Anew piece of equipment costs $18,000 with a residual value of $600 and an estimated useful life of
five years. assuming twice the straight-line rate, the book value at the end of year 2 using the decliningbalance
method is

What is the "straight line rate?"  To obtain this, subtract the $600 residual value from the "new cost," $18,000.  Result:  $17,400.

The straight line rate would then be $17,400/5, or $3,480; twice that would be $6,960.  

After one year, the book value at the end of year 1 would be $18,000-$6,960 = $11,040.

Follow a similar process to find the book value at the end of year 2.  Twice the original depreciation at this point would be $6,960, as before.  Subtracting this from $11,040 results in a book value at the end of year 2 of $11,040-$6,960= $4,080.

There may be other interpretations dictating what to do here.  I'd suggest you look up "declining balance method" and compare it to what we have done here.