Insperity (NSP) 10-Q 2015 Q1 Quarterly 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 Quarterly Report of Insperity, Inc. (the “Company”) on Form 10-Q for the period ending March 31, 2015, (the “Report”), as filed with the Securities and Exchange Commission on the date hereof, I, Paul J. Sarvadi, Chairman of the Board and Chief Executive Officer of the Company, certify, pursuant to 18 U.S.C. §1350, as adopted pursuant to §906 of the Sarbanes-Oxley Act of 2002, to the best of my knowledge, that:

1. The Report fully complies with the requirements of section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and

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

/s/ Paul J. Sarvadi

Paul J. Sarvadi

Chairman of the Board and Chief Executive Officer

May 1, 2015