Suppose an individual invests $35,000 in a load mutual fund for two years. The l

Question

Suppose an individual invests $35,000 in a load mutual fund for two years. The load fee entails an up-front commission charge of 3.9 percent of the amount invested and is deducted from the original funds invested. In addition, annual fund operating expenses (or 12b-1 fees) are 0.70 percent. The annual fees are charged on the average net asset value invested in the fund and are recorded at the end of each year. Investments in the fund return 6 percent each year paid on the last day of the year. If the investor reinvests the annual returns paid on the investment, calculate the annual return on the mutual funds over the two-year investment period.

Explanation / Answer

up-front commission charge=3.9 percent of the amount invested

up-front commission charge=3.9%*$35,000=0.039*$35,000=$1365

Therefore the actual funds investment=$35,000 -$1365=$ 33,635

net asset value at the starting of the year 1=$ 33,635

net asset value at the end of the year 1=$ 33,635*(1.06)=$ 35653.10

average net asset value invested in the fund during year 1=($ 33,635+$ 35653.10)/2=$ 34644.05

The annual fund operating expense for year 1=0.7%*$ 34644.05=0.007*$ 34644.05=$ 242.50835

Thus net asset value at the end of the year 1 after deducting the annual fund operating expense for year 1

=$ 35653.10-$ 242.50835

=$ 35410.59165

net asset value at the starting of the year 2=$ 35410.59165

net asset value at the end of the year 2=$ 35410.59165*(1.06)=$ 37535.227149

average net asset value invested in the fund during year 2=($ 35410.59165+$ 37535.227149)/2=$ 36472.9093995

The annual fund operating expense for year 1=0.7%*$ 36472.9093995=0.007*$ 36472.9093995=$ 255.3103657965

Thus net asset value at the end of the year 2 after deducting the annual fund operating expense for year 2

=$ 37535.227149-$ 255.3103657965

=$ 37279.9167832035

Thus, annual return on the mutual funds over the two-year investment period.

=(net asset value at the end of the year 2/$ 35,000)^(1/2)-1

=($37279.9167832035/$35,000)^(1/2)-1

=0.032056

=3.21%

Therefore the annual return on the mutual funds over the two-year investment period is 3.21%.

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