An asset has a cost of 50,000, with a residual value of 10,000. it has a life of 5 years and was purchased on january 1. under double-declining-balance, what is the asset's fourth full year of decpreciation expense?

Under a straight-line method, the annual depreciation would be (50,000 - 10,000) / 5 years = 8,000/year. In percentage, this is equivalent to 8,000/50,000 = 16% of the original cost.

The double-declining-balance method uses double of the straight line depreciation: 2*16% = 32%, and this is deducted from the book value at the start of the year (not the original initial cost). If we deduct 32% of the cost per year, this means that the remaining value will be (100-32) = 68%.

Therefore, after 4 years of depreciation, the remaining value will be:
50,000*(0.68)^4 = 10,690.69

Note that since at this point, the book value is close to the residual value of 10,000, we generally switch to straight line depreciation beyond the 4 years.