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Hannah Company purchased an intangible asset for $$450,000$ on January $1$ of Year $1.$ The asset is assumed to have a $15-$year useful life with zero salvage value. Amortization expense is computed using the straight$-$line method. On January $1$ of Year $2,$ the asset was evaluated to determine whether it was impaired. As of January $1$ of Year $2,$ the intangible asset was expected to generate future cash flows of $$25,000$ per year $($at the end of the year$)$ for the remaining $14$ years of its life. The appropriate discount rate is $13\%$ compounded annually.

What impairment loss should be recognized in Year $2?$

$$262,438$

$$185,942$

$$70,000$

$$100,000$