Exhibit 10.4

BB&T Corporation

200 West Second Street

Winston-Salem, NC 27101

April 1, 2016

U.S. Bank National Association

as Institutional Trustee

190 S. LaSalle St, 8th Floor

Chicago, IL 60603

Christiana Bank & Trust Company

as Delaware Trustee

1314 King Street

Wilmington, DE 19801

Attention: Corporate Trust Administration

Ladies and Gentlemen:

By virtue of the merger between National Penn Bancshares, Inc., a bank holding company incorporated in the Commonwealth of Pennsylvania (“National Penn”) and BB&T Corporation, a North Carolina corporation (“BB&T”), pursuant to the Agreement and Plan of Merger, dated as of August 17, 2015, by and between BB&T and National Penn (the “Merger Agreement”), BB&T, as the surviving corporation, does hereby agree, affirm and acknowledge that, effective as of the Effective Time (as defined in the Merger Agreement), it expressly assumes all the duties, warranties, and obligations of National Penn under (i) the Junior Subordinated Debt Securities due March 15, 2036 (the “Debt Securities”) issued pursuant to the Indenture, dated as of January 19, 2006, between National Penn and LaSalle Bank National Association, as Trustee (the “Indenture”), (ii) the Indenture, (iii) the Amended and Restated Declaration of Trust of NPB Capital Trust VI, dated as of January 19, 2006 (the “Declaration”), among National Penn, as Sponsor, U.S. Bank National Association, as successor to Bank of America, N.A. (formerly known as LaSalle Bank National Association), as Institutional Trustee, Christiana Bank & Trust Company, as Delaware Trustee, the Administrators named therein, and the holders from time to time of undivided beneficial interests in the assets of the Trust (as defined therein) and (iv) the Guarantee Agreement, dated as of January 19, 2006 (the “Guarantee”), between National Penn, as Guarantor, and U.S. Bank National Association, as successor to Bank of America, N.A. (formerly known as LaSalle Bank National Association), as Guarantee Trustee, for the benefit of the Holders (as defined therein) from time to time of the Capital Securities (as defined therein) of NPB Capital Trust VI.

As to all matters relating to the Declaration, this letter shall be governed by, and construed in accordance with, the laws of the State of Delaware without regard to its conflict of laws principles. Except as set forth in the immediately preceding sentence, this letter shall be

governed by, and construed in accordance with, the laws of the State of New York without regard to its conflict of laws principles other than Section 5-1401 of the New York General Obligations Law. The undersigned (i) irrevocably submits itself to the non-exclusive jurisdiction and venue of any United States federal court or New York state court, in each case located in the Borough of Manhattan, The City of New York in any action arising out of this letter, and (ii) consents to the service of process by mail.

[Signature page follows.]

NPB Capital Trust VI Assumption Letter

[Signature Page to NPB Capital Trust VI Assumption Letter]