How to create a redirect that appends .html

How do I create a redirect that adds .html to urls entered. My pages have the following format

It looks like some people are leaving off the .html and then being redirected to the home page. Is there a way to check if there is a page with the url they entered + .html ? If there is a page name with url+html redirect to that otherwise redirect to homepage.

The htaccess rewrite rule might look something like this:

RewriteCond %{REQUEST_FILENAME}.html -f
RewriteRule ^(.*)$ /$1.html [R=301,L]

thanks jeff! that works perfect.