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 1%/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 5%/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? (Hint: How much are you

willing to give to the manager today if he is willing to waive the management fee in

the future.)

(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).