Final answer:
The declining balance method results in the largest depreciation amount in the first year for an asset with a service life of four years, as it applies a constant rate to the asset's diminishing book value.
Step-by-step explanation:
The method of depreciation that will always result in the largest amount of depreciation in the first year when an asset is used evenly over a four-year service life is the declining balance method, also known as the accelerated depreciation method.
This method involves applying a constant rate of depreciation to the reducing book value of the asset each year, which results in larger depreciation charges in the earlier years and smaller ones as the asset's book value decreases. In contrast, methods like straight-line depreciation spread the cost evenly over the asset's useful life.