A private equity fund has a $20\%$ carried interest rate and a $7\%$ preferred return. The fund has a net asset value of $$100$ million, and the general partner has invested $$5$ million.

The fund has realized gains of $$50$ million. What is the total amount of distributions to the limited partners and the general partner under an American waterfall structure?

A $$47\mathrm{.}5$ million to the limited partners and $$2\mathrm{.}5$ million to the general partner

B$$45$ million to the limited partners and $$5$ million to the general partner

C $$40$ million to the limited partners and $$10$ million to the general partner

D $$39\mathrm{.}33$ million to the limited partners and $$10\mathrm{.}675$ million to the general partner