Exhibit 2.1

AGREEMENT AND Plan of Merger

THIS AGREEMENT AND PLAN OF MERGER (the “Agreement”) by and between Farmers and Merchants Bancshares, Inc., a Maryland corporation (“Parent”) and Carroll Bancorp, Inc., a Maryland corporation (“Carroll”) is dated as of September 28, 2020.

RECITALS

WHEREAS, Parent, Anthem Acquisition Corp. (“Merger Sub”), and Carroll entered into an Agreement and Plan of Merger, dated as of March 6, 2020 (the “Parent Merger Agreement”), pursuant to which Merger Sub will be merged with and into Carroll, with Carroll as the surviving corporation and wholly-owned subsidiary of Parent (the “Parent Merger”);

WHEREAS, the parties to the Parent Merger Agreement contemplate that the Parent Merger will be effected at 12:01 a.m., local time, on October 1, 2020;

WHEREAS, the Parent Merger Agreement provides that Carroll will be merged with and into Parent, with Parent as the surviving corporation (the “Roll-Up Merger”), immediately following the effective time of the Parent Merger pursuant to an agreement and plan of merger;

WHEREAS, the Parent Merger Agreement further provides, and Parent and Carroll intend, that the Roll-Up Merger shall qualify as a parent-subsidiary liquidation under Section 332 of the Internal Revenue Code of 1986, as amended (the “Code”), and that the agreement and plan of merger with respect thereto constitute a plan of liquidation with respect to such liquidation; and

WHEREAS, each of the Boards of Directors of Parent and Carroll has determined that the Roll-Up Merger is in the best interests of Parent and Carroll, has approved the Roll-Up Merger, and has approved and authorized Parent and Carroll, respectively, to enter into this Agreement.

NOW, THEREFORE, in consideration of the premises and mutual covenants and agreements contained herein, and other good and valuable consideration, the receipt of which is hereby acknowledged, the parties, intending to be legally bound, hereby agree as follows:

ARTICLE I

Subject to the terms and conditions of this Agreement, Carroll shall be merged with and into Parent (and the separate existence of Carroll shall cease and Parent shall be the surviving institution) pursuant to, and shall have the effect provided in and by, Section 3-114 of the Maryland General Corporation Law (the “MGCL”).

ARTICLE II

The name of the surviving corporation in the Roll-Up Merger (hereinafter referred to as the “Surviving Corporation”) shall be “Farmers and Merchants Bancshares, Inc”.

ARTICLE III

The business of the Surviving Corporation shall be that of a Maryland corporation and a financial holding company registered with the Board of Governors of the Federal Reserve System (the “FRB”) under the Bank Holding Company Act of 1956, as amended. This business shall be conducted by the Surviving Corporation at its principal office at 4510 Lower Beckleysville Road, Suite H, Hampstead, Maryland 21074, at all offices and facilities of Parent and Carroll as of the Effective Time (as defined in Section 9.2 below).

ARTICLE IV

Section 4.1.     At the Effective Time, the separate existence of Carroll shall cease and the corporate existence of Parent, as the Surviving Corporation, shall continue unaffected and unimpaired by the Roll-Up Merger, and the Surviving Corporation shall be deemed to be the same business and corporate entity as each of Parent and Carroll. At the Effective Time, by virtue of the Roll-Up Merger and without any further act, deed, conveyance or other transfer, all of the property, rights, powers and franchises of Carroll shall vest in Parent as the Surviving Corporation, and the Surviving Corporation shall be subject to and be deemed to have assumed all of the debts, liabilities, obligations and duties of Carroll, and to have succeeded to all of the relationships, fiduciary or otherwise, of Carroll as fully and to the same extent as if such property, rights, powers, franchises, debts, liabilities, obligations, duties and relationships had been originally acquired, incurred or entered into by the Surviving Corporation; provided, however, that the Surviving Corporation shall not, through the Roll-Up Merger, acquire power to engage in any business or to exercise any right, privilege or franchise which is not conferred on the Surviving Corporation by the laws of the State of Maryland or the laws of the United States.

Section 4.2.     The Surviving Corporation, upon the consummation of the Roll-Up Merger and without any order or other action on the part of any court or otherwise, shall hold and enjoy all rights of property, franchises and interests, including appointments, designations and nominations, and all other rights and interests as agent, trustee, executor, administrator, registrar of stocks and bonds, guardian of estates, conservator, assignee, receiver and committee of estates of incompetents, bailee or depository of personal property, and in every other fiduciary and/or custodial capacity, in the same manner and to the same extent as such rights, franchises and interests were held or enjoyed by Carroll immediately prior to the Effective Time.

ARTICLE V

Section 5.1.     At the Effective Time, all of the issued and outstanding shares of capital stock of Carroll (the “Carroll Shares”) shall, by virtue of the Roll-Up Merger and without any action on the part of the holder thereof, be canceled and retired, and no cash, securities, or other property shall be delivered in exchange therefor.

Section 5.2.     At and after the Effective Time, certificates evidencing the Carroll Shares shall not evidence any interest in Carroll.

Section 5.3.     The stock transfer book of Carroll shall be closed as of the Effective Time and, thereafter, no transfer of Carroll Shares shall be recorded therein.

- 2 -

ARTICLE VI

Section 6.1.     Upon the Effective Time, the Board of Directors of the Surviving Corporation shall be comprised of those persons serving as directors of Parent immediately prior to the Effective Time. Each director of the Surviving Corporation shall hold office until the expiration of his or her term, unless sooner removed, disqualified or deceased, or unless such director resigns, and until his successor has been elected and qualified.

Section 6.2.     Upon the Effective Time, the executive officers of the Surviving Corporation shall be comprised of those persons serving as executive officers of Parent immediately prior to the Effective Time.

ARTICLE VII

Section 7.1.     From and after the Effective Time, (a) the charter of the Surviving Corporation shall be the charter of Parent in effect immediately prior to the Effective Time and shall thereafter continue in full force and effect until further altered, amended or repealed in accordance with law, and (b) the bylaws of the Surviving Corporation shall be the bylaws of Parent in effect immediately prior to the Effective Time and shall thereafter continue in full force and effect until further altered, amended or repealed in accordance with law.

ARTICLE VIII

This Agreement may be amended by mutual consent of Parent and Carroll at any time prior to the Effective Time, except that no provision in Article IX may be amended or waived at any time pursuant to its terms.

ARTICLE IX

Section 9.1.     This Agreement and the Roll-Up Merger were adopted and approved by: (a) resolutions adopted by the board of directors of Parent at a meeting thereof held on September 21, 2020; and (b) resolutions adopted by the board of directors of Carroll at a meeting thereof held on September 21, 2020. Pursuant to Section 3-106 of the MGCL, the Roll-Up Merger need not be approved by the stockholders of Parent or Carroll.

Section 9.2.     The Merger shall be effective on the date and time the Articles of Merger reflecting the Roll-Up Merger are filed with the State Department of Assessments and Taxation of Maryland (the “Effective Time”); provided, however, that in no event shall the Effective Time be earlier than, or at the same time as, the effective date and time of the Parent Merger.

- 3 -

ARTICLE X

All notices under this Agreement shall be in writing and shall be deemed sufficient and duly given: (a) on the date established by the sender as having been personally delivered to the recipient; (b) on the date delivered by a private courier as established by the sender by evidence obtained from the courier; (c) on the date sent by electronic correspondence if sent during normal business hours of the recipient, if not, then on the next business day; or (d) on the fifth day after the date mailed, by certified or registered mail, return receipt requested, postage prepaid. Such communications, to be valid, must be addressed as follows:

if to Parent:

James R. Bosley, Jr.

President

Farmers and Merchants Bancshares, Inc.

4510 Lower Beckleysville Road, Suite H

Hampstead, Maryland 21074

E-mail: jim.bosley@fmb1919.bank

if to Carroll:     

Russell J. Grimes, Jr.

President and Chief Executive Officer

Carroll Bancorp, Inc.

1321 Liberty Road,

Sykesville, Maryland, 21784

E-mail: rgrimes@carrollcobank.com

or to such other address as such party may designate by notice to the others and shall be deemed to have been given upon receipt.

ARTICLE XI

From time to time as and when reasonably requested by the Surviving Corporation and to the extent permitted by law and at the expense of the Surviving Corporation, the officers and directors of Carroll last in office shall execute and deliver such assignments, deeds and other instruments and shall take or cause to be taken such further or other action as shall be necessary in order to vest or perfect in or to confirm of record or otherwise to the Surviving Corporation title to, and possession of, all of the property, rights, power and franchises of Carroll, including, without limitation, all rights and interests of Carroll in any fiduciary and/or custodial capacity, and otherwise to carry out the purposes of this Agreement, and the proper officers and directors of the Surviving Corporation as the receiving and surviving entity, are fully authorized to take any and all such action in the name of Carroll or otherwise.

ARTICLE XII

This Agreement is binding upon and is for the benefit of Parent and Carroll and their respective successors and permitted assigns; provided, however, that neither this Agreement nor any rights or obligations hereunder may be assigned by any party hereto to any other person without the prior consent in writing of each other party hereto. This Agreement is not made for the benefit of any person, firm, corporation or association not a party hereto and no other person, firm, corporation or association shall acquire or have any right under or by virtue of this Agreement.

- 4 -

ARTICLE XIII

Notwithstanding any other provision of this Agreement, the parties may, by mutual agreement, terminate this Agreement at any time prior to the Effective Time.

ARTICLE XIV

This Agreement shall in all respects be interpreted, enforced, and governed under the laws of the State of Maryland, without regard to Maryland’s conflict of laws rules or provisions, except to the extent federal law may be applicable. The parties hereby submit to the jurisdiction and venue of the courts of Maryland, and any legal or equitable action to enforce this or any related agreements may only be brought in the circuit courts therein.

ARTICLE XV

The parties hereto intend that the Roll-Up Merger shall qualify as a parent-subsidiary liquidation under Code Section 332, and they hereby adopt this Agreement as a plan of liquidation with respect to such liquidation.

ARTICLE XVI

Any term or provision of this Agreement which is invalid or unenforceable in any jurisdiction shall, as to that jurisdiction, be ineffective only to the extent of such invalidity or unenforceability without rendering invalid or unenforceable the remaining terms and provisions of this Agreement or affecting the validity or enforceability of any of the terms or provisions of this Agreement in any other jurisdiction. If any provision of this Agreement is so broad as to be unenforceable, the provision shall be interpreted to be only as broad as is enforceable.

ARTICLE XVII

This Agreement may be executed in several counterparts, each of which shall be deemed an original, but all of which together shall constitute one and the same instrument. The exchange of copies of this Agreement and of signature pages by facsimile transmission or electronic transmission shall constitute effective execution and delivery of this Agreement as to the parties and may be used in lieu of the original Agreement for all purposes. Signatures of the parties transmitted by facsimile shall be deemed to be their original signatures for all purposes.

[Signatures Appear on Next Page]

- 5 -

IN WITNESS WHEREOF, the parties have each caused this Agreement and Plan of Merger to be executed as of the date first above written.

ATTEST:	FARMERS AND MERCHANTS
	BANCSHARES, INC.

By:	/s/ Lynnette Kitzmiller	By:	/s/ James R. Bosley, Jr.
Name:	Lynnette Kitzmiller	Name:	James R. Bosley, Jr.
Title:	Secretary	Title:	President

ATTEST: CARROLL BANCORP, INC.

By:	/s/ Michael Gallina	By:	/s/ Russell J. Grimes, Jr.
Name:	Michael Gallina	Name:	Russell J. Grimes, Jr.
Title:	Assistant Secretary	Title:	President & CEO

- 6 -