SOLUTION: A person has $50,000 to invest. As the​ person's financial​ consultant, you recommend that the money be invested in Treasury bills that yield 4% Treasury bonds that yield 8% a

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Question 1186746: A person has $50,000 to invest. As the​ person's financial​ consultant, you recommend that the money be invested in Treasury bills that yield 4% Treasury bonds that yield 8% and corporate bonds that yield  12% The person wants to have an annual income of $3920 and the amount invested in corporate bonds must be half that invested in Treasury bills. Find the amount in each investment.
Answer by ikleyn(52834) About Me  (Show Source):
You can put this solution on YOUR website!
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A person has $50,000 to invest. As the​ person's financial​ consultant, you recommend that
- - - the money be invested in Treasury bills that yield 4%,
- - - Treasury bonds that yield 8%, and
- - - corporate bonds that yield  12%.
The person wants to have an annual income of $3920 and the amount invested in corporate bonds
must be half that invested in Treasury bills. Find the amount in each investment.
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            Look how nicely I re-formatted your post to make major key info easy readable.
            By the way,  it is  IMPORTANT  PART  of the reading stage and the solution procedure  ( ! ) 


Let x be the amount invested in corporate bonds (12%), in dollars.

Then the amount invested in Treasury bills (4%) is twice of it, i.e. 2x dollars,

and the amount invested in Treasury bonds (8%) is the rest  (50000-x-2x) = (50000-3x)  dollars.



At this point, you can write the total annual interest equation

    0.12x + 0.04*(2x) + 0.08*(50000-3x) = 3920.



The setup is completed.  To solve the equation, simply it step by step

    0.12x + 0.08x + 0.08*50000 - 0.24x = 3920

    0.12x + 0.08x - 0.24x = 3920 - 0.08*50000

           - 0.04x        = -80

                 x        = -80/(-0.04) = 80/0.04 = 8000/4 = 2000.



Thus the amount invested in corporate bonds is  x = 2000  dollars;

                invested in Treasury  bills is  2x = 2*2000 = 4000  dollars,

           and  invested in Treasury  bonds is the rest 50000 - 2000 - 4000 = 44000  dollars.


CHECK.  0.12*2000 + 0.04*4000 + 0.08*44000 = 3920  dollars, the total annual interest.    ! Correct !

Solved.

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The most interesting in my solution is that I managed to solve the problem using only one unknown and one single equation.

It is the major lesson for you to learn.