Joe, Inc. purchased a machine on January 1, 2009 for $60,000; the machine had an estimated salvage value of $5,000 and an estimated useful life of 10 years. Early in 2012, it was estimated that the equipment would have a remaining useful life of 5 years (including 2012) and a salvage value of $3,000. If Joe, Inc. uses sum-of-the-years-digits depreciation method, how much depreciation expense will be recognized for 2012?

In 2012, the answer doesn't consider the depreciated periods, which is 3 years. Then, (5(5+1))/2.

I think it should have been new estimated useful life - depreciated period = 5-3 = 2. Then, (2(2+1))/2.

Could you explain why it didn't take into consideration, please? and when should I take it into consideration?