Question

Suppose an individual invests $10,000 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 12 b−1 fees) are 0.85 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 5 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.

Answer 1

The annual return on the mutual fund over the two-year investment period is 9.8%.

Step-by-step explanation:

To calculate the annual return on the mutual fund over the two-year investment period, we need to consider the load fee, annual fund operating expenses, and the annual return on the investment.

First, we will calculate the amount after deducting the load fee. The load fee is 2% of $10,000, which is $200. So, the amount after deducting the load fee is $10,000 - $200 = $9,800.

Next, let's calculate the annual fees. The average net asset value invested in the fund is $9,800 for both years. The annual fees are 0.85% of $9,800, which is $83.30 per year.

Finally, let's calculate the annual return on the investment. The investment returns 5% each year. So, the return on the investment for the first year is 5% of $9,800, which is $490. The return on the investment for the second year is also 5% of $9,800, which is another $490.

Now, let's calculate the total return over the two-year investment period. The total return is the sum of the returns for each year, which is $490 + $490 = $980.

Finally, let's calculate the annual return on the mutual fund. The annual return is the total return divided by the original investment amount, which is $980 / $10,000 = 0.098 or 9.8%.

Answer 2

Answer and Explanation:

To calculate the annual return on the mutual fund over the two-year investment period, we need to consider the initial investment, the load fee, the annual fund operating expenses, and the annual returns.

1. Calculate the load fee deduction:

The load fee is 2% of the initial investment of $10,000.

Load fee deduction = 2% of $10,000 = $200

2. Calculate the net initial investment:

Net initial investment = Initial investment - Load fee deduction

Net initial investment = $10,000 - $200 = $9,800

3. Calculate the average net asset value for each year:

At the end of each year, the annual fees are charged on the average net asset value.

Year 1: Average net asset value = Net initial investment

Year 2: Average net asset value = Net initial investment + Return from Year 1

4. Calculate the return for each year:

The investment returns 5% each year, paid on the last day of the year.

Year 1 return = 5% of Net initial investment

Year 2 return = 5% of (Net initial investment + Return from Year 1)

5. Calculate the annual fees for each year:

The annual fund operating expenses are 0.85% of the average net asset value.

Year 1 fees = 0.85% of Net initial investment

Year 2 fees = 0.85% of (Net initial investment + Return from Year 1)

6. Calculate the total return after two years:

Total return = Return from Year 1 + Return from Year 2

7. Calculate the total fees after two years:

Total fees = Year 1 fees + Year 2 fees

8. Calculate the net return after fees:

Net return = Total return - Total fees

9. Calculate the annual return on the mutual fund:

Annual return = (Net return / Net initial investment) ^ (1 / number of years) - 1

Substitute the values into the formula and calculate the annual return on the mutual fund over the two-year investment period.

Please note that the calculations involve multiple steps, so it's essential to pay attention to each intermediate calculation and round the final answer to three decimal places as specified in the question.