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

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(52855) (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 >=  = 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.

RELATED QUESTIONS
Using simple interest, a foundation invests $65,000: a part at 7%, twice that... (answered by VFBundy)

A university invests $600,000 at simple interest, part at 6%, half that amount at 4.5%,... (answered by lwsshak3)

Larry Mitchell invested part of his $30,000 advance at 5% annual simple interest and the... (answered by greenestamps)

Larry Mitchell invested part of his $31,000 advance at 5% annual simple interest and the... (answered by amoresroy)

Joe invests $6000, part at 5% interest and the rest at 7%. If his annual interest income... (answered by mananth)

A woman invests $33,000, part at 8% and the rest at 9 1/2% annual interest. If the 9 1/2% (answered by Boreal)

A man invested $6,000, part of it at 5% simple interest and the rest at 7% simple... (answered by Earlsdon)

A man invested $6000, part of it at 5% simple interest and the rest at 7% simple... (answered by checkley71)

a man invested $6000, part of it at 5%simple interest and the rest at 7% simple interest. (answered by checkley77)