On January $1,2025,$ a corporation acquired a truck for $$100,000.$ Residual value was estimated to be $$20,000.$ The truck can be driven for $120,000$ miles or a useful life of four years. Actual usage of the truck was recorded as $8,000$ miles for the first year and $11,000$ miles for the second year. What is the book value at the end of year $2,$ calculated by the units $-$ of $-$ production method? $($Round any intermediate calculations to the nearest cent, and round your final answer to the nearest dollar.$)$

A$.$ $$50,000$

B$.$ $$84,230$

C$.$ $$87,270$

D$.$ $$12,730$