AMENDMENT AGREEMENT NO. 3 TO AMENDED AND RESTATED CREDIT AGREEMENT

Exhibit (k)(6)

AMENDMENT AGREEMENT NO. 3 TO AMENDED AND RESTATED CREDIT AGREEMENT

This AMENDMENT AGREEMENT NO. 3 TO AMENDED AND RESTATED CREDIT AGREEMENT (this “Amendment”) is made as of March 1, 2013, by and among BLACKROCK FLOATING RATE INCOME STRATEGIES FUND, INC., a Maryland corporation (the “Borrower”), the lending institutions listed on the signature pages hereof (collectively, the “Banks”) and STATE STREET BANK AND TRUST COMPANY, as agent for itself and such other Banks (in such capacity, the “Agent”);

WHEREAS, the Borrower, the Banks and the Agent are parties to that certain Amended and Restated Credit Agreement, dated as of March 3, 2011 (as amended and in effect from time to time, the “Credit Agreement”); and

WHEREAS, the parties hereto wish to amend the Credit Agreement as more fully set forth herein;

NOW, THEREFORE, in consideration of these premises and other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereto hereby agree as follows:

§1.  Definitions. Capitalized terms which are used herein without definition and which are defined in the Credit Agreement shall have the same meanings herein as in the Credit Agreement.

§2.  Amendments to Credit Agreement.

(a)  Section 1.01 of the Credit Agreement is hereby amended by deleting the definitions of “Aggregate Commitment Amount”, “LIBOR Margin”, “Overnight Rate”, and “Termination Date” in their entirety and restating each such definition as follows:

“Aggregate Commitment Amount” means, as of any date, the aggregate of all Commitment Amounts as of such date. On the Third Amendment Effective Date, the Aggregate Commitment Amount is $280,000,000.

“LIBOR Margin” 0.80%.

“Overnight Rate” means, for any day, the higher of (a) 0.80% above the Federal Funds Rate as in effect on that day and (b) 0.80% above the Overnight LIBOR Rate as in effect on such date.

“Termination Date” means the Specified Termination Date on which the Commitments of those Banks still remaining in effect at such time are terminated in full pursuant to Section 2.08 hereof (without replacement pursuant to Section 2.08(d) such that the Aggregate Commitment Amount has been reduced to zero, or such earlier date on which the Commitments terminate or are terminated pursuant to the terms hereof.

(b)  Section 1.01 of the Credit Agreement is further amended by inserting the following definitions in the appropriate alphabetical order:

“Applicable Day” has the meaning set forth in Section 2.07(a) hereof.

“Joining Bank” has the meaning set forth in Section 2.08(d)(i) hereof.

“Reducing Bank” has the meaning set forth in Section 2.08(c) hereof.

“Reduction Amount” has the meaning set forth in Section 2.08(c) hereof.

“Reduction Notice” has the meaning set forth in Section 2.08(c) hereof.

“Requested Reduction Amount” has the meaning set forth in Section 2.08(c) hereof.

“Specified Termination Date” has the meaning set forth in Section 2.08(b) hereof.

“Substitute Bank” has the meaning set forth in Section 2.08(d)(i) hereof.

“Terminating Bank” has the meaning set forth in Section 2.08(b) hereof.

“Termination Notice” has the meaning set forth in Section 2.08(b) hereof.

“Third Amendment Effective Date” means March 1, 2013.

“Utilization Fee” has the meaning set forth in Section 2.07(a) hereof.

(c)  Section 1.01 of the Credit Agreement is further amended by deleting the definitions of “Consent Date”, “Existing Termination Date” and “Non-Extending Bank” in their entirety.

(d)  Section 2.05(a) of the Credit Agreement is hereby amended by deleting Section 2.05(a) in its entirety and restating it as follows:

(a)  Each Loan owing to any Bank shall mature, and the principal amount thereof shall be due and payable to such Bank, on the earlier of (x) such Bank’s Specified Termination Date and (y) the Termination Date. The Borrower promises to pay on such date, and there shall become absolutely due and payable on such date, all of the Loans outstanding to such Bank on such date, together with all accrued and unpaid interest thereon and such other amounts outstanding to such Bank hereunder.

(e)  Section 2.05(h) of the Credit Agreement is hereby amended by deleting Section 2.05(h) in its entirety and restating it as follows:

(h)  Subject to the satisfaction of the conditions set forth in Section 3.02, Loans prepaid prior to the Termination Date may be reborrowed prior to

the Termination Date, provided, however, that Loans of any Terminating Bank prepaid prior to such Bank’s Specified Termination Date may be reborrowed prior to the earlier of (x) such Bank’s Specified Termination Date and (y) the Termination Date.

(f)  The last sentence of Section 2.06(a) of the Credit Agreement is hereby amended by deleting the last sentence of Section 2.06(a) in its entirety and restating it as follows:

Interest on each Overnight Rate Loan shall be payable in arrears on the last day of each calendar month and on the Termination Date (or, if earlier, with respect to the Loans of any Terminating Bank, on such Bank’s Specified Termination Date).

(g)  The last sentence of Section 2.06(b) of the Credit Agreement is hereby amended by deleting the last sentence of Section 2.06(b) in its entirety and restating it as follows:

Interest on each LIBOR Loan shall be payable in arrears on the last day of the Interest Period in effect with respect thereto and on the Termination Date (or, if earlier, with respect to the Loans of any Terminating Bank, on such Bank’s Specified Termination Date).

(h)  Section 2.07(a) of the Credit Agreement is hereby amended by deleting Section 2.07(a) in its entirety and restating it as follows:

(a)  During the Revolving Credit Period, the Borrower shall pay to the Agent for the pro rata accounts of each Bank a utilization fee (the “Utilization Fee”) at the rate of 0.05% per annum times an amount equal to the unused portion of the Aggregate Commitment Amount on each day (each, an “Applicable Day”) on which the total outstanding Loans are less than fifty percent (50%) of the actual daily amount of the Aggregate Commitment Amount then in effect (calculated after taking into account any reductions in any Commitments, repayment of Loans, prepayment of Loans and borrowings made on such day in accordance with the terms hereof). Such Utilization Fee shall accrue for the pro rata account of each Bank with respect to each Applicable Day occurring from the Third Amendment Effective Date to but excluding the Termination Date (or, if earlier, with respect to any Terminating Bank, such Bank’s Specified Termination Date). The Utilization Fee shall be due and payable quarterly in arrears on the last day of each calendar quarter, commencing on the first such day after the Third Amendment Effective Date, and on the Termination Date (or, if earlier, with respect to any Terminating Bank, such Bank’s Specified Termination Date).

(i)  Section 2.08 of the Credit Agreement is hereby amended by deleting Section 2.08 in its entirety and restating it as follows:

SECTION 2.08. Termination and Reduction of Commitments.

(a)  Reductions and Terminations by the Borrower. Subject to Section 2.05(d), during the Revolving Credit Period, the Borrower may, upon at least three (3) Domestic Business Days’ prior written notice to the Agent, (i) terminate the Commitments in full at any time, or (ii) reduce from time to time the Aggregate Commitment Amount by an aggregate amount of at least $5,000,000 or integral multiples of $1,000,000 in excess thereof, whereupon the Commitment Amounts of each of the Banks shall be reduced pro rata in accordance with their Commitment Percentage of the amount specified in such notice, or, as the case may be, each Bank’s Commitment shall be terminated. Promptly after receiving any notice of the Borrower delivered pursuant to this Section 2.08(a), the Agent will notify the Banks of the substance thereof. Upon the effective date of any such reduction or termination, the Borrower shall pay to the Agent for the respective accounts of the Banks the full amount of any Utilization Fee then accrued. No reduction in the Commitment Amounts or termination of the Commitments made in accordance with this Section 2.08(a) may be reinstated.

(b)  Termination in Full by Bank or Banks. Each Bank’s Commitment Amount shall permanently reduce to $0 and each Bank’s Commitment shall terminate on the Termination Date. Notwithstanding anything to the contrary contained herein, each Bank shall have the right at any time from and after February 24, 2014 (or, to the extent such Bank becomes a Bank hereunder after the Third Amendment Effective Date, on the 360th day after such Bank becomes a Bank hereunder) to elect to terminate its Commitment in full upon no less than 360 days’ prior written notice to the Borrower and the Agent thereof (such notice being hereinafter referred to as a “Termination Notice”; any Bank so delivering a Termination Notice in accordance with the provisions of this Section 2.08(b) shall hereinafter be referred to as a “Terminating Bank”). The Commitment of such Terminating Bank shall automatically terminate in full, and the Commitment Amount of such Bank shall permanently reduce to $0, on the date (with respect to such Bank, its “Specified Termination Date”) which is the earlier of (x) the 360th day after the date of such Termination Notice and (y) a date selected by the Borrower by written notice to the Agent and agreed to by the Agent (such agreement not to be unreasonably withheld or delayed). In accordance with Section 2.05(a), the Borrower promises to pay each Terminating Bank on the earlier of (x) such Bank’s Specified Termination Date and (y) the Termination Date, and there shall become absolutely due and payable on such date, the aggregate principal amount of all Loans outstanding to such Terminating Bank on such date, together with any and all accrued and unpaid interest thereon and all other amounts outstanding hereunder (including, without limitation, the Utilization Fee owing to such Terminating Bank) and owing to such Terminating Bank as of such date.

(c)  Reduction by Bank or Banks. Each Bank shall have the right at any time from and after February 24, 2014 (or, to the extent such Bank becomes a Bank hereunder after the Third Amendment Effective Date, on the 360th day after such Bank becomes a Bank hereunder) to elect to reduce its Commitment Amount in part upon no less than 360 days’ prior written notice to the Borrower and the Agent thereof specifying the amount of such reduction (the “Requested

Reduction Amount”; such a notice being hereinafter referred to as a “Reduction Notice”; any Bank so delivering such a Reduction Notice shall hereinafter be referred to as a “Reducing Bank”). The Commitment Amount of such Reducing Bank shall automatically reduce on the date (the “Reduction Date”) which is the earlier of (x) the 360th day from the date of such Reduction Notice and (y) a date selected by the Borrower by written notice to the Agent and agreed to by the Agent (such agreement not to be unreasonably withheld or delayed) by an amount (a “Reduction Amount”) equal to the greater of (i) the Requested Reduction Amount and (ii) an amount selected by the Borrower in the written notice to the Agent; it being understood that (I) the Borrower shall have the right to permanently reduce or terminate such Reducing Bank’s Commitment Amount in full or in part at any time after delivery of the Reduction Notice and prior to the Reduction Date and (II) nothing in this Section 2.08(c) shall limit the Borrower’s right to reduce the Aggregate Commitment Amount or terminate the Commitments pursuant to and in accordance with the terms of Section 2.08(a) above. The Borrower promises to pay to each Reducing Bank on the applicable Reduction Date, and there shall become absolutely due and payable on each such date, the portion of the aggregate principal amount of all Loans outstanding to such Reducing Bank, together with any and all accrued and unpaid interest thereon, which exceeds such Reducing Bank’s new Commitment Amount (immediately after giving effect to the reduction by the Reduction Amount on such date); provided that if the Borrower elects to reduce the Commitment Amount of a Reducing Bank to $0 by terminating such Reducing Bank’s Commitment in full, the Borrower promises to pay to such Reducing Bank on the applicable Reduction Date, and there shall become absolutely due and payable on such date, the aggregate principal amount of all Loans outstanding to such Reducing Bank , together with any and all accrued and unpaid interest thereon and all other amounts outstanding hereunder and owing to such Reducing Bank as of such date.

(d)  Substitute Bank. (i) To the extent any Bank delivers a Termination Notice pursuant to Section 2.08(b) above or a Reduction Notice pursuant to Section 2.08(c) above, so long as no Default or Event of Default has occurred and is continuing, the Borrower may, upon prior written notice to the Agent, such Terminating Bank or Reducing Bank, as applicable, request that one or more additional banks reasonably satisfactory to the Agent (each, a “Joining Bank”) and/or existing Banks (each such existing Bank or Joining Bank, a “Substitute Bank”) assume all or any portion of the Commitment Amount of such Terminating Bank or Reducing Bank, as applicable. Each Terminating Bank or Reducing Bank agrees that, should it be identified for replacement prior to its Specified Termination Date or Reduction Date, as applicable, pursuant to this Section 2.08(d)(i), it will promptly execute and deliver all documents and instruments reasonably required by the Borrower and/or the Agent to assign the relevant portion such Terminating Bank’s or Reducing Bank’s Loans and Commitment to the applicable Substitute Bank on the applicable Specified Termination Date or Reduction Date, as applicable. The parties hereto hereby acknowledge and agree that no existing Bank shall be obligated to assume any portion of the Commitment Amount of a Terminating Bank or Reducing Bank

hereunder, and any election to do so shall be in the sole and absolute discretion of such Bank.

(ii)  In the event that any Terminating Bank was not replaced pursuant to Section 2.08(d)(i) above prior to its Specified Termination Date, so long as no Default or Event of Default has occurred and is continuing, the Borrower may, at any time prior to the Termination Date, with prior written notice to the Agent, request that one or more Substitute Banks (x) in the case of Joining Banks, join this Agreement as Banks with Commitments and/or (y) in the case of existing Banks, increase their existing Commitments, in an aggregate Commitment Amount of up to the applicable Commitment Amount of such Terminating Bank immediately prior to the applicable Specified Termination Date. In the event that Commitments of any Reducing Bank equal to the applicable Reduced Amounts were not replaced with Commitments of Substitute Banks pursuant to Section 2.08(d)(i) above prior to the applicable Reduction Date, so long as no Default or Event of Default has occurred and is continuing, the Borrower may, at any time prior to the Termination Date, with prior written notice to the Agent, request that one or more Substitute Banks (x) in the case of Joining Banks, join this Agreement as Banks with Commitments and/ or (y) in the case of existing Banks, increase their existing Commitments, in an aggregate Commitment Amount of up to the applicable Reduction Amounts. Each Joining Bank shall be required to execute and deliver to the Agent such joinder documents as the Agent shall reasonably require. The parties hereto hereby acknowledge and agree that no existing Bank shall be obligated to assume any portion of the Commitment Amount of a Terminating Bank or Reducing Bank hereunder, and any election to do so shall be in the sole and absolute discretion of such Bank.

(j)  Section 2.09 of the Credit Agreement is hereby amended by deleting the text of Section 2.09 and substituting in place thereof the words “Intentionally Omitted”.

(k)  Section 9.06(f) of the Credit Agreement is hereby amended by deleting such Section 9.06(f) in its entirety and restating it as follows:

No bank may become an Assignee pursuant to clause (c) above or a Substitute Bank pursuant to Section 2.08(d) unless such bank constitutes a “bank” (as such term is used in Section 18(f)(1) of the Investment Company Act) in the reasonable judgment of the Borrower and the Agent. No bank may become an Assignee pursuant to clause (c) above or a Substitute Bank pursuant to Section 2.08(d) if that bank is an Affiliate of the Borrower.

(1)  Schedule 1 to the Credit Agreement is hereby amended by deleting Schedule 1 in its entirety and replacing it with the Schedule 1 attached hereto as Exhibit A.

§3.  Representations and Warranties. The Borrower hereby represents and warrants as follows:

(a)  Representations and Warranties in Credit Agreement. The representations and warranties of the Borrower contained in the Credit Agreement (as amended by this Amendment) are true and correct on and as of the date hereof and with the same force and effect as it made on and as of such date (or, if any such representation or warranty is expressly stated to have been made as of a specific date, as of such specific date).

(b)  No Default. No Default or Event of Default has occurred and is continuing.

(c)  Authority, Etc. The execution and delivery by the Borrower of this Amendment and the Borrower’s performance of this Amendment and the Credit Agreement as amended hereby (as so amended, the “Amended Agreement”) (i) are within the Borrower’s corporate powers, (ii) have been duly authorized by all necessary corporate action on the part of the Borrower, (iii) require no Governmental Authorizations, Private Authorizations or Governmental Filings by the Borrower which have not already been obtained or made, (iv) do not contravene, or constitute a default under, any provision of (A) any Applicable Law unless the violation of such Applicable Law could not reasonably be expected to have a Material Adverse Effect, (B) the Charter Documents of the Borrower, or (C) any agreement, judgment, injunction, order, decree or other instrument binding upon the Borrower unless such contravention or violation could not reasonably be expected to have a Material Adverse Effect, and (v) do not result in the creation or imposition of any Lien on any asset of the Borrower (other than Liens in favor of the Agent to secure the Obligations and Liens permitted pursuant to Section 5.08 of the Credit Agreement).

(d)  Enforceability of Obligations. This Amendment has been duly executed and delivered by the Borrower. Each of this Amendment and the Amended Agreement constitutes the valid and legally binding agreement of the Borrower, in each case enforceable in accordance with their terms, subject to applicable bankruptcy, insolvency, reorganization, moratorium or other similar laws affecting creditors’ rights generally and general principles of equity (regardless of whether enforcement is sought in equity or at law).

§4.  Effectiveness. This Amendment shall be effective as of the date first written above (the “Third Amendment Effective Date”) upon the receipt by the Agent of the following:

(a)  counterparts of this Amendment duly executed and delivered by each of the Borrower, the Banks and the Agent and an updated Form FRU-1, duly executed by the Borrower;

(b)  a certificate duly executed by an officer of the Borrower which is reasonably satisfactory to the Agent certifying that (i) the representations and warranties of the Borrower contained in the Credit Agreement (as amended by this Amendment) and the other Loan Documents shall be true on and as of the Third Amendment Effective Date and with the same force and effect as if made on and as of such date (or, if any representation or warranty is expressly stated to have been made as of a specific date, as of such specific date) and (ii) no Default or Event of Default has occurred and is continuing;

(c)  a duly executed certificate from the Secretary or Assistant Secretary of the Borrower in form and substance reasonably satisfactory to the Agent and dated as of the Third Amendment Effective Date as to the incumbency of, and bearing specimen signatures of, the

Authorized Signatories who are authorized as of the date hereof to execute and take actions hereunder and under the Loan Documents for and on behalf of the Borrower (or a certification that the incumbency of the Authorized Signatories set forth on that certificate delivered to the Agent pursuant to Section 4(d) of Amendment Agreement No. 2 to Amended and Restated Credit Agreement on the Second Amendment Effective Date (the “Prior Certificate”) remains true and accurate as of the date hereof); and certifying and attaching copies of (i) the Borrower’s Charter Documents, with all amendments thereto (or a certification that the Borrower’s Charter Documents previously delivered to the Agent and referenced in the Prior Certificate have not been amended, supplemented or modified and are in full force and effect); (ii) an excerpt from the Minutes of Joint Regular Meeting of the Board of Directors/Trustees of the BlackRock Closed-End Funds dated February 7, 2013, authorizing the transactions contemplated hereby; (iii) the current Prospectus as then in effect (or a certification that the Prospectus previously delivered to the Agent and referenced in the Prior Certificate has not been amended, supplemented or modified and is currently in effect); (iv) the investment management agreement between the Borrower and the Investment Adviser as then in effect (or a certification that the investment management agreement previously delivered to the Agent and referenced in the Prior Certificate has not been amended, supplemented or modified and is in full force and effect); and (v) the Custody Agreement (or a certification that the Custody Agreement previously delivered to the Agent and referenced in the Prior Certificate has not been amended, supplemented or modified and is in full force and effect);

(d)  a legal existence and good standing certificate for the Borrower from the Secretary of State of the State of Maryland dated as of a recent date;

(e)  a copy of the certificate of incorporation of the Borrower, with all amendments, certified as of a recent date by the Secretary of State of the State of Maryland; and

(f)  the legal opinion of ▇▇▇▇▇▇▇, Arps, Slate, ▇▇▇▇▇▇▇ & ▇▇▇▇ LLP and Miles & Stockbridge P.C., special counsel to the Borrower, each in form and substance reasonably satisfactory to the Agent.

§5.  Ratification of the Borrower. The Borrower ratifies and confirms in all respects all of its obligations to the Agents and the Banks under the Credit Agreement and the other Loan Documents and hereby affirms its absolute and unconditional promise to pay to the Banks and the Agents the Loans made to it and all other amounts due from it under the Credit Agreement as amended hereby. The Credit Agreement and this Amendment shall be read and construed as a single agreement. All references in the Credit Agreement or any related agreement or instrument to the Credit Agreement shall hereafter refer to the Credit Agreement as amended hereby.

§6.  Miscellaneous. This Amendment shall be a Loan Document for all purposes under the Credit Agreement. This Amendment shall be governed by and construed in accordance with the laws of the State of New York. Except as specifically amended by this Amendment, the Credit Agreement and all other agreements and instruments executed and delivered in connection with the Credit Agreement, including, without limitation, the other Loan Documents, shall remain in full force and effect. This Amendment is limited specifically to the matters set forth herein and does not constitute directly or by implication an amendment or waiver of any other provision of the Credit Agreement or any of the other Loan Documents.

Nothing contained herein shall constitute a waiver of, impair or otherwise affect any Obligations, any other obligation of the Borrower or any rights of the Agents and the Banks consequent thereon. This Amendment may be executed in several counterparts and by each party on a separate counterpart, each of which when so executed and delivered shall be an original, and all of which together shall constitute one instrument. Delivery of an executed signature page to this Amendment by facsimile transmission or other electronic transmission shall be as effective as delivery of a manually signed counterpart of this Amendment, provided, the Borrower does agree to provide the Agent with an original manually signed counterpart of this Amendment within five (5) Business Days of the Third Amendment Effective Date. In proving this Amendment it shall not be necessary to produce or account for more than one such counterpart signed by the party against whom enforcement is sought.

[Signature page follows.]

IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be duly executed by their respective authorized officers as of the date first above written.

[SIGNATURE PAGE TO FRA AMENDMENT]

IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be duly executed by their respective authorized officers as of the date first above written.

[SIGNATURE PAGE TO FRA AMENDMENT]

Exhibit A

Schedule 1

BORROWER:

BLACKROCK FLOATING RATE INCOME

STRATEGIES FUND, INC.

▇▇▇ ▇▇▇▇▇▇▇▇ ▇▇▇▇▇▇▇

Wilmington, DE 19809

Domestic Lending Office:

Mutual Fund Lending Department

▇▇▇▇▇▇ ▇▇▇▇▇, ▇▇▇▇▇ ▇

Boston, MA 02206

Attn. ▇▇▇▇▇ ▇. ▇▇▇▇▇▇▇, Assistant Vice

President - CSU Manager

Tel: (▇▇▇) ▇▇▇-▇▇▇▇

Fax: (▇▇▇) ▇▇▇-▇▇▇▇

Email: ▇▇▇▇▇▇▇▇▇@▇▇▇▇▇▇▇▇▇▇▇.▇▇▇

LIBOR Lending Office:

Mutual Fund Lending Department

▇▇▇▇▇▇ ▇▇▇▇▇, ▇▇▇▇▇ ▇

Boston, MA 02206

Attn: ▇▇▇▇▇ ▇. ▇▇▇▇▇▇▇, Assistant Vice

President - CSU Manager

Tel: (▇▇▇) ▇▇▇-▇▇▇▇

Fax: (▇▇▇) ▇▇▇-▇▇▇▇

Email: ▇▇▇▇▇▇▇▇▇@▇▇▇▇▇▇▇▇▇▇▇.▇▇▇

For non-funding or payment notices:

Mutual Fund Lending Department

▇▇▇▇▇▇ ▇▇▇▇▇ ▇▇▇▇▇ ▇

Boston, MA 02206

Attn: ▇▇▇▇▇ ▇▇▇▇▇▇▇▇▇, Vice President

Tel: (▇▇▇)▇▇▇-▇▇▇▇

Fax: (▇▇▇)▇▇▇-▇▇▇▇