OwI Ventures has raised their $$500M$ fund, OwI Ventures IX $($fund size $$500$ million$),$ with terms as given in Appendix $2.$C$.$ The management fees given in this appendix are as follows.

Management Fees: All management fees are computed based on committed capital. These fees are $2$ percent in years $1$ and $2,2\mathrm{.}25$ percent in years $3$ and $4,2$ percent in year $5,1\mathrm{.}75$ percent in year $6,1\mathrm{.}50$ percent in year $7,1\mathrm{.}25$ percent in year $8,1$ percent in year $9,$ and $0\mathrm{.}75$ pertent in year $10.$ These fees will be paid quarterly, with equal installments within each year.

Given this description, what are the lifetime fees and investment capital for this fund?

Lifetime fees $=$$$83\mathrm{.}75M,$ Investment capital $=$$$416\mathrm{.}25M$

Lifetime fees $=$$$416\mathrm{.}25M,$ Investment capital $=$$$500M$

Lifetime fees $=$$$416\mathrm{.}25M,$ Investment capital $=$$$83\mathrm{.}75M$

Lifetime fees $=$$$83\mathrm{.}75M,$ Investment capital $=$$$500M$