a$)$ On January $1,2020$ Gamma Ltd$.$ signed an agreement to operate a franchise. The franchise fee was $$40,000,$ of which $$15,000$ was paid when the agreement was signed and the balance is payable in five annual payments of $$5,000$ each beginning January $1,2021.$ Gamma can borrow money at $12\%$ for a loan of this type.

Calculate the amount to be recorded as "Franchise" on January $1,2020.$

b $)$A corporation paid $$50,000$ in legal fees defending a patent in an infringement lawsuit. The company was suing another company for using the protected patent process and won the lawsuit.

Provide the necessary journal entry and provide an explanation.