Question

You are considering an investment in a mutual fund with a 4% load and an expense ratio of 0.5%. You can invest instead in a bank CD paying 6% interest. ) You are considering an investment in a mutual fund with a 4% load and an expense ratio of 0.5%. You can invest instead in a bank CD paying 6% interest. ) You are considering an investment in a mutual fund with a 4% load and an expense ratio of 0.5%. You can invest instead in a bank CD paying 6% interest. ) You are considering an investment in a mutual fund with a 4% load and an expense ratio of 0.5%. You can invest instead in a bank CD paying 6% interest.

How does your answer change if you plan to invest for six years? Assume annual compounding of returns.  How does your answer change if you plan to invest for six years? Assume annual compounding of returns. ?

Answer 1

Let 'r' be the annual rate of return for mutual funds, with an expense ratio of 0.5% and load of 4%.

Return after 6 years would be as follows:

Year6 return = ($1 - 4% of $1) * ($1 + r - 0.5% of $1)6

= ($0.96) * ($0.995 + r)6

Similarly, return on CD at the rate of 6% on $1 would be:

CD return = ($1 + 6% of $1)6   = ($1.06)6

For the fund, to be better off than CD, return on fund should be more than CD, hence r can be calculated:

($0.96) * ($0.995 + r)6   > ($1.06)6

($0.96) * ($0.995 + r)6   > $1.418519112256

($0.995 + r)6   > $1.47762407526667

($0.995 + r) > $1.06723647506276

r > 0.072236475062757 or 7.22%

Hence, for a period of 6 years, rate of interest should be 7.22%.