Travis Thompson uses his credit card to obtain a cash advance of $$600$ to pay for his textbooks in medical school. The interest rate charged for the loan is $0\mathrm{.}05924\%$ per day. Travis repays the money plus the interest after $20$ days.

a$)$ Determine the interest charged for the cash advance.

b$)$ When he repaid the loan, how much did he pay the credit card company?