Exhibit 10.1

THIRD AMENDMENT TO AMENDED AND RESTATED

SENIOR PREFERRED STOCK PURCHASE AGREEMENT

THIRD AMENDMENT dated as of August 17, 2012, to the AMENDED AND RESTATED SENIOR PREFERRED STOCK PURCHASE AGREEMENT dated as of September 26, 2008, between the UNITED STATES DEPARTMENT OF THE TREASURY (“ Purchaser ”), and FEDERAL HOME LOAN MORTGAGE CORPORATION (“ Seller ”), acting through the Federal Housing Finance Agency (the “ Agency ”) as its duly appointed conservator (the Agency in such capacity, “ Conservator ”).

Background

A. Purchaser and Seller have heretofore entered into the Amended and Restated Senior Preferred Stock Purchase Agreement dated as of September 26, 2008 (the “ Amended and Restated Agreement ”).

B. In the Amended and Restated Agreement, Purchaser committed itself to provide to Seller, on the terms and conditions provided in the Amended and Restated Agreement, immediately available funds in an amount as determined from time to time as provided in the Amended and Restated Agreement, but in no event in an aggregate amount exceeding $100,000,000,000.

C. In consideration for Purchaser’s commitment, Seller agreed to sell, and did sell, to Purchaser 1,000,000 shares of senior preferred stock, in the form of the Variable Liquidation Preference Senior Preferred Stock of Seller attached as Exhibit A to the Amended and Restated Agreement, with an initial liquidation preference equal to $1,000 per share.

D. The Amended and Restated Agreement provides that the aggregate liquidation preference of the outstanding shares of senior preferred stock shall be automatically increased by an amount equal to the amount of each draw under Purchaser’s funding commitment, and the senior preferred stock sold by Seller to Purchaser provides that the senior preferred stock shall accrue dividends at the annual rate per share equal to 10 percent on the then-current liquidation preference.

E. Purchaser and Seller have heretofore entered into the Amendment dated as of May 6, 2009, to the Amended and Restated Agreement (the “ First Amendment ”).

F. In the First Amendment, Purchaser increased to $200,000,000,000 the maximum aggregate amount permitted to be provided to Seller under the Amended and Restated

Agreement, and amended the terms of the Amended and Restated Agreement in certain other respects.

G. Purchaser and Seller have heretofore entered into the Second Amendment dated as of December 24, 2009, to the Amended and Restated Agreement (the “ Second Amendment ”).

H. In the Second Amendment, Purchaser modified the maximum aggregate amount permitted to be provided to Seller under the Amended and Restated Agreement, as previously amended, by replacing the fixed maximum aggregate amount with the new formulaic maximum amount specified therein, and amended the terms of the Amended and Restated Agreement, as previously amended, in certain other respects.

I. Purchaser and Seller are each authorized to enter into this Third Amendment to the Amended and Restated Agreement (“ this Third Amendment ”) that (i) includes an agreement by Seller to modify the dividend rate provision of the senior preferred stock sold by Seller to Purchaser, and (ii) amends the terms of the Amended and Restated Agreement, as previously amended, in certain other respects.

THEREFORE, for and in consideration of the mutual agreements herein contained and for other good and valuable consideration, the receipt and sufficiency of which is hereby acknowledged, Purchaser and Seller agree as follows:

Terms and Conditions

Capitalized terms used and not defined in this Third Amendment shall have the respective meanings given such terms in the Amended and Restated Agreement, as amended by the First Amendment and the Second Amendment (the Amended and Restated Agreement, as amended by the First Amendment and the Second Amendment, being the “ Existing Agreement ”).

With respect to the Certificate of Creation, Designation, Powers, Preferences, Rights, Privileges, Qualifications, Limitations, Restrictions, Terms and Conditions of Variable Liquidation Preference Senior Preferred Stock (Par Value $1.00 Per Share) dated September 7, 2008 (the “ Senior Preferred Stock Certificate ”), sold by Seller to Purchaser and purchased by Purchaser from Seller, Seller agrees either to amend the existing paragraph 2(a) of the Senior Preferred Stock Certificate, or to issue a replacement Senior Preferred Stock Certificate, in either case so that, by not later than September 30, 2012, paragraph 2(a) reads as follows:

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(a) For each Dividend Period from the date of the initial issuance of the Senior Preferred Stock through and including December 31, 2012, holders of outstanding shares of Senior Preferred Stock shall be entitled to receive, ratably, when, as and if declared by the Board of Directors, in its sole discretion, out of funds legally available therefor, cumulative cash dividends at the annual rate per share equal to the then-current Dividend Rate on the then-current Liquidation Preference. For each Dividend Period from January 1, 2013, holders of outstanding shares of Senior Preferred Stock shall be entitled to receive, ratably, when, as and if declared by the Board of Directors, in its sole discretion, out of funds legally available therefor, cumulative cash dividends in an amount equal to the then-current Dividend Amount. Dividends on the Senior Preferred Stock shall accrue from but not including the date of the initial issuance of the Senior Preferred Stock and will be payable in arrears when, as and if declared by the Board of Directors quarterly on March 31, June 30, September 30 and December 31 of each year (each, a “Dividend Payment Date”), commencing on December 31, 2008. If a Dividend Payment Date is not a “Business Day,” the related dividend will be paid not later than the next Business Day with the same force and effect as though paid on the Dividend Payment Date, without any increase to account for the period from such Dividend Payment Date through the date of actual payment. “Business Day” means a day other than (i) a Saturday or Sunday, (ii) a day on which New York City banks are closed, or (iii) a day on which the offices of the Company are closed.

If declared, the initial dividend will be for the period from but not including the date of the initial issuance of the Senior Preferred Stock through and including December 31, 2008. Except for the initial Dividend Payment Date, the “Dividend Period” relating to a Dividend Payment Date will be the period from but not including the preceding Dividend Payment Date through and including the related Dividend Payment Date. For each Dividend Period from the date of the initial issuance of the Senior Preferred Stock through and including December 31, 2012, the amount of dividends payable on the initial Dividend Payment Date or for any Dividend Period through and including December 31, 2012, that is not a full calendar quarter shall be computed on the basis of 30-day months, a 360-day year and the actual number of days elapsed in any period of less than one month. For the avoidance of doubt, for each Dividend Period from the date of the initial issuance of the Senior Preferred Stock through and including December 31, 2012, in the event that the Liquidation Preference changes in the middle of a Dividend Period, the amount of dividends payable on the Dividend Payment Date at the end of such Dividend Period shall take into account such change in Liquidation Preference and shall be computed at the Dividend Rate on each Liquidation Preference based on the portion of the Dividend Period that each Liquidation Preference was in effect.

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With respect to the Senior Preferred Stock Certificate sold by Seller to Purchaser and purchased by Purchaser from Seller, Seller agrees either to amend the existing paragraph 2(c) of the Senior Preferred Stock Certificate, or to issue a replacement Senior Preferred Stock Certificate, in either case so that, effective September 30, 2012, paragraph 2(c) reads as follows:

(c) For each Dividend Period from the date of the initial issuance of the Senior Preferred Stock through and including December 31, 2012, “Dividend Rate” means 10.0%; provided, however, that if at any time the Company shall have for any reason failed to pay dividends in cash in a timely manner as required by this Certificate, then immediately following such failure and for all Dividend Periods thereafter until the Dividend Period following the date on which the Company shall have paid in cash full cumulative dividends (including any unpaid dividends added to the Liquidation Preference pursuant to Section 8) the “Dividend Rate” shall mean 12.0%.

For each Dividend Period from January 1, 2013, through and including December 31, 2017, the “Dividend Amount” for a Dividend Period means the amount, if any, by which the Net Worth Amount at the end of the immediately preceding fiscal quarter, less the Applicable Capital Reserve Amount, exceeds zero. For each Dividend Period from January 1, 2018, the “Dividend Amount” for a Dividend Period means the amount, if any, by which the Net Worth Amount at the end of the immediately preceding fiscal quarter exceeds zero. In each case, “Net Worth Amount” means (i) the total assets of the Company (such assets excluding the Commitment and any unfunded amounts thereof) as reflected on the balance sheet of the Company as of the applicable date set forth in this Certificate, prepared in accordance with GAAP, less (ii) the total liabilities of the Company (such liabilities excluding any obligation in respect of any capital stock of the Company, including this Certificate), as reflected on the balance sheet of the Company as of the applicable date set forth in this Certificate, prepared in accordance with GAAP. “Applicable Capital Reserve Amount” means, as of any date of determination, for each Dividend Period from January 1, 2013, through and including December 31, 2013, $3,000,000,000; and for each Dividend Period occurring within each 12-month period thereafter, $3,000,000,000 reduced by an equal amount for each such 12-month period through and including December 31, 2017, so that for each Dividend Period from January 1, 2018, the Applicable Capital Reserve Amount shall be zero. For the avoidance of doubt, if the calculation of the Dividend Amount for a Dividend Period does not exceed zero, then no Dividend Amount shall accrue or be payable for such Dividend Period.

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Section 3.2 of the Existing Agreement is hereby amended to read as follows:

3.2. Periodic Commitment Fee . (a) Commencing March 31, 2011, Seller shall pay to Purchaser quarterly, on the last day of March, June, September and December of each calendar year (each a “Periodic Fee Date”), a periodic commitment fee (the “Periodic Commitment Fee”). The Periodic Commitment Fee shall accrue from January 1, 2011.

(b) The Periodic Commitment Fee is intended to fully compensate Purchaser for the support provided by the ongoing Commitment following December 31, 2010. The amount of the Periodic Commitment Fee shall be set not later than December 31, 2010 with respect to the ensuing five-year period, shall be reset every five years thereafter and shall be determined with reference to the market value of the Commitment as then in effect. The amount of the Periodic Commitment Fee shall be mutually agreed by Purchaser and Seller, subject to their reasonable discretion and in consultation with the Chairman of the Federal Reserve; provided , that Purchaser may waive the Periodic Commitment Fee for up to one year at a time, in its sole discretion, based on adverse conditions in the United States mortgage market.

(c) At the election of Seller, the Periodic Commitment Fee may be paid in cash or by adding the amount thereof ratably to the liquidation preference of each outstanding share of Senior Preferred Stock so that the aggregate liquidation preference of all such outstanding shares of Senior Preferred Stock is increased by an amount equal to the Periodic Commitment Fee. Seller shall deliver notice of such election not later than three (3) Business Days prior to each Periodic Fee Date. If the Periodic Commitment Fee is not paid in cash by 12:00 pm (New York time) on the applicable Periodic Fee Date (irrespective of Seller’s election pursuant to this subsection), Seller shall be deemed to have elected to pay the Periodic Commitment Fee by adding the amount thereof to the liquidation preference of the Senior Preferred Stock, and the aggregate liquidation preference of the outstanding shares of Senior Preferred Stock shall thereupon be automatically increased, in the manner contemplated by the first sentence of this section, by an aggregate amount equal to the Periodic Commitment Fee then due.

(d) Notwithstanding anything to the contrary in paragraphs (a), (b), or (c) above, and in consideration of the modification made to the Senior Preferred Stock effective September 30, 2012, for each quarter commencing January 1, 2013, and continuing for as long as paragraph 2 of the Senior Preferred Stock remains in form and content substantially the same as the form and content of the Senior Preferred Stock in effect on September 30, 2012, no Periodic Commitment Fee shall be set, accrue, or be payable.

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Section 5.4 of the Existing Agreement is hereby amended to read as follows:

5.4. Transfer of Assets. Seller shall not, and shall not permit any of its subsidiaries to, in each case without prior written consent of Purchaser, sell, transfer, lease or otherwise dispose of (in one transaction or a series of related transactions) all or any portion of its assets (including Equity Interests in other persons, including subsidiaries), whether now owned or hereafter acquired (any such sale, transfer, lease or disposition, a “ Disposition ”), other than Dispositions for fair market value:

(a) to a limited life regulated entity (“ LLRE ”) pursuant to Section 1367(i) of the FHE Act;

(b) of assets and properties in the ordinary course of business, consistent with past practice;

(c) of assets and properties having fair market value individually or in aggregate less than $250,000,000 in one transaction or a series of related transactions;

(d) in connection with a liquidation of Seller by a receiver appointed pursuant to Section 1367(a) of the FHE Act;

(e) of cash or cash equivalents for cash or cash equivalents; or

(f) to the extent necessary to comply with the covenant set forth in Section 5.7 below.

Section 5.7 of the Existing Agreement is hereby amended to read as follows:

5.7. Mortgage Assets. Seller shall not own, as of any applicable date, Mortgage Assets in excess of (i) on December 31, 2012, $650 billion, or (ii) on December 31 of each year thereafter, 85.0% of the aggregate amount of Mortgage Assets that Seller was permitted to own as of December 31 of the immediately preceding calendar year; provided , that in no event shall Seller be required under this Section 5.7 to own less than $250 billion in Mortgage Assets.

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Section 5 of the Existing Agreement is hereby amended by inserting after section 5.10 the following:

5.11. Annual Risk Management Plans. Not later than December 15, 2012, and not later than December 15 of each year thereafter while Seller remains in conservatorship pursuant to Section 1367 of the FHE Act, Seller shall, under the direction of Conservator, deliver a risk management plan to Purchaser. Each annual risk management plan shall set out Seller’s strategy for reducing its enterprise-wide risk profile and shall describe, in reasonable detail, the actions Seller will take, to reduce both the financial and operational risk associated with each reportable business segment of Seller. Plans delivered subsequent to December 15, 2012 shall also include an assessment of Seller’s performance relative to the planned actions described in the prior year’s plan. The submission of annual risk management plans under this section shall not in any way limit or affect the Agency in any of its capacities to carry out its statutory responsibilities, including but not limited to providing direction to and oversight of Seller.”

Except as expressly modified by this Third Amendment, the Existing Agreement shall continue in full force and effect.

This Third Amendment shall not become effective until it has been executed by both of Purchaser and Seller. When this Third Amendment has been so executed, it shall become effective as of the date first above written.

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