You are going to invest in a stock mutual fund with a 6 percent front-end load a

Question

You are going to invest in a stock mutual fund with a 6 percent front-end load and a 1.91 percent expense ratio. You also can invest in a money market mutual fund with a 3 percent return and an expense ratio of 0.3 percent. If you plan to keep your investment for 2 years, what annual return must the stock mutual fund earn to exceed an investment in the money market fund? What if your investment horizon is 9 years? (Round your answer to 2 decimal places. Omit the "%" sign in your response.)

2 years %

9 years %

Explanation / Answer

Ans)

Let r denote the annual rate of return of Stock mutual fund

Each year the net return to a buyer will be 1 + r - 0.0191. Therefore, the return after 2year of $1 invest in the stock mutual funds is   

(1 - 0.06) x ( 1 + r - 0.0191)2

On the other hand the compound return on $1 invested in the money market mutual fund will be

(1 + 0.03 - 0.003)2

Hence for the stock mutual fund to do better than the money market mutual fund , we need

(1 - 0.06) x ( 1 + r - 0.0191)2 > (1 + 0.03 - 0.003)2

r => 7.83%

Now, We are comparing the same returns but over 9 years instead of 2 years....

(1 - 0.06) x ( 1 + r - 0.0191)9  > (1 + 0.03 - 0.003)9

r = 5.32 %

the difference is due to the front-end load is spread over 9 years instead of 2, reducing its effective cost to the
investor.

Therefore in the above given option, the answer is

2 years =7.83%

9 years = 5.32%

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