EXHIBIT 10.51

Execution Copy

PURCHASE OBLIGATION AGREEMENT

This PURCHASE OBLIGATION AGREEMENT (this “Agreement”) is dated as of January 20, 2010 and is by and among ITT EDUCATIONAL SERVICES, INC., a Delaware corporation (the “Guarantor”), DEUTSCHE BANK TRUST COMPANY AMERICAS, as indenture trustee and collateral agent (in such capacities, the “Secured Party”) and each of the Senior Creditors (as hereinafter defined) whose names appear on the signature pages hereof.

RECITALS

A. The Guarantor offers certain programs of education through schools that it owns and operates.

B. PEAKS Trust 2009-1 (the “Trust”) has been established pursuant to a Trust Agreement dated as of December 23, 2009 (as amended, supplemented, restated or otherwise modified from time to time, the “Trust Agreement”), between Access Group, Inc., as depositor, and Deutsche Bank Trust Company Delaware, as owner trustee, for the purpose of purchasing and holding loans made to students attending the Guarantor’s schools.

C. The Trust Agreement and that certain Indenture and Credit Agreement dated as of the date hereof (as amended, supplemented, restated or otherwise modified from time to time, the “Indenture and Credit Agreement”) by and among the Trust, the Secured Party and the Lender Trustee, provide for student loan asset-backed senior notes to be issued by the Trust (the “Senior Notes”) to provide a portion of the funds for the Trust to purchase and hold Financed Loans.

D. The Senior Notes will be purchased by certain of the Senior Creditors pursuant to a Note Purchase Agreement dated as of the date hereof between the Trust and the Note Purchasers (as defined therein) and acknowledged by the Secured Party (as amended, supplemented, restated or otherwise modified from time to time, the “Note Purchase Agreement”).

E. The Trust Agreement and the Indenture and Credit Agreement also provide for the terms of a loan (the “Loan” and together with the Senior Notes, the “Senior Credit”) to be made to the Trust in order to provide a portion of the funds for the Trust to purchase and hold Student Loans.

F. The Loan will made by a lender (the “Lender” and together with the Note Purchasers, the “Senior Creditors”) to the Trust pursuant to a Loan Agreement (as amended, supplemented, restated or otherwise modified from time to time, the “Loan Agreement”) dated as of the date hereof between the Trust, the Secured Party and such Lender.

G. The proceeds of the Senior Credit will be used to purchase Financed Loans pursuant to that certain Private Education Loan Origination and Sale Agreement dated as of the date hereof among Liberty Bank, N.A., as Originating Lender, the Guarantor, the Lender Trustee, the Secured Party and Access Group, Inc. as Origination Agent (as amended, supplemented, restated or otherwise modified from time to time, the “Loan Purchase Agreement”).

H. The Guarantor has agreed to guarantee all Guaranteed Payments in respect of the Senior Credit pursuant to the terms of that certain Guarantee Agreement dated as of the date hereof between the Guarantor and the Secured Party (as amended, supplemented, restated or otherwise modified from time to time, the “Guarantee Agreement”).

I. The Senior Creditors desire that the Guarantor grant the Senior Creditors an option pursuant to which such Senior Creditors may elect to require the Guarantor to purchase, in whole or in part, the Senior Credit, on the terms herein described.

J. The parties desire to provide for the amendment of this Agreement in certain circumstances.

K. Capitalized terms used but not defined herein (including in the preamble and the recitals hereto) shall have the meanings assigned to such terms in the Indenture and Credit Agreement.

I. PURCHASE OBLIGATION AND MOST FAVORED NATION PROVISION

1. The Guarantor hereby grants to the Senior Creditors an irrevocable option to require the Guarantor to purchase (the “Purchase Obligation”), in whole or in part, the Senior Credit, in the circumstances and on the terms set forth below:

1.1. If, subsequent to the Closing Date, any legislative change is enacted into law to reduce the maximum allowable percentage of the Guarantor’s cash revenues derived from funding under Title IV of the Higher Education Act from 90% to 75% or less (a “Legislative Change”), the Guarantor will give written notice (a “Purchase Notice”) of such fact not more than five (5) days after the date upon which a Legislative Change shall have become effective (the “Legislative Change Date”) to the Secured Party and the Secured Party shall deliver such Purchase Notice to each of the Senior Creditors not more than five (5) days after receipt of the same from the Guarantor.

1.2. The Purchase Notice shall (i) describe the scope of the Legislative Change in reasonable detail, (ii) designate a purchase date (the “Purchase Date”), which Purchase Date shall be not less than forty (40) days and not more than sixty (60) days following the Legislative Change Date, (iii) specify the date by which the Senior Creditors must accept the Offer to Purchase (the “Required Acceptance Date”), which

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Required Acceptance Date shall be not less than ten (10) days prior to the Purchase Date and (iv) refer to this Agreement and the right of the Senior Creditors to require the Guarantor to offer to purchase (the “Offer to Purchase”) upon the same terms and conditions pro rata the Outstanding Senior Credit, in whole or in part, at the purchase price for such Senior Credit, payable in immediately available funds, equal to the unpaid principal amount of such Senior Credit, together with interest accrued and unpaid thereon to the Purchase Date (the “Purchase Amount”), without Call Premium or any other amounts.

1.3. Each Senior Creditor shall have the right to accept an Offer to Purchase made by the Guarantor pursuant to Section 1.2 hereof and require the purchase of the Senior Credit held by such Senior Creditor, in whole or in part, by written notice (the “Senior Creditor Acceptance Notice”) to the Guarantor on or before the Required Acceptance Date. If 25% or more of the Senior Credit then Outstanding is tendered to the Guarantor for purchase, the Guarantor shall promptly notify or cause the Secured Party to notify the Senior Creditors of such fact (the “25% Acceptance Notice”) and (i) the Required Acceptance Date shall be adjusted by the number of days necessary to give each such remaining Senior Creditor at least thirty (30) days from its receipt of such 25% Acceptance Notice to accept such Offer to Purchase and (ii) the Purchase Date shall be extended such that the number of days between the Required Acceptance Date and the Purchase Date shall remain unchanged. Failure to timely respond by a Senior Creditor to any Purchase Notice or 25% Acceptance Notice shall constitute a rejection of the Offer to Purchase by such Senior Creditor.

1.4. On the Purchase Date, upon receipt of the applicable Purchase Amount by each Senior Creditor having delivered a Senior Creditor Acceptance Notice to the Guarantor as to all or any portion of such Senior Creditor’s then Outstanding Senior Credit, such Senior Creditor shall surrender the Senior Notes or Loan Notes corresponding to such portion of the then Outstanding Senior Credit for transfer, duly endorsed or accompanied by an assignment to the Guarantor duly executed by such Senior Creditor, and the Trust shall deliver on the Purchase Date such new Senior Notes or Loan Notes reflecting the Guarantor as a Senior Creditor as may be required in accordance with the terms of Section 2.03 of the Indenture and Credit Agreement. The Trust and the Secured Party undertake and agree that notwithstanding the terms of said Section 2.03 and the right of the Trust, the Secured Party and the Registrar to execute, authenticate and register, respectively, any Senior Note or Loan Note within ten Business Days upon surrender at the Principal Office of the Registrar, the parties shall effect any transfer of Senior Notes or Loan Notes in respect of the Purchase Obligation on the Purchase Date.

2. In furtherance of the transactions described in the Trust Agreement, the Indenture and Credit Agreement, the Note Purchase Agreement, the Loan Agreement, the Loan Purchase Agreement and the Guarantee Agreement, the Trust has entered into the several related

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transactions contemplated by that certain (i) Administration Agreement, dated as of the date hereof, among the Trust, the Owner Trustee, the Guarantor, Access Group, Inc., as Administrator, and the Secured Party (as amended, supplemented, restated or otherwise modified from time to time, the “Administration Agreement”), (ii) Syndication Agent Agreement dated as of the date hereof among the Trust, Deutsche Bank Securities Inc., as Syndication Agent, and the Guarantor (as amended, supplemented, restated or otherwise modified from time to time, the “Syndication Agreement”), and (iii) Agreement for Servicing Private Student Loans, dated as of the date hereof, among the Trust, the Secured Party, the Guarantor and Access Group, Inc., as Servicer (as amended, supplemented, restated or otherwise modified from time to time, the “Servicing Agreement”) (the transactions contemplated by the agreements referenced in this Section 2, collectively, the “PEAKS 2009-1 Transaction”).

3. The Guarantor covenants and agrees that in the event that the Guarantor enters into a transaction related to private education loans for its students and graduates that (i) is similar, in form or substance, to the PEAKS 2009-1 Transaction, and in which Deutsche Bank Securities Inc. (or an affiliate thereof) acts as arranging agent, collateral agent, placement agent, syndication agent, indenture trustee, lender trustee or owner trustee and in which the Guarantor guarantees payments on any loan, note or other debt obligation (each, a “Debt Obligation”) issued in connection therewith (a “Similar Transaction”), and (ii) contains an obligation of the Guarantor to purchase, in whole or in part, any Debt Obligation in the event that the maximum allowable percentage of the Guarantor’s cash revenues derived from funding under Title IV of the Higher Education Act is reduced from 90% to a percentage above 75% but below 90%, then the Guarantor shall (A) on the Business Day immediately following the closing date of such Similar Transaction, provide the Secured Party with notice and a description of the obligation of the Guarantor contained in the Similar Transaction (the “Similar Transaction Notice”), and (B) execute an amendment to this Agreement that increases the percentage from 75% in the definition of Legislative Change to the percentage utilized in the Similar Transaction.

4. The Secured Party covenants and agrees to deliver any Similar Transaction Notice to the Senior Creditors not more than five (5) days after receipt of the same from the Guarantor.

II. MISCELLANEOUS PROVISIONS

5. Any notice or other communication required or permitted hereunder shall be in writing and shall be delivered either personally or by next day courier, in each case, addressed as follows:

(a) if to the Guarantor or the Secured Party, at the address set forth in the Indenture and Credit Agreement; and

(b) if to any Senior Creditor, at the address set forth in the Credit Register maintained by the Credit Registrar, together with a copy to the Senior Creditors’ counsel: Winston & Strawn LLP, 200 Park Avenue, New York, New York 10166, Attn: Alan S. Hoffman, Esq.,

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or at such other place as the respective party may, from time to time, designate in a written notice to the other party.

6. This Agreement and all of the provisions hereof shall be binding upon and inure to the benefit of the parties hereto and their respective successors and assigns including in connection with an assignment or transfer of the Senior Credit pursuant to the terms of the Indenture and Credit Agreement.

7. Notwithstanding anything contained herein to the contrary, this instrument has been executed by Deutsche Bank Trust Company Delaware, not in its individual or personal capacity but solely in its capacity as Owner Trustee, and in no event shall Deutsche Bank Trust Company Delaware in its individual or personal capacity or any beneficial owner of the Issuer have any liability for the obligations of the Trust hereunder.

8. This Agreement is governed by, and shall be construed in accordance with, the laws of the State of New York.

9. In connection with any suit, claim, action or proceeding arising out of or relating to the transactions contemplated hereby: each party hereto hereby consents to the in personam jurisdiction of the United States District Court for the Southern District of New York and of the Supreme Court of New York County (and each party hereto agrees not to commence any action, suit or proceeding relating thereto except in any such United States District Court or, if subject matter jurisdiction therefor is not available in such court, in such Supreme Court); each party hereto agrees that service by prepaid recorded delivery or registered post, or any other form equivalent thereto (or, in the alternative, by any other means sufficient under applicable law, rules and regulations) at the addresses referred to in Section 5 hereof shall be valid and sufficient for all purposes and hereby waives to the fullest extent it may effectively do so any challenges to the validity of service of process if service is given in accordance herewith; and each party hereto agrees to, and irrevocably waives to the fullest extent it may effectively do so any objection based on forum non conveniens or venue not to appear in such courts.

10. EACH OF THE PARTIES HERETO HEREBY IRREVOCABLY AND UNCONDITIONALLY WAIVES TRIAL BY JURY IN ANY LEGAL ACTION OR PROCEEDING RELATING TO ANY OF THE AGREEMENTS AND FOR ANY COUNTERCLAIM THEREIN.

11. The Guarantor acknowledges that the Senior Creditors will have no adequate remedy at law if the Guarantor fails to perform its obligations under this Agreement. In such event, the Guarantor agrees that the Senior Creditors shall have the right, in addition to any other rights it may have, to specific performance of such obligations and that the Guarantor will not take any action to impede the Senior Creditor’s efforts to enforce such right of specific performance.

12. If, at any time, any provision hereof is or becomes illegal, invalid or unenforceable in any respect under the law of any jurisdiction, neither the legality, validity or enforceability of the remaining provisions hereof nor the legality, validity or enforceability of such provision under the law of any other jurisdiction shall in any way be affected or impaired thereby.

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13. This Agreement shall continue in force and effect until the earlier of: (i) the Senior Credit being paid in full and (ii) the purchase of the Senior Credit in full by the Guarantor as described in Section 1, at which time this Agreement shall terminate and be of no further force and effect.

14. This Agreement constitutes the only agreement between the parties relating to the Purchase Obligation granted hereunder and supersedes and extinguishes any prior drafts, agreements, undertakings, representations, warranties and arrangements of any nature whatsoever, whether or not in writing, relating thereto.

15. This Agreement may be executed in multiple counterparts, each of which shall be deemed an original, but all of which together shall constitute one and the same instrument.

[Remainder of Page Intentionally Left Blank]

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IN WITNESS WHEREOF, the parties have hereunto signed their names as of the date first above written.

Section 1.4 of this Agreement is hereby

acknowledged and agreed to as of the

date thereof.

PEAKS TRUST 2009-1, a Delaware statutory

trust