Question

You are considering an investment in a mutual fund with a 4% front-end load and an expense ratio of 1.1%. You can invest instead in a bank CD paying 6% interest. 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. (Do not round intermediate calculations. Enter your answer as a decimal rounded to four decimal places.)

Annual rate of return:  

Answer 1

Solution:

Assuming, required annual rate of return is r

After 2 years:

i)Each dollar invested in a fund with a 4% load and a portfolio return equal to r will grow to;

=$1(1-0.04)*(1+r-0.0110)^2

ii)Each dollar invested in the bank CD will grow to;

=$1*(1+0.06)^2

If the mutual fund is to be better investment,then the portfolio return(r) must satisfy:

=$0.96(1+r-0.110)^2>1.06^2

=$0.96(1+r-0.0110)^2>1.1236

=(1+r-0.011)^2>1.1704

=1+r-0.011>1.0819

=1+r>1.0929

r>0.0929

therefore,annual rate of return must be greater than 9.29%