ROK Corporation acquired the following intangible assets during $2023$

Goodwill $$ Acquired Jan $1,2023$ for $$50,000$

Trademark $$ Acquired Jan $1,2023$ $$100,000$ remaining useful life of $5$ years, renewable every $10$ years. ROK expects to continue to renew the Trademark

Copyright $$ Acquired May $1,2023$ for $$200,000$; useful life of $50$ years, legal life $70$ years

Franchise $$ Acquired July $1,2023$ for $$150,000-$ ROK expects to operate the Franchise for $20$ years.

Patent $$ Acquired Oct $1,2023$ for $$120,000.$ The Patent is expected to have a useful life of $25$ years, which is longer than the legal life of $20$ years.

For each acquisition: Record $(1)$ the amount of amortization $($if any$)$ to be recorded for the year and $(2)$ The balance of the account at the end $2023($December $31,2023)$