Exhibit (a)(34)

THORNBURG INVESTMENT TRUST

THIRTY-FIFTH AMENDMENT AND SUPPLEMENT TO

AGREEMENT AND DECLARATION OF TRUST

THIS THIRTY-FIFTH AMENDMENT AND SUPPLEMENT is made by Garrett Thornburg, David A. Ater, Sally Corning, Susan H. Dubin, David L. Gardner, Brian J. McMahon, Patrick J. Talamantes, Owen D. Van Essen and James W. Weyhrauch (the “Trustees”).

The Trust was formed on June 3, 1987 by an Agreement and Declaration of Trust - Limited Term Trust dated June 3, 1987 (the “Declaration of Trust”). The Trustees created a series, Thornburg Low Duration Bond Fund, by the execution of a Twenty-Fifth Amendment and Supplement to Agreement and Declaration of Trust, effective as of September 16, 2013. The Trustees changed the name of the described series to “Thornburg Low Duration Income Fund” by the execution of a Twenty-Sixth Amendment and Supplement to Agreement and Declaration of Trust, effective as of December 18, 2013. Section 11.7 of the Declaration of Trust permits the Trustees to make certain amendments to the Declaration of Trust.

Accordingly, by execution of this Amendment and Supplement, the Trustees change the name of the described series to “Thornburg Ultrashort Income Fund,” such name change to take effect on the effective date of an amendment to the Trust’s registration statement reflecting the new name.

The Trustees effect this Amendment and Supplement as of May 13, 2020, though the name change effected by this Amendment and Supplement will not take effect until the effective date of an amendment to the Trust’s registration statement reflecting the new name. The Trustees also execute and direct the Trust’s president to file, or cause to be filed, this Amendment and Supplement in the appropriate governmental offices.

/s/ Garrett Thornburg

Garrett Thornburg