To determine To calculate: The amounts Ellen must invest in a money market account, a bond fund, an international stock fund, and a domestic stock fund to achieve an annual return of $4000. Explanation Given: The amount to be invested is $100000. The amount invested in international stocks must be one-fourth of the amount in domestic stocks and 60% of her investment to be conservative(money market and bonds). The annual returns in a money market account, a bond fund, an international stock fund, and a domestic stock fund are 2.5%, 3.5%, 4% and 6% respectively. Calculation: Consider Ellen invest $ x in money market account, $ y in a bond fund, $ z in an international stock fund, and $ w a domestic stock fund. As Ellen invests a total of $100000 hence, x + y + z + w = 100000 …...…...(1) As the annual returns in a money market account, a bond fund, an international stock fund, and a domestic stock fund are 2.5%, 3.5%, 4% and 6% respectively. Therefore, the total annual return will be 0.025 x + 0.035 y + 0.04 z + 0.06 w and hence, 0.025 x + 0.035 y + 0.04 z + 0.06 w = 4000 …...…...(2) As Ellen wants the amount in international stocks to be one-fourth of the amount indomestic stocks hence, z = 1 4 w That is: z − 0.25 w = 0 …...…...(3) As the amount in conservative investments ( x + y ) must be 60% of the total amount $100000 hence, x + y = 0.6 × 100000 That is: x + y = 60000 …...…...(4) The system of equation (1) (2) (3) and (4) can be written as in the matrix form as: [ 1 1 1 1 0.025 0.035 0.04 0.06 0 0 1 − 0.25 1 1 0 0 ] [ x y z w ] = [ 100000 4000 0 60000 ] Therefore, the corresponding augmented matrix is: [ 1 1 1 1 100000 0.025 0.035 0.04 0.06 4000 0 0 1 − 0.25 0 1 1 0 0 60000 ] Apply the elementary row operation R 2 = R 2 − 0.025 R 1 , and R 4 = R 4 − R 1 : [ 1 1 1 1 100000 0 0

Mathematics with Applications In the Management, Natural, and Social Sciences Plus NEW MyLab Math with Pearson eText -- Access Card Package (11th Edition)

11th Edition

ISBN: 9780321935441

Author: Margaret L. Lial, Thomas W. Hungerford, John P. Holcomb, Bernadette Mullins

Publisher: PEARSON

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Chapter 6.3, Problem 2E

To determine

To calculate: The amounts Ellen must invest in a money market account, a bond fund, an international stock fund, and a domestic stock fund to achieve an annual return of $4000.

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Chapter 6.3, Problem 1E

Chapter 6.3, Problem 3E

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Mathematics with Applications In the Management, Natural, and Social Sciences Plus NEW MyLab Math with Pearson eText -- Access Card Package (11th Edition)

Ch. 6.1 - Checkpoint1 Use the substitution method tosolve...Ch. 6.1 - Checkpoint 2 Use the elimination method to solve...Ch. 6.1 - Checkpoint 3 Solve the system of equations . Draw...Ch. 6.1 - Checkpoint 4 Solve the following system: Ch. 6.1 - Checkpoint 5 Solve the system Draw the graph of...Ch. 6.1 - Prob. 6CP Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Use substitution to solve each system. (See...Ch. 6.1 - Use substitution to solve each system. (See...

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