Question

You are considering an investment in a mutual fund with a 3% load and expense ratio of 0.75%. You can invest instead in a bank CD paying 2% interest.

a. If you plan to invest for 5 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

Annual rate of return =

b. What annual rate of return must the fund portfolio earn if you plan to invest for 10 years to be better off in the fund than in the CD?

Annual rate of return =

c. Now suppose that instead of a front-end load the fund assesses a 12b-1 fee of .50% per year. What annual rate of return must the fund portfolio earn for you to be better off in the fund than in the CD?

Annual rate of return =

Answer 1

a. If you plan to invest for 5 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
Annual rate of return of the fund’s assets be r
Annual net return to a buyer of the fund = 1 + r − .0075
Return after five years of $1 invested in the fund = (1− 0.03) × (1+ r−0.0075)^5   = .97 x (r -.9923)^5
Compounded return on $1 invested in CD = (1+2%)^5
.97 x (r -.9923)^5 >   (1+2%)^5
Annual rate of return = r > 0.033933	3.39%
b. What annual rate of return must the fund portfolio earn if you plan to invest for 10 years to be better off in the fund than in the CD?
.97 x (r -.9923)^10 >   (1+2%)^10
Annual rate of return = r > 0.030812	3.08%
c. Now suppose that instead of a front-end load the fund assesses a 12b-1 fee of .50% per year. What annual rate of return must the fund portfolio earn for you to be better off in the fund than in the CD?
Annual rate of return = 1 + r − 0.0075 − 0.0050 > 1.02
Annual rate of return r  = > 0.0325	3.25%