Thant's understandable. I did find a few free ones by searching the app store. I think the words I used wore "free remote desktop".
I have not looked through all of them, many require Windows, but I did find
Remote Desktop Plus for iPhone, iPod touch, and iPad on the iTunes App Store According to the developer's website it has a desktop client that needs to be installed on the Mac but it appears that is also free. There is also a free version of Team Viewer Available.
There are more free options than there were when I looked a few months ago. there are two things to keep in mind though:
1. Many of these types of apps do not play any of the sounds that would normally come through the Mac you are controlling.
2. Some of these programs may only work if you and the Mac you are controlling are on the same wifi network so ask lots of questions. In looking at the developer's website Remote Desktop Plus for iPhone, iPod Touch, and iPad might have this issue.
3. I'm not sure whether a credit card is required to set up an App Store account but probably so.