Please answer this question very thoroughly. Thank you!

A hedge fund has a 2 and 20 fee structure. The fund has $200 million of AUM in the beginning of the year. At the end of that year, an additional $20 million was invested. Including this inflow of the capital, at the end of that year, the total AUM was $260 million. What is the annual management fee collected by the fund manager? What was the total profit and the incentive fee on the profit collected by the fund manager? Show your work.