Question

You are considering an investment in a mutual fund with a 4% front-end load. The fund charges a back-end load of 5, 4, 3, 2, and 1 percent if the shares are redeemed within the first 5 years, respectively. The expense ratio of 0.5%. Alternatively, you can invest instead in a bank saving account paying 6% interest per year.

a. If you plan to invest for 3 years, what annual rate of return must the fund portfolio earn for you to be better off in the fund than in the bank saving account? Assume annual compounding of returns.

Answer 1

Annual rate of return should be greater than 9.05%

Here

Front-end load = 4% = 0.04

Back-end load = 3% = 0.03    (As the plan is to invest for 3 years)

Expense ratio = 0.5% = 0.005

Let r be the rate of return on the fund

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

Suppose $1 is invested, then

Return after 3 years = (1 – 0.04) * (1+r-0.005)³ * (1 – 0.03) (As 4% and 3% are the Front-end load and Back-end load respectively)

Considering the annual compounding of returns, the compound interest on $1 for 3 years will be (1 + 0.06)³

Hence for the fund to do better than the bank saving account, we need

(1 – 0.04) * (1+r-0.005)³ * (1 – 0.03) > (1 + 0.06)³

⇒ 0.96 * (0.995 + r)³ * (0.97) > (1.06)³

⇒ (0.995 + r)³ > 1.191016/0.9312

⇒ (0.995 + r)³ > 1.27901202749

⇒ (0.995 + r)³ > (1.08548762369)³

⇒ 0.995 + r > 1.08548762369
⇒ r > 1.08548762369 – 0.995

⇒ r > 0.09048762369

⇒ r > 9.05%