Hansen Industries purchased a machine that cost $$500,000.$ It is expected that the machine will last $15$ years and have a $$50,000$ salvage value.

a$.$ Calculate the $1$st and $2$nd year of depreciation using the straight$-$line method.

b$.$ What is the book value of the machine at the end of the $1$st year? What is the book value at the end of the $3$rd year?