Mathematics
MAT 104 NYU The Average Annual Return Project Worksheet

MAT 104

New York University

MAT

Question Description

I’m stuck on a Mathematics question and need an explanation.

MAT104 Project 1.xlsx 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:

just do the project for me


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Project 1 The average annual return (over 5-year period prior to September 29, 2006) of three mutual funds offered by AXA Equitable Average Annual Return Mutual Fund 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 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 ቐ 𝑥 + 𝑦 + 𝑧 = 5000 𝑥 − 𝑦 = 200 0.0518𝑥 + 0.0566𝑦 + 0.1232𝑧 = 5000𝑖 Total invested $ 200 more in the Moderate Allocations Total rate of return With: Matrix A = 1 1 1 1 −1 0 0.0518 0.0566 0.1232 𝑥 Matrix B = 𝑦 𝑧 Matrix X = The system of equations is given by: AX = B The solution of the system is X = A-1B A: 1 1 0.0518 Then X = A-1B Meaning that 1 -1 0.0566 1 0 0.1232 5000 200 5000 ∗ 0.09 We proceed to find A-1 0.892754 0.482609 -7.24638 0.892754 -0.51739 -7.24638 -0.78551 0.034783 14.49275 1299.42029 1099.42029 2601.15942 x y z 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 B 5000 200 450 ...
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Final Answer

Attached.

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
Annual
Return

Mutual Fund
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 wi...

Lincolvin (13681)
University of Virginia

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