An investor has invested $$10$ million in a private equity fund with a $2\%$ management fee and a $20\%$ incentive fee.

The fund has an onshore feeder with a gross asset value of $$100$ million and an offshore feeder with a gross asset value of $$50$ million. The fund has a soft hurdle rate of $10\%.$

The fund has not yet crystallized any gains and has not yet conducted any equalizations. The net asset value of the fund is $$125$ million.

b$)$ What is the total incentive fee charged by the fund?

A $$22\mathrm{.}4$m

B$$22\mathrm{.}3$m

C $$22\mathrm{.}5$m

D $$22\mathrm{.}2$m