All I can say is what I was told.
$9.95 per year for domain name registration.
Plus $9.95 for the actual transfer for the registrar.
Plus you have the option of 1 year free registration,Which I used.
When I moved the registration I was charged $9.95 only.
But the renewal says 19.95 so ???
Just make sure you start early on the transfer. If there is a issue releasing your domain name from the old registrar it may take several days to a week or so.
Looking at domaintools I see your name status as
Registrar Status: clientTransferProhibited
So you or network solutions will need to update that to a OK status to allow the transfer.