Question

# Suppose an individual invests \$5,000 in a load mutual fund for two years. The load fee...

Suppose an individual invests \$5,000 in a load mutual fund for two years. The load fee entails an up-front commission charge of 2 percent of the amount invested and is deducted from the original funds invested. In addition, annual fund operating expenses (or 12b-1 fees) are 0.75 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 8 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 fund over the two-year investment period. (Do not round intermediate calculations. Round your answer to 3 decimal places. (e.g., 32.161))

Annual return

Initial investment = \$5000

Front end load = \$5000 * 2% = \$100

Total investment = \$5000 + \$100 = \$5100

Amount of investment at the end of year one = \$5,100 * (1+8%) = \$5,508

Operating expenses based on average NAV = ((\$5100 + \$5508) / 2) * 0.75%
= \$5304 * 0.75%
= \$39.78

Net investable fund for year 2 = \$5,508 - \$39.78 = \$5,468.22

Amount of investment at the end of year 2 = \$5,468.22 * (1+8%) = \$5,905.6776

Operating expense = ((\$5,468.22 + \$5,905.6776) / 2) * 0.75%
= \$5,686.9488 * 0.75%
= \$42.652116

Net value of investment at the end of year 2 = \$5,905.6776 - \$42.652116 = \$5,863.025484

Annual return = (\$5,863.025484 / \$5,000)^(1/2) - 1
= 8.287%

Annual return = 8.287%