Equipment acquired on January $8$ at a cost of $$100,870$ has an estimated useful life of $12$ years, has an estimated residual value of $$9,550,$ and is depreciated by the straight$-$line method.a$.$What was the book value of the equipment at December $31$ the end of the fifth year?b$.$Assuming that the equipment was sold on April $1$ of the sixth year for $$54,047,$ journalize the entries to record $(1)$ depreciation for the $3$ months until the sale date and $(2)$ the sale of the equipment.