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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.