SOLUTION: A foundation invests $50,000 at simple interest, a part at 7%, twice the amount at 2%, and the rest at 5.5%. What is the most the foundation can invest at 2% and be guaranteed $2,4

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: A foundation invests $50,000 at simple interest, a part at 7%, twice the amount at 2%, and the rest at 5.5%. What is the most the foundation can invest at 2% and be guaranteed $2,4      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1141790: A foundation invests $50,000 at simple interest, a part at 7%, twice the amount at 2%, and the rest at 5.5%. What is the most the foundation can invest at 2% and be guaranteed $2,420 in interest per year?
Answer by ikleyn(52854) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let x dollars be the amount invested at 7%.


Then the amount invested at 2% is 2x dollars,

and the amount invested at 5.5% is the rest  (50000-x-2x) = (50000-3x) dollars.


Your total interest INEQUALITY is then


    0.07x + 0.02*(2x) + 0.055*(50000 - 3x) >= 2420   dollars.


Simplify and solve for x


    0.07x + 0.04x - 0.165x >= 2420 - 0.055*50000

    -0.055x <= -330

    x >= %28-330%29%2F%28-0.055%29 = 6000 dollars.


Hence, investment at 2% must be greater than or equal to 12000 dollars.    ANSWER

--------------

Notice that the question in the post is formulated  INCORRECTLY  (!)

The correct question should be 

    What is the minimum amount the foundation can invest at 2% and be guaranteed $2,420 in interest per year?


    Then the answer is : the minimum is $12000.