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ou invest $1000 in a mutual fund. You expect that the fund will earn a 8% return annually before expenses (~this is how much the fund's assets go up). You have a choice between purchasing class A mutual fund shares with a front-end load of 4% and no expenses or class C mutual fund shares with no loads but a 1% 12b-1 fee. What is your investment horizon if you are indifferent between these two

Respuesta :

Answer:

4.3883 years

Explanation:

The investment horizon to be indifferent between both investments is the number of years it takes for the total investment sum + interest on both investments to be the same. If that value is 'n', then

the value of class A mutual fund at n years = [tex]1000(1-0.04)*(1.08)^{n}[/tex]

the value of class C mutual fund after n years = [tex]1000*(1.08-0.01)^{n}[/tex]

At the point of indifference, the values of both investments will be the same.

Therefore,

[tex]1,000(1-0.04)(1.08)^{n} =1,000(1.08-0.01)^{n} \\960*(1.08)^{n} =1,000*1.07^{n}\\\frac{1.08^{n} }{1.07^{n}} =\frac{1,000}{960}\\(\frac{1.08}{1.07})^{n} =1.041667\\1.009346^{n} =1.041667\\n=4.3883[/tex]

This is the value of n that solves the equation (deduced by interpolation).

Therefore the investment horizon of indifference = 4.3883 years.

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