Reparking A Domain

I bought a domain several years ago from a company offering no monthly fees, and a one time payment of $200, and then a yearly payment of $70. It was a good deal at the time, but now it's sort of ridiculous for what I get. I recently bought a new domain, and I would like to park my old domain on a subdomain of my new domain. The problem is, that this domain was "free" when I bought the hosting account from the no monthly fee guys. My question is, will I have to start paying a registar fee for parking my old domain at whatever.mynewdomain.com, so that when people go to my old site, it redirects them to the subdomain of my new domain? The service I have now specifically states that I can park 3 domains, including the one I bought from them, so technically I have 2 slots open. What I am afraid of is that I will discontinue my service with the old company, they will park my domain at whatever.mynewdomain.com and then I will owe some company $70 for some registar fee or something. I am not very familiar with the the whole registar/domain registering policies so any insight on this would be greatly appreciated.

As far as I know you can contact your old company and pay some one-time registrar changing fees, and get your old domain to be transferred to your new registrar - i.e. have all your domains/subdomains under one roof. Besides, even if they offered you the domain for free - it must have come as a part of your hosting package. In such a case, you should logically retain rights over your domain and should be able to transfer it to anywhere you like. Contact your earlier no-monthly fees guy and find out the details. That's how these deals always work out.

A better way is to redirect your subdomain to your old domain, or you can add on your subdomain on your hosting site if it support the add-on funtionality. Of course, a A record of the subdomain must be made into the dns of your new domain.