$1.$ Show all work utilizing written formulas, conversion notations when applicable, and numeric values for answers. Youngblood Shipbuilding Yard just purchased $$800,000$ in capital equipment for Ship$-$repairing functions on dry$-$docked ships. Estimated salvage is $$150,000$ for any year after $5$ years of use. Compare the depreciation and book value for year $3$ for each of the following depreciation methods:

$($a$)$ MACRS$-$GDS with a recovery period of $10$ years

$($b$)$ Double$-$declining balance with a recovery period of $15$ years

$($c$)$ MACRS$-$SL with a recovery period of $15$ years