Final answer:
The 200 percent declining balance method provides the most accelerated depreciation by applying a high constant rate to the depreciable asset's book value each year.
Step-by-step explanation:
The method that allows the most accelerated depreciation is the 200 percent declining balance method. This method applies a constant depreciation rate, which is double the straight-line rate, to the reducing book value of the asset at the start of each period. In comparison, the 150 percent declining balance also offers accelerated depreciation but at a slower pace than the 200 percent. The straight-line method provides equal depreciation expenses each year over the useful life of the asset, thus, offers no acceleration. Lastly, the Sum of the years' digits is an accelerated method, however, it typically does not depreciate assets as fast as the declining balance methods.