23) Actively managed mutual funds charge higher management fees than passive fun

Question

23) Actively managed mutual funds charge higher management fees than passive funds. Assume that the net return to an active fund (after fees) is 9.5% (0.79% per month) and the net return to a passive fund is 10.5% (0.875% per month). Consider an investor who invests $600 per month (end-of-month) over thirty years in the passive fund. What is the future value of her savings? Now consider an investor who invests on a monthly basis over thirty years in the active fund. If the active fund investor wants the same future value as the passive fund investor, then how much more must she invest per month?

A) $145.79

B) $150.62

C) $59.86

D) $152.33

E) $167.92

Answer:  

Explanation / Answer

FV (passive) = 600 * [(1+0.00875)^360 -1]/0.00875 = 1509840.6

FV(active) =1509840.6

x * [(1+0.0079)^360 -1]/0.0079 = 1509840.6

x = 745.79

much more to invest = 745.79 - 600 = 145.79

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