You are going to invest in a stock mutual fund with a 5 percent front-end load a

Question

You are going to invest in a stock mutual fund with a 5 percent front-end load and a 1.71 percent expense ratio. You also can invest in a money market mutual fund with a 3.1 percent return and an expense ratio of.20 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 12 years? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)

Explanation / Answer

2 years:

stock Mutual fund wealth index after 2 years = (1-FL)*(1+r - expenses)^2

= (1-0.05)*(1+r-0.0171)^2 = 0.95*(1+r-0.0171)^2

money market mutual fund wealth index = (1+r-expenses)^2

= (1+0.031-0.002)^2 = 1.058841

Now, 0.95*(1+r-0.0171)^2 >1.058841 (for the stock mutual fund to exceed the money market fund)

(1+r-0.0171)^2 >1.114569

(1+r-0.0171)>1.05573

or r>0.072831 (7.28%)

12 years:

Here the

stock Mutual fund wealth index after 12 years = (1-FL)*(1+r - expenses)^12

= (1-0.05)*(1+r-0.0171)^12 = 0.95*(1+r-0.0171)^12

money market mutual fund wealth index = (1+r-expenses)^12

= (1+0.031-0.002)^12 = 1.409238

Now, 0.95*(1+r-0.0171)^12 >1.409238 (for the stock mutual fund to exceed the money market fund)

(1+r-0.0171)^12 >1.4834089

(1+r-0.0171)>1.033407

r>0.50507814 (5.05%)

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