer and Reinstate.  AspenTech irrevocably grants and licenses to FBC the right to effect and carry out any termination, transfer and/or reinstatement of Software rights as may be required of AspenTech under Sections (a)-(c).  All such actions taken by FBC will have the same force and effect as if taken by AspenTech.

5.                                       “Software” May Include Services.  The Letter Agreement will be construed to cover and permit financing service products that are included in this Addendum’s definition of Software.  Letter Agreement references to Software, development and licensing, and provisions that apply to Software, development and licensing will be broadly construed to constitute parallel references to services and the provision of services.

6.                                       Indemnities.

(a)                                  Section 3 Warranties.  If any of the warranties specified in Section 3 shall not be true, correct or satisfied, FBC may request or demand that AspenTech indemnify FBC for losses, not to exceed the license and support fees received by AspenTech in connection with the Software financed under the Direct Finance Contract, incurred by FBC associated with a breach of such warranties.  This indemnity is not intended to cover, and will not apply to, without limitation, FBC’s loss of investment or non-receipt of payments resulting solely from an Obligor’s financial inability to pay.

(b)                                 Software Claims Indemnity.  AspenTech agrees to indemnify FBC for and save it harmless from any losses, damages, penalties, claims, costs, expenses (including court costs and reasonable attorneys’ fees) or liabilities which may be brought, incurred, assessed or adjudged against FBC, not caused by FBC’s negligence or willful misconduct, related to or arising from any breach by AspenTech of any of its representations, warranties, covenants or other obligations or agreements contained in this Addendum or any Software Agreement.

7.                                       Override of Certain Sections of Letter Agreement (Concerning Direct Finance Contracts Only).  With respect to any Direct Finance Contracts, the provisions of this Addendum supersede

and control over the Letter Agreement.  Sections 2, 3, 5, 8, 9, 10, 11, 11A, and 12 of the Letter Agreement will not apply to Direct Finance Contracts.

8.                                       Termination.

This Addendum shall continue in effect until terminated and may be terminated by either party at any time upon thirty (30) days’ written notice to the other, provided, however, that all indemnities and all of the rights and obligations of the parties which apply to any Direct Finance Contracts entered into prior to such termination shall survive such termination until two (2) years after the later of (i) such time as the Net Contract Balance of all Direct Finance Contracts (after giving effect to all recoveries and payments received on account of the Direct Finance Contracts) has been reduced to zero, or (ii) termination of this Addendum.

9.                                       Miscellaneous.

(a)                                  Interest on Overdue AspenTech Obligations. AspenTech shall pay FBC interest at a rate equal to eighteen percent (18%) per annum or the maximum rate permitted by applicable law on any payments due to FBC from AspenTech which are more than 30 days past due.

(b)                                 Misdirected Payments.  If AspenTech receives a Payment on account of a Direct Finance Contract, AspenTech agrees to receive the amount in trust for FBC and promptly forward the Payment to FBC in kind.

(c)                                  Authority.  AspenTech represents and warrants (each representation and warranty shall be considered as having been made concurrently with any financing by FBCC, as an inducement to FBC to enter into such financing) that it is duly authorized to execute and deliver this Addendum, and is and will (as long as this Addendum is in effect and thereafter until FBC receives full payment of all amounts due under the Direct Finance Contracts and the Agreement) continue to be, duly authorized to originate the Direct Finance Contracts and perform all of its obligations under this Addendum.

(d)                                 Scope, Ratification.  This Addendum provides specific terms and conditions which apply supplementally to the Letter Agreement for Direct Finance Contracts only.  Except as specifically provided in this Addendum, and then only with respect to Direct Finance Contracts, the Letter Agreement is effective and is hereby ratified and confirmed.

(e)                                  Not Applicable to International Contracts.  This Addendum will not apply to International Contracts.  Direct Finance Contracts will not be offered for international transactions unless Aspen and FBC specifically agree in writing.

(f)                                    Severability.  Any provision of this Addendum which is prohibited by or is unlawful or unenforceable under any applicable law of any jurisdiction, such provision shall, as to such jurisdiction, be ineffective to the extent of such prohibition or unenforceability without invalidating the remaining provisions hereof; provided, however, that any such prohibition in any jurisdiction shall not invalidate such provision in any other jurisdiction; provided, further, that where the provisions of any such applicable law may be waived, they hereby are waived by

AspenTech and FBC to the full extent permitted by applicable law to the end and that this Addendum shall be deemed to be a valid and binding agreement in accordance with its terms.

(g)                                 Counterparts.  This Addendum may be executed in any number of counterparts, and each such counterpart shall be deemed to be an original, but all such counterparts together shall constitute one and the same Addendum.

(h)                                 Governing Law.  This Addendum shall be construed and governed according to the laws of (but not the choice of law rules of) the State of Illinois.

IN WITNESS WHEREOF, the parties hereto have caused their duly authorized officers to execute this Addendum, and to amend and completely restate the existing Direct Finance Addendum to Letter Agreement, effective as of December 30, 2004.

Consent

FBC-UK and FBC-Germany have reviewed and hereby consent to the foregoing Amended and Restated Direct Finance and Services Addendum to Letter Agreement.