The graphic I posted is from the
ICANN site and explains the life cycle of a com/net/org/info/biz domain
Other extensions work quite differently
Normally you can renew the domain with the current registrar within the first 30 days without getting hit for extra fees. If it goes past that period you can get hit for more ...
Was the domain registered directly with a registrar or via a reseller?
In any case 10 days is a silly number that they've pulled out of the air