IIS redirect into subdirectory

I have under my default web site the directories:

/myapp/
/myapp/v1/
/myapp/v2/
/myapp/v3/
/myapp/administration/

Now I would like to http-redirect all users who type /myapp or /myapp/ or /myapp/index.html in their browser, to /myapp/v3/index.html.

Requests coming to

/myapp/favicon.ico
/myapp/typeyourfilenamehere.html

should not be forwarded. But the only option I found was "Only redirect requests to content in this directory", but that would include not only the index.html, but also typeyourfilenamehere.html.

How can I configure the aforementioned behaviour in IIS?

EDIT: Thanks to the quick answer of @JamesRyan, "IIS URL rewrite 2.0" has just put the following into my Web.config:

    <rewrite>
        <rewriteMaps>
            <rewriteMap name="/myapp">
                <add key="/myapp" value="/myapp/v3/" />
                <add key="/myapp/" value="/myapp/v3/" />
                <add key="/myapp/index.html" value="/myapp/v3/" />
            </rewriteMap>
        </rewriteMaps>
        <rules>
            <rule name="Umschreibregel1 für /myapp" stopProcessing="true">
                <match url=".*" />
                <conditions>
                    <add input="{/myapp:{REQUEST_URI}}" pattern="(.+)" />
                </conditions>
                <action type="Redirect" url="{C:1}" appendQueryString="false" />
            </rule>
        </rules>
    </rewrite>

At a quick glance, it works as indented, but perhaps someone could explain me what each line tells the rewrite engine.