<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2015-07-30</periodOfReport>

    <noSecuritiesOwned>1</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001202806</issuerCik>
        <issuerName>FEDERATED PREMIER INTERMEDIATE MUNICIPAL INCOME FUND</issuerName>
        <issuerTradingSymbol>FPT</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001648530</rptOwnerCik>
            <rptOwnerName>Van Meter Stephen</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>FEDERATED INVESTORS TOWER</rptOwnerStreet1>
            <rptOwnerStreet2>1001 LIBERTY AVENUE</rptOwnerStreet2>
            <rptOwnerCity>PITTSBURGH</rptOwnerCity>
            <rptOwnerState>PA</rptOwnerState>
            <rptOwnerZipCode>15222-3779</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chief Compliance Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <footnotes></footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Clair E. Pagnano, By Power of Attorney</signatureName>
        <signatureDate>2015-07-30</signatureDate>
    </ownerSignature>
</ownershipDocument>
