You are considering an investment in a mutual fund with a $4\%$ load and an expense ratio of $0\mathrm{.}5\%.$ You can invest instead in a bank CD paying $6\%$ interest. $($LO $4-5,$ pg $67-68)($Bodie $2019)$

a$)$ If you plan to invest for two years, what annual rate of return must the fund portfolio earn for you

to be better off in the fund than in the CD$?$ Assume annual compounding of returns.

b$)$ How does your answer change if you plan to invest for six years? Why does your answer change?

c$)$ Now suppose that instead of a front$-$end load the fund assesses a $12$b$-1$ fee of $0\mathrm{.}75\%$ per year.

i$)$ What annual rate of return must the fund portfolio earn for you to be better off in the fund than

in the CD$?$

ii$)$ Does your answer in this case depend on your time horizon?