Citigroup Inc. 399 Park Avenue New York, NY 10022

Exhibit 10.33

CONFIDENTIAL

Citigroup Inc.

399 Park Avenue

New York, NY 10022

December 30, 2010

Discover Bank

12 Read’s Way

New Castle, Delaware 19720

Attention: Michael F. Rickert

Vice President, Chief Financial Officer

and Treasurer

The Student Loan Corporation

750 Washington Blvd.

Stamford, Connecticut 06901

Attention: Michael J. Reardon

Chief Executive Officer

Re: Amendment to Purchase Price Adjustment Agreement

Ladies and Gentlemen:

Reference is made to (a) the Purchase Price Adjustment Agreement, dated as of September 17, 2010 (the “Purchase Price Adjustment Agreement”), by and among Citibank, N.A., a national banking association (“CBNA”), The Student Loan Corporation, a Delaware corporation (the “Company”), and Discover Bank, a Delaware banking corporation (“Buyer” and, collectively with CBNA and the Company, the “Parties”) and (b) the Commutation Agreement and Release, effective as of December 30, 2010, by and between United Guaranty Commercial Insurance Company of North Carolina, a North Carolina insurer (“United Guaranty”) and the Company (the “Commutation Agreement”). Capitalized terms not otherwise defined herein shall have the same meanings assigned to them in the Purchase Price Adjustment Agreement unless otherwise noted.

The Parties hereby acknowledge and agree that, pursuant to Section 4.10 of the Purchase Price Adjustment Agreement, Section 2.2(c)(ii) of the Agreement is hereby amended in its entirety as follows:

(ii) “Closing Adjustment Amount” means (A) the Aggregate Merger Consideration, minus (B) the Closing Trust Certificate Purchase Price, plus (C) the absolute value of all Reimbursable Liabilities, minus (D) all cash or cash equivalents reflected on the Closing Balance Sheet (excluding any cash and cash equivalents taken into account in determining the Closing Trust Certificate Purchase Price), plus (E) $16,300,000.00, minus (F) the Release Payment (as defined in the Commutation Agreement) in the event that such payment is made to the Company after the Closing,

The Parties hereby acknowledge and agree that, pursuant to Section 4.10 of the Agreement, Section 2.2(c)(iv) of the Purchase Price Adjustment Agreement is hereby amended in its entirety as follows:

(iv) “Pre-Closing Adjustment Amount” means: (A) the Aggregate Merger Consideration, minus (B) the Estimated Trust Certificate Purchase Price, plus (C) the absolute value of all Reimbursable Liabilities, minus (D) all cash or cash equivalents reflected on the Estimated Pro Forma Balance Sheet (excluding any cash and cash equivalents taken into account in determining the Estimated Trust Certificate Purchase Price), plus (E) $16,300,000.00,

The Parties hereby acknowledge and agree that, pursuant to Section 4.10 of the Purchase Price Adjustment Agreement, a new Section 3.3 of the Purchase Price Adjustment Agreement is hereby inserted as follows:

“Section 3.3 Payments to Company Employees

(a) The Parties acknowledge that all Liabilities related to the transaction awards payable under the Company’s Retention and Severance Program (the “Change of Control Payments”) constitute both (i) Reimbursable Liabilities pursuant to this Agreement and (ii) Excluded Liabilities (as defined in the Indemnification Agreement). Accordingly, CBNA acknowledges and agrees that the Buyer Indemnified Parties (as defined in the Indemnification Agreement) are entitled to indemnification from CBNA under the Indemnification Agreement with respect to the Change of Control Payments.

(b) At the request of CBNA, Buyer has agreed that, provided that CBNA complies with its obligations in Section 3.3(c), Buyer and the Company will not include the Change of Control Payments as Reimbursable Liabilities to be taken into account in connection with the calculations of the Pre-Closing Adjustment Amount and Post-Closing Adjustment Amount pursuant to this Agreement.

(c) CBNA agrees that with respect to each of the Change of Control Payments, no later than 30 days following the date on which Buyer (or the Company, as applicable) provides written notice to CBNA that a Change of Control Payment has been made by Buyer, the Company or one of their respective Affiliates to a Company Employee, CBNA shall reimburse Buyer (or the Company, as applicable) for the amount of such payment, plus all expenses and taxes incurred by Buyer, the Company or their applicable Affiliate arising from any and all Change of Control Payments by wire transfer of immediately available funds to an account specified in writing by Buyer.

The Parties hereby acknowledge and agree that, pursuant to Section 4.10 of the Agreement, Section 2.2(c) of the Purchase Price Adjustment Agreement is hereby amended to include the following subsections:

(ix) “Change of Control Payments” shall have the meaning set forth in Section 3.3(a).

(x) “Commutation Agreement” shall mean the Commutation Agreement and Release, effective as of December 30, 2010, by and between United Guaranty Commercial Insurance Company of North Carolina, a North Carolina insurer and the Company.

(xi) “United Guaranty” shall mean United Guaranty Commercial Insurance Company of North Carolina, a North Carolina insurer.

CBNA hereby represents and warrants to, and agrees with, Buyer that none of CBNA, its Affiliates, the Company or any of the Company’s Affiliates is a party to any Contract with United Guaranty or any of United Guaranty’s Affiliates relating to or entered into in connection with the Commutation Agreement, other than any reinsurance arrangements entered into between CBNA and United Guaranty with respect to insurance policies not subject to the Commutation Agreement. Except as modified hereby, the terms of the Purchase Price Agreement shall remain in full force and effect. This letter may be signed in counterparts, each of which shall be deemed an original and all of which together will be deemed one and the same instrument.

[SIGNATURE PAGE FOLLOWS]

ACCEPTED AND AGREED AS OF THE

DATE AND YEAR FIRST SET FORTH ABOVE: