Project 1 The average annual return (over 5-year period prior to September 29, 2006) of three mutual funds offered by AXA Equitable is shown in the table A: Average Mutual Fund Annual Return Moderate Allocations 5.18 Equity 500 Index 5.66 Small Company Index 12.32 Suppose you have $ 5000 to invest in these three funds. You want to invest $ 200 more in the Moderate Allocations fund that you will in the Equity 500 Index fund. Questions: a. Assuming the accounts will earn the annual rates shown, how much should you invest for a year in each fund if you want you average return to be 9% b. How much should you invest in each fund if you want your average return to be 10% c. How much if you want 11% Solving part a: We begin by naming the variables Let x represent the amount invested in the Moderate Allocations Let y represent the amount invested in the Equity 500 Index Let z represent the amount invested in the Small Company Index Total invested x + y + z = 5000 x - y = 200 10.0518x + 0.0566y + 0.1232z = 5000i $ 200 more in the Moderate Allocations Total rate of return With: Matrix A = 1 Matrix - Li 1 1 -1 0 10.0518 0.0566 0.12321 Matrix B = o nel Matrix X = 5000 200 15000 + 0.09) The system of equations is given by: AX = B The solution of the system is X = A-1B We proceed to find A-1 0.892754 0.482609 -7.246377 0.892754 -0.517391 -7.246377 -0.785507 0.034783 14.49275 5000 200 450 0.0518 0.0566 0.1232 Then X = A-1B 1299.42029 1099.42029 2601.15942 Meaning that 1299.42 1099.42 2601.16 The amount to invest in each fund to achieve the three rates of return are summarized in the following table: Expected Rate of Return 9% 10% 11% Moderate Allocations 1299.42 Equity 500 Index 1099.42 Small Company Index 2601.16 Fill out the table by solving b and c based on the example given to solve a Note: Even though inverse of the matrix A is found, you need to recreate it for parts b and c using the Excel formula