Explanation:

1. End-of-year AUM calculation:

   • Beginning AUM: $500 million
   • Annual return: 22%
   • End-of-year AUM = $500 million * 1.22 = $610 million.

2. Management fee calculation:

   • Management fee = $610 million * 2% = $12.2 million.

3. Hard hurdle rate application:

   • The hard hurdle rate is 10% of the beginning AUM.
   • Hard hurdle = $500 million * 10% = $50 million.

4. Incentive fee calculation (net of management fees):

   • Net return = End-of-year AUM - Beginning AUM - Management fee - Hard hurdle.
   • Net return = $610 million - $500 million - $12.2 million - $50 million = $47.8 million.
   • Incentive fee = $47.8 million * 15% = $7.17 million ≈ $7.2 million.

Why not B or C?

• Option B incorrectly calculates the hurdle rate on the annual return before fees instead of the beginning AUM.
• Option C assumes a soft hurdle rate, which is not applicable here.