On April $1,2023,$ Ice Drilling Co$.$ purchased a trencher for $$200,000.$ The machine was expected to last five years and have a residual value of $$20,000.$

Required:

Calculate depreciation expense for $2023$ and $2024$ to the nearest month, using $($a$)$ the straight$-$line method, and $($b$)$ the double$-$declining$-$balance method. The company has a December $31$ year$-$end. $($Do not round intermediate calculations.$)$