Suppose a $$10,000$ machine will be used for five years. At that time, the machine$$s salvage value will be $$2,000.$ It was placed in service January $1$st of year $1.$

Please complete the following using the double$-$declining balance $($DDB$)$ method:

$(1)$ A full annual depreciation schedule for the useful life of the asset.

$(2)$ The journal entry to record the acquisition of the machine.

$(3)$ The journal entry to record the first month of depreciation on the machine.