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%

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