Exhibit (a)(1)(vi) – Letter to Shareholders

July 14, 2017

Dear Common Shareholder:

Federated Premier Intermediate Municipal Income Fund (NYSE: FPT) (the “Fund”), is offering to purchase for cash up to 20% of its outstanding common shares of beneficial interest, par value $0.01 per share (the “Common Shares”), upon the terms and subject to the conditions set forth in the Offer to Purchase and the related Letter of Transmittal (the “Offer”). The Offer will expire at 5:00 p.m., New York City time, on August 11, 2017, unless extended by the Fund in its sole discretion (the “Expiration Date”).

On the terms and subject to the conditions of the Offer, the Fund will pay a purchase price per share for Common Shares properly tendered and not properly withdrawn in the Offer, net to you in cash, equal to 98% of its net asset value per share in U.S. dollars determined by the Fund as of the close of regular trading on the New York Stock Exchange (“NYSE”) on the Expiration Date, provided that the total number of Common Shares tendered does not exceed 20% of the Fund’s outstanding Common Shares. In the event that more than 20% of the Fund’s outstanding Common Shares are tendered, the Fund will purchase 20% of its outstanding Common Shares on a pro rata basis (with appropriate adjustment to avoid purchase of fractional Common Shares).  You should carefully consider the economics involved when tendering Common Shares in the event that more than 20% of the Fund’s outstanding Common Shares are tendered and not withdrawn, and the Fund purchases the tendered Common Shares on a pro rata basis (with appropriate adjustment to avoid purchase of fractional Common Shares).

The Fund’s Offer and withdrawal rights expire at 5:00 p.m., New York City time, on the Expiration Date. The Fund’s NAV will be calculated daily and may be obtained on the Fund’s investment adviser’s website at http://www.federatedinvestors.com/FII/ closedendfunds/details/performance.do?fundshareid=7358&basketid=10462 or by contacting Georgeson LLC, the Information Agent for the Offer, at (866) 856-6388 (toll free) Monday - Friday 9:00 a.m. to 11:00 p.m. New York City time, and Saturday 12:00 p.m. to 6:00 p.m. New York City time, prior to 5:00 p.m., New York City time, on the Expiration Date. All Common Shares that the Fund does not accept for purchase because of proration or otherwise will be returned at the Fund’s expense to the shareholders that tendered such Common Shares promptly after the Expiration Date.

The Board of Trustees has approved the Offer. However, none of the Fund, its Board of Trustees, its investment adviser or its information agent makes any recommendation to you as to whether you should tender or refrain from tendering your Common Shares. You must make your own decision as to whether to tender your Common Shares and, if so, how many Common Shares to tender. In doing so, you should read carefully the information in the Offer to Purchase and in the related Letter of Transmittal. You may contact Georgeson LLC, the information agent, toll free at 866-856-6388 during the hours listed above, if you have questions regarding how to tender your Common Shares.

Very truly yours,

J. Christopher Donahue

President