A VC firm is considering two compensation structures. The fund is $$100$m$.$ Management fees will be $2\mathrm{.}5\%$ per year on committed capital for all $10$ years.

$1.$ Option A: the fund will charge $25\%$ carry with committed capital as the basis.

$2.$ Option B: the fund would have $20\%$ carry on all investment capital.

Q$1.$ Suppose that total exit proceeds from all investments are $$150$m at the end of the fund's life. How much carried interest would be earned under A and B$?$ Q$2$: For what amount of exit proceeds would these two structures generate the same amount of carried interest?