Staples incurred the following costs during $2022$ and $2023$:

$$ Research and Development costs of $$2,400$ were incurred on a new product to sell in future years. A product was successfully developed in $2022.$ Staples is unsure of the period benefited by the research but believes the product will result in increased sales over the next $8$ years.

$$ Legal costs and application fees of $$4,800$ for the patent were incurred on January $1,2022.$ The legal life of this patent is $20$ years.

$$ A patent infringement suit was successfully defended at a cost of $$8,400.$ Assume all costs were incurred on January $1,2023.$

Determine the book value of the patent as of December $31,2023$: