$1.$ A patent was purchased on January $2$ of Year $1$ for $$130,000$ when the remaining legal life was $16$ years. On January $2$ of Year $3,$ Denzel determined that the remaining useful life of the patent was only eight years from the date of its acquisition.

$2.$ On January $1$ of Year $3,$ Denzel Company purchased a second patent for $$160,000$ cash. At January $1$ of Year $3,$ a total of $6$ years of the patent$$s legal life of $20$ years had expired.

$3.$ On June $30$ of Year $3,$ Denzel Company paid a firm $$16,000$ for a new trademark. Denzel considers the life of the trademark to be indefinite.

$4.$ On November $1$ of Year $3,$ Denzel Company acquired all noncash assets and assumed all liabilities of Lee Company at a cash purchase price of $$240,000.$ Denzel determined that the fair value of the identifiable net assets acquired in the transaction is $$234,000.$

Required

a$.$ What is the carrying value of each intangible asset on December $31$ of Year $3?$ Assume no impairment losses were recognized in prior periods.

b$.$ What is amortization expense for Year $3?$

$$ Note: When answering the following questions, do not round until your final answer. Round your final answer to the nearest whole number.