Explanation Given information: Total amount available with Cyndee is $ 50 , 000 . Pay percentage of lowest-yielding account, intermediate account and highest-yielding account is 3 % , 5.5 % and 9 % respectively. Total annual income is $ 2540 . Amount invested in lowest-yielding accountis twice the amount invested in highest-yielding account. Concept used: Triangular form of linear equation: A system of linear equations in four variables is said to be in triangular form if the first equation has all the four variables, while second equation has three variables, the third equation has two variables and the fourth equation has only one variable in its equivalent form. Calculation: Let x be the amount invested in lowest-yielding account at 3%, y the amount invested in intermediate account at 5.5%, and z the amount invested in highest-yielding accountat 9%. Thus the given financial model can be set up using the given facts as, Total amount available with Cyndee is $ 50 , 000 : x + y + z = 50000 ...... (1) Total Annual Income for Cyndee is $ 2540 and the pay percentage of lowest-yielding account is 3% of invested amount, pay percentage for intermediate account is 5.5% of invested amount and pay percentage for highest-yielding account is 9% of invested amount: 3 100 x + 5.5 100 y + 9 100 z = 2540 6 x + 11 y + 18 z = 508000 Label the above modeled equation as, 6 x + 11 y + 18 z = 508000 ...... (2) Amount invested in lowest-yielding account is twice the amount invested in highest yielding account: x = 2 z x − 2 z = 0 Label the above modeled equation as, x − 2 z = 0 ...... (3) Here, the second equation 6 x + 11 y + 18 z = 508000 involves all the threevariables Multiply equation (1) by 6 as, 6 ⋅ ( x + y + z ) = 6 ⋅ ( 50000 ) 6 x + 6 y + 6 z = 300000 Subtract the above equation from equation (2) to eliminate variable x as, 6 x + 11 y + 18 z = 508000 6 x + 6 y + 6 z = 300000 _ 5 y + 12 z = 208000 Thus, the equivalent second equation is 5 y + 12 z = 208000 ...... (4) Now, the third equation x − 2 z = 0 involves two variables x and y , Subtract equation (1) for equation (3) to eliminate variable x , x − 2 z = 0 x + y + z = 50000 _ − y − 3 z = − 50000 The equation (3) becomes, − y − 3 z = − 50000

7th Edition

ISBN: 9781305115545

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

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Chapter 5.2, Problem 40E

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The amount to be invested by Cyndee in the lowest-yielding account, the intermediate account and the highest-yielding account to achieve a total annual return of $2540.

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Chapter 5.2, Problem 39E

Chapter 5.2, Problem 41E

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The amount to be invested by Cyndee in the lowest-yielding account, the intermediate account and the highest-yielding account to achieve a total annual return of $ 2540 .

Solution Summary: The author calculates the amount to be invested by Cyndee in the lowest-yielding account, the intermediate account and the highest-young account to achieve a total annual return of 2540

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To find:

The amount to be invested by Cyndee in the lowest-yielding account, the intermediate account and the highest-yielding account to achieve a total annual return of $2540.

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Chapter 5 Solutions

The amount to be invested by Cyndee in the lowest-yielding account, the intermediate account and the highest-yielding account to achieve a total annual return of $ 2540 .

Solution Summary: The author calculates the amount to be invested by Cyndee in the lowest-yielding account, the intermediate account and the highest-young account to achieve a total annual return of 2540

Concept explainers

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To find: The amount to be invested by Cyndee in the lowest-yielding account, the intermediate account and the highest-yielding account to achieve a total annual return of $2540.

Want to see the full answer?

Chapter 5 Solutions

To find:

The amount to be invested by Cyndee in the lowest-yielding account, the intermediate account and the highest-yielding account to achieve a total annual return of $2540.