Jones Financial Companies LLLP (JNFC) 10-K 2012 FY Annual report

Exhibit 32.1

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the annual report of The Jones Financial Companies, L.L.L.P. (the “Partnership”) on Form 10-K for the year ending December 31, 2012, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, James D. Weddle, Chief Executive Officer of the Partnership, certify, pursuant to 18 U.S.C. § 1350, as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, that:

(1) The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

(2) The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Partnership.

/s/ James D. Weddle

Chief Executive Officer

The Jones Financial Companies, L.L.L.P.

April 1, 2013