A private equity fund has a $20\%$ performance fee with a $8\%$ hurdle rate and a $5-$year investment period. The fund has a total of $$500$ million in committed capital and invests in several portfolio companies.

At the end of the investment period, the fund has generated a net internal rate of return $($IRR$)$ of $15\%.$

Calculate the performance fee

A $$70$ million

B $$10$ million

$$11$ million

D $$7$ million