You are about to invest some money in a bond fund. The management fee of the fund is quite low, it only charges a fee of 2%/year on the assets managed. However, you do not believe the bond fund manager has superior ability to beat the market and you expect him to earn a return of 10%/year (before management fee) on the assets of the fund. This is the same return that you (and everyone else) will be able to get but you just do not want the hassle of managing your own money.
(a) Suppose you plan to leave the money in the bond fund for 20 years. For every dollar that you invest in the bond fund today, how much are you effectively giving to the fund manager for his service over the next 20 years?
(b) How would your answer in part (a) change if you plan to leave the money in the bond fund for a very long period of time (say for T years, where T is a very large number).