To find the closing balance of the accumulated depreciation account, we need to consider the starting balance and any additional depreciation recorded during the period.
- The initial balance as of January 1, 2012, is [tex]$1,000.
- Additional depreciation recorded on December 31, 2012, is $[/tex]2,000.
To find the closing balance, we add the initial balance and the depreciation amount:
[tex]\[ 1,000 + 2,000 = 3,000 \][/tex]
Therefore, the closing balance of the accumulated depreciation account is [tex]\( \boxed{3000} \)[/tex].