Question

You are considering an investment in a mutual fund with a 4% load and expense ratio of 0.5%. You can invest instead in a bank CD paying 6% interest.
a. If you plan to invest for 2 years, what annual rate of return must the fund portfolio earn for you to be better off in the fund than in the CD?

Answer 1

Answer:

r>8.68695%

Annual rate of return is r>8.68695%

Explanation:

The net return, the buyer will get= 1+r-0.005

Where:

r is the interest rate

0.005 is expense ratio (0.5%)

Let suppose $1 is invested, then the return after two years is as below:

$(1-0.04)*(1+r-0.005)^2$

Considering the annual compounding of returns, the compound interest on $1 for 2 years will be $(1+0.06)^2$

The fund portfolio earn for you to be better off is:

$(1-0.04)*(1+r-0.005)^2$>$(1+0.06)^2$

$0.96*(r+0.995)^2>1.1236$

$0.96*(r^2+1.99r+0.990)>1.1236\\0.96r^2+1.9104r+0.9504-1.1236>0\\0.96r^2+1.9104r-0.173>0$

Solving the above equation, we will get:

r>0.0868695                     r>-2.0768 (Ignore this value as it is -ve

r>8.68695%

Annual rate of return is r>8.68695%