3. Mutual Funds IV [16 points] With \$10,000, you are considering investing in one of the two competing mutual funds A and B, with the information given below. The annual operating expense of both funds is charged at year end, based on the value of investment at the year end. Assume that both funds' return (before annual operating expense) for the 3 invested money for each year is 10%. (a) [1 points] Assume the load in the table is a front load, if you plan to invest for exactly 5 years, calculate the future value in 5 years if you put $1000 today in each of the funds, considering the load and annual expense. Which fund would you pick? (b) [1 points] Assume the load in the table is a front load, if you plan to invest for exactly 10 years, calculate the future value in 10 years if you put $1000 today in each of the funds, considering the load and annual expense. Which fund would you pick? (c) [2 points] Continue with (a) and (b), using Excel, draw the future values of your investment in fund A vs fund B, with x-axis: number of years from now; y-axis: future value. There should be two curves for A and B respectively, and each curve contains 11 data points, starting at 0 years from now, and ending at 10 years from now. Label the graph properly. (d) [2 points] Based on the curve in (c), answer the following: i) if you plan to invest for more than 6 years, which fund would you pick? ii) if you plan to invest for less than 4 years, which fund would you pick? (e) [1 points] Using the formula, FV=P(1L)(1+r)T(1F)T. Approximately at which point in time are you indifferent in investing in the two funds? (f) [4 points] A back load is a load that only applies if you sell your ownership in funds and get your money back in cash. Assume back load applies after the annual operating cost is charged. Assume that the load in the table is back load instead of front load; ie, back load is charged but front load is not. Assume in addition that annual operating expenses do not change in the table. For fund A, calculate the future value in cash that you can get back in 5 years. Compare the result with future value for fund A in (a), what do you find? For fund A, calculate the future value in cash that you can get back in 10 years. Compare the result with future value for fund A in (b), what do you find? (g) [2 points] Continue with (f), using Excel, for fund A, draw the curve for future value in cash 4 that you could possibly get back at the end of each year, for the future 10 years. X-axis: number of years from now; y-axis: future value in cash after back load. Label the graph properly. (h) [2 points] Continue with (g), putting the curve in (g) and the curve in (c) for fund A in the same graph. X-axis: number of years from now; Y-axis: future value; title: future value in cash (back load vs front load). Label the graph properly. What do you find? (i) [1 points] Based on the result in (h), write down the formula for the future value in cash that you could possibly get back for a given year, with the notations in (e)