Billy invests $$2$ million in mutual fund. At the end of the next $3$ years, Billy invest additional amounts in that same mutual fund. The annual returns to the fundare $-5\%$ for the first year, $-1\%$ for the second year, $+6\%$ for the third year, and $+9\%$ for the fourth year. Which one of the following responses is correct?

a$.$ The time$-$weighted geometric average annual return is $2\mathrm{.}099\%,$ which is less than dollar$-$weighted$-$average annual return

b$.$ The time$-$weighted geometric average annual return is $2\mathrm{.}250\%,$ which is less than dollar$-$weighted$-$average annual return

c$.$ The time$-$weighted geometric average annual return is $8\mathrm{.}665\%,$ which is greater than dollar$-$weighted$-$average annual return

d$.$ The time$-$weighted geometric average annual return is $2\mathrm{.}250\%,$ which is greater than dollar$-$weighted$-$average annual return

e$.$ The time$-$weighted geometric average annual return is $8\mathrm{.}665\%,$ which is equal to the dollar$-$weighted$-$average annual return

f$.$ The time$-$weighted geometric average annual return is $2\mathrm{.}099\%,$ which is equal to the dollar$-$weighted$-$average annual return

g$.$ The time$-$weighted geometric average annual return is $2\mathrm{.}250\%,$ which is equal to the dollar$-$weighted$-$average annual return

h$.$ The time$-$weighted geometric average annual return is $2\mathrm{.}099\%,$ which is greater than dollar$-$weighted$-$average annual return

i$.$ The time$-$weighted geometric average annual return is $8\mathrm{.}665\%,$ which is less than dollar$-$weighted$-$average annual return