On October $1,2020,$ ABAC Farms purchased a machine with a cost of $$120,000$ and a salvage value of $$20,000$ and a useful life of $10$ years. The machine was rated to produce $200,000$ parts over its lifetime. In $2020,$ the machine produced $5,000$ parts; in $2021,$ it produced $20,000$ parts and in $2022,$ it produced $20,000$ parts. Assuming ABAC Farms uses units of production depreciation, what is the balance in the accumulated depreciation account for this asset at the end of $2022?$