Where are you seeing $13000 over 12 months for the personal Gold card???

Those kind of spend offers tend to only be for business cards.
I just googled "amex gold card", and this turned up as a sponsored link at the top my results:
Earn 60,000 75,000 Membership RewardsŪ Points
after you spend $4,000 on purchases on your new Card in your first 6 months of Card Membership.† This offer may not be available if you leave this web page and return later.
...
While $4000 is more then $3000, 75000 is much more than 55000.