Your personal information is not released publicly with a free wordpress.com account or blog.
You do not have to buy any upgrade to keep your personal info private. I wonder if you were looking at something about a domain name registration / upgrade?
or perhaps this:
If you don’t have a domain yet but you want one, you’ve come to the right place. You can register a new domain with (or without, if you prefer) the private registration option.
Domain Registration is a paid upgrade that costs $18.00 per domain, per blog, per year. The optional private registration upgrade is an additional $8.00 per domain per year.
I'm not sure what other upgrade which would make you total cost be $16?
Did you intend to buy the domain mapping upgrade? If not, then you certainly don't need to have the $8 fee for private registration of the mapping.