$(20$ points$)$ Englehard purchases a slurry$-$based separator for the mining of clay that costs $$700,000$ and has an estimated useful life of $10$ years, a MACRS$-$GDS property class of $7$ years, and an estimated salvage value after $10$ years of $$75,000.$ It was financed using a $$200,000$ down payment and a loan of $$500,000$ over a period of $5$ years with interest at $10\%.$ Loan payments are made in equal annual amounts $($principal plus interest$)$ over the $5$ years.

a$.$ What is the amount of the MACRS$-$GDS depreciation taken in the $3$rd year?

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

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