Sheffield Technologies holds a valuable patent $($No$.782)$ for Dance$-$o$-$matic, an electronic system that provides individualized,

interactive dance instruction that also provides real$-$time feedback. Sheffield does not manufacture or sell the products and

processes it develops. Instead, it conducts research and develops products and processes which it patents, and then assigns the

patents to manufacturers on a royalty basis. Occasionally it sells a patent. The history of Sheffield's patent number $782$ is as follows:

Sheffield assumed a useful life of $14$ years when it received the initial patent. On January $1,2024,$ it revised its useful life estimate

downward to $6$ remaining years. Amortization is computed for a full year if the cost is incurred prior to July $1,$ and no amortization for

the year if the cost is incurred after June $30.$ The company's year ends December $31.$

Compute the carrying value of patent No$.782$ on each of the following dates:

$($a$)$ December $31,2019,$$

$($b$)$ December $31,2023,$$

$($c$)$ December $31,2026,$$