Exhibit 10.1

AMENDMENT TO MANAGEMENT AGREEMENT

THIS AMENDMENT TO MANAGEMENT AGREEMENT (this “Amendment”) is made and entered into as of this 2 day of May, 2018 by and between MTGE Investment Corp., a Maryland corporation (the “Company”), MTGE TRS, LLC, a Delaware limited liability company and a subsidiary of the Company (“MTGE TRS”), MTGE Management, LLC, a Delaware limited liability company (the “Manager”), and Annaly Capital Management, Inc., a Maryland corporation (“Parent”), solely for the purposes of Section 7 hereof. The Company, MTGE TRS, the Manager and Parent are each sometimes referred to herein as a “Party” and collectively as the “Parties”. Capitalized terms used herein but not defined shall have the meanings ascribed to such terms in the Merger Agreement (as defined below). For the avoidance of doubt, any reference herein to the Company shall mean, from and after the Effective Time, the Surviving Corporation.

RECITALS

WHEREAS, the Company (f/k/a American Capital Mortgage Investment Corp.), MTGE TRS (f/k/a American Capital Mortgage Investment TRS, LLC) and the Manager (f/k/a American Capital MTGE Management, LLC) previously entered into that certain Amended and Restated Management Agreement, dated as of July 1, 2016 (the “Management Agreement”);

WHEREAS, contemporaneously with the entry into this Amendment, the Company has entered into that certain Agreement and Plan of Merger, dated as of May 2, 2018, by and among Parent, Mountain Merger Sub Corporation, a Maryland corporation and a wholly owned subsidiary of Parent, and the Company (as may be amended from time to time, the “Merger Agreement”); and

WHEREAS, in connection with the Merger Agreement and the transactions contemplated thereby, the Parties desire, subject to the terms and conditions set forth herein, to amend the Management Agreement to provide, among other things, for: (i) the termination of the Management Agreement effective as of the Termination Time (as defined below); and (ii) certain additional obligations and agreements among the Parties and for the benefit of Parent.

NOW THEREFORE, in consideration of the mutual covenants and other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the Parties hereby agree as follows:

1. TERMINATION

Notwithstanding anything to the contrary in the Management Agreement, the Parties hereby agree that the Management Agreement and all rights and obligations of the Parties thereunder shall be terminated effective as of one (1) month following the Closing Date (as defined in the Merger Agreement) (the “Termination Time”, and such termination, the “Termination”) and without any further notice or action by each of the Parties, except that: (i) the Company shall reimburse the Manager for the Unreimbursed Expenses (as defined below) within five (5) business days following delivery to the Company of the Manager’s report of such expenses; (ii) the Company shall pay to the Manager the Accrued Management Fees (as defined below) within five (5) business days following delivery to the Company of the Manager’s written statement setting forth the

computation of such fees; (iii) the Manager shall take those actions required by Section 13 of the Management Agreement upon the terms and conditions set forth therein; and (iv) Sections 3(c), 5, 7 (to the extent any Unreimbursed Expenses (as defined below) have previously been incurred or are incurred in connection with the Termination (which includes, for the avoidance of doubt, all third-party legal, expert and other fees and expenses relating to any actions, proceedings, lawsuits, demands, causes of action and claims, whether actual or threatened, made by or against the Company in connection with, or after public announcement of, the Merger Agreement, the Offer, the Merger or other Transactions)), 8, 13 and 14 of the Management Agreement shall survive the Termination. The Termination shall be deemed a Termination Without Cause (as defined in the Management Agreement) for the purposes of Section 3(c) of the Management Agreement. For the avoidance of doubt, any covenant or agreement of the Parties contained in this Amendment which by its terms contemplates performance after the Termination Time shall survive the Termination, including, without limitation, such covenants and agreements contained in this Section 1 and Sections 4 through 11 hereof. For purposes of this Amendment, “Unreimbursed Expenses” shall mean unreimbursed expenses incurred by the Manager pursuant to the terms of the Management Agreement prior to the Termination Time in the ordinary course of business and consistent with past practice, to the extent reimbursable pursuant to Section 7 of the Management Agreement (including, for the avoidance of doubt, pursuant to the last sentence of Section 7(c) of the Management Agreement), subject to compliance with the provisions of Section 7(c) of the Management Agreement, and “Accrued Management Fees” shall mean an amount equal to the greater of (A) management fees payable for the period ending on the date ninety (90) days after the date hereof or (B) unpaid management fees accrued under Section 6 of the Management Agreement prior to the Termination Time, in each case calculated in accordance with the terms of the Management Agreement and whereby “Equity” (as defined in the Management Agreement) shall be determined as of the end of the month which occurred immediately prior to the Closing Date for any period following the Closing Date; provided, however, that the management fees for the month in which the Termination Time occurs shall be pro-rated based on the number of days in such month that have elapsed up to and including the date on which the Termination Time occurs compared to the total number of days in such month.

Following the Closing Date and until the Termination Time, the Manager hereby agrees to continue to provide the services and activities (other than investment advisory or investment management services) necessary or appropriate to allow for an orderly transition of the management of the Company’s assets to Parent or Parent’s manager, as Parent may determine, or as otherwise reasonably requested by Parent. For the avoidance of doubt, the Manager shall not provide data migration services (but nothing herein shall limit Parent’s ability to retain a third party service provider at its sole cost to provide such services, and the Manager shall reasonably cooperate at Parent’s sole cost in connection therewith).

The Parties shall comply in all respects with all the terms and conditions of the Management Agreement and shall not amend the Management Agreement or this Amendment, in each case without the prior written consent of Parent. Except as specifically permitted or required by the Merger Agreement, as required by law, or as consented to in writing by Parent (which consent shall not be unreasonably withheld, delayed or conditioned), the Manager shall conduct its activities with respect to the Company and the Company’s subsidiaries in the ordinary course of business consistent with past practice in all material respects.

2

2. TERMINATION PAYMENT

In consideration for the Termination and the other promises, undertakings and releases of the Manager hereunder, the Company shall pay the termination fee amount of $41,659,461.54 (the “Termination Payment”), which shall be the “Termination Fee” under the Management Agreement, to the Manager as follows: (i) on the Closing Date, $36,659,461.54 and (ii) on the date the Termination Time occurs, $5,000,000 (such payment, the “Post-Closing Termination Payment”), subject in each case to the Manager’s compliance with the terms and conditions of the Management Agreement (including, for the avoidance of doubt, as amended by this Amendment). Notwithstanding anything to the contrary in the Management Agreement, the Parties acknowledge and agree that the Termination Payment, together with any Unreimbursed Expenses and Accrued Management Fees payable hereunder, if any, shall be the entire amount payable to the Manager or any of its affiliates in connection with the Termination and thereafter under or in respect of the Management Agreement, as amended by this Amendment, unless the Merger Agreement is validly terminated pursuant to Section 9.1 of the Merger Agreement without the occurrence of the Effective Time, and except with respect to those rights and obligations which, pursuant to Section 1 of this Amendment, survive the Termination. For the avoidance of doubt, prior to the Termination, the Manager shall only be entitled to receive payments from the Company that are consistent with past practice and pursuant to the terms of the Management Agreement; provided that this sentence shall not be deemed to limit any bona fide claims the Manager may have (and payment thereof) pursuant to Sections 3(c), 7 (to the extent any Unreimbursed Expenses have previously been incurred or are incurred in connection with the Termination (which includes, for the avoidance of doubt, all third-party legal, expert and other fees and expenses relating to any actions, proceedings, lawsuits, demands, causes of action and claims, whether actual or threatened, made by or against the Company in connection with, or after public announcement of, the Merger Agreement, the Offer, the Merger or other Transactions)), 8, 13 or 14 of the Management Agreement.

3. NON-SOLICITATION

From and after the date hereof until the earlier of the Acceptance Time or the date, if any, on which the Merger Agreement is validly terminated pursuant to Section 9.1 of the Merger Agreement without the occurrence of the Effective Time, the Manager agrees that it shall not intentionally and knowingly take any action, directly or indirectly, that is prohibited to be taken by the Company’s Representatives (as defined in the Merger Agreement), and shall otherwise comply with all obligations applicable to the Company’s Representatives, pursuant to Section 6.3 of the Merger Agreement. The Manager shall not intentionally and knowingly take any action that would reasonably be expected to cause any of the conditions to the Offer or the Merger to be failed to be satisfied, other than actions which the Company is permitted to take pursuant to the Merger Agreement or as required by applicable law. For the avoidance of doubt, nothing in this Amendment shall (i) restrict the Manager from assisting the Company in discussions or negotiations regarding an Acquisition Proposal with any Person, solely to the extent to which the Company is permitted to, and does, engage in such discussions or negotiations with such Person pursuant to Section 6.3 of the Merger Agreement, in each case in all respects in accordance with the Merger Agreement or (ii) limit or otherwise modify the Company’s obligations pursuant to Section 6.3 of the Merger Agreement. Notwithstanding the foregoing, actions or inactions taken or not taken by any affiliate of the Manager in its capacity as a stockholder of the Company with

3

respect to the Company’s common stock owned by such stockholder shall not be deemed to be a breach by the Manager of this Section 3. Nothing in Section 6.3 of the Merger Agreement or this Section 3 shall require the Manager to issue any press release or make any public statement.

5. WAIVER

The Parties hereby waive, whether exercisable now or at any time in the future, any and all rights to notice under the Management Agreement, to the extent relating to the transactions contemplated by the Merger Agreement or this Amendment.

6. RELEASE

Effective as of, and contingent upon, the Termination, each Party and its affiliates hereby fully and unconditionally release and forever discharge each other Party and the affiliates of each other Party (including, as applicable, the Company Subsidiaries, Parent, the affiliates of Parent and the Surviving Corporation, and the affiliates of the Manager), and their respective administrators, executors, representatives, successors and assigns, from any and all actions, causes of action, suits, debts, accounts, covenants, liabilities, disputes, agreements, promises, damages, judgments, executions, claims, and demands whatsoever in law or in equity that they ever had, now have, or that they or their administrators, executors, representatives, successors and assigns hereafter can or may have, arising under or pursuant to the Management Agreement, except with respect to those rights and obligations which, pursuant to Section 1 of this Amendment, survive the Termination.

7. SUCCESSORS AND ASSIGNS; THIRD PARTY BENEFICIARIES; GUARANTEE

This Amendment shall be binding upon and inure to the benefit of the Parties and their respective heirs, personal representatives, successors and assigns as provided in this Amendment. Parent and its affiliates, successors and assigns shall be entitled to rely on this Amendment in connection with the consummation of the transactions contemplated by the Merger Agreement. Parent shall be an express third party beneficiary of this Amendment (including applicable provisions of the Management Agreement) and Parent shall be entitled to enforce such provisions as though it was a party hereto or thereto.

Effective as of, and contingent upon, the Closing, Parent fully and unconditionally guarantees the timely and full performance of the indemnification and payment obligations of the Company under this Amendment and the Management Agreement as if it were the Company. Parent waives promptness, diligence, notice of acceptance and any other notice with respect to its guaranteed obligations and this paragraph and all demands whatsoever. Parent covenants that the guarantee in this paragraph will not be discharged, except by complete performance of the obligations contained in this Amendment. In addition, effective as of, and contingent upon, the Closing, Parent shall deposit the Post-Closing Termination Payment into an escrow fund or provide to the Manager a letter of credit in respect of the Post-Closing Termination Payment, in each case upon terms and conditions reasonably acceptable to the Manager and Parent.

4

8. ENTIRE AGREEMENT

The Management Agreement and this Amendment constitute the entire understanding between the Parties with respect to the subject matter hereof and supersede all prior discussions between them relating thereto. Any amendment or modification to this Amendment shall be effective only if in writing and signed by each Party, with the prior written consent of Parent. This Amendment shall terminate and be of no force or effect in the event that the Merger Agreement is terminated without the occurrence of the Effective Time.

9. COUNTERPARTS

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

10. PAYMENTS

All payments to be made pursuant to Section 1 and Section 2 hereof shall be made by wire transfer, in immediately available funds, to the account set forth on Schedule 1 or such other account designated by the Manager in writing at least three (3) business days prior to such payment.

11. GOVERNING LAW

This Amendment shall be governed by and interpreted and construed in accordance with the laws of the State of New York, without regard to conflict of laws principles thereof.

[Signature Pages Follow]

5

IN WITNESS WHEREOF, the Parties have executed this Amendment to Management Agreement as of the day and year first above written.

[Signature Page to Amendment to Management Agreement]