$2.$ XYZ fund is an index fund. The fund has a promising return of $12\%$ per year on average. Assume that an investor invests $$1,000,000.$

a$.$ If the fund charges no fee, what would be the return after $5,10,$ and $20$ years?

b$.$ If the fund charges front$-$load fee of $1\%,$ what would be the return after $5,10,$ and $20$ years?

c$.$ If the fund charges end$-$load fee of $1\%,$ what would be the return if the investor decides to sell the fund after $20$ years?