Skysong corporation purchased a new machine for its assembly process on August $1,2025.$ The cost of this machine was $$132,000.$ The company estimated that the machine would have a salvage value of $$15,000$ at the end of its service life. Its life is estimated at $5$ years, and its working hours are estimated at $20,000$ hours. Year$-$end is December $31.$

Compute the depreciation expense under the following methods. Each of the following should be considered unrelated:

$($a$)$ Straight$-$line depreciation for $2025$

$($b$)$ Activity method for $2025,$ assuming that machine usage was $700$ hours

$($c$)$ Sum$-$of$-$the$-$years'$-$digits for $2026$

$($d$)$ Double$-$declining$-$balance for $2026$