Hi, Pommo is a free open source newsletter application. You may need the help of a web developer to install it on your server, but once there you can set-up and send newsletters to your list at zero expense.
Pommo does not require a double opt-in like Aweber or similar commercial newsletter applications but be sure you have peoples permission to contact them before hitting the send button. If your site is identified as sending spam Google could drop you out of their search results which could be a disaster for your business.
Full Pommo details and download here: http://pommo.org/Main_Page
One other free option and one you can probably do without the assistance and cost of a web developer is to set-up a mailing list on your web server. I'm sure your web hosting company will help you with any support issues for free as part of their service.
Hope that helps, Peter from http://www.StarterWebsites.net.