SOLUTION: A pension fund manager has been given a total of $900,000 by a corporate client to invest in certain types of stocks over the next year. Stuck must be restricted to a certain clas

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Question 1197167: A pension fund manager has been given a total of $900,000 by a corporate client to invest in
certain types of stocks over the next year. Stuck must be restricted to a certain class of low - risk
stocks and another class of medium risk stocks. The pension fund manager assumes from
historical data that the low-risk stocks should return 6 % annually and the medium risk stocks
12% annually. If the client demands an annual return of 8%, what should the pension fund
manager do?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52908)   (Show Source): You can put this solution on YOUR website!
.
A pension fund manager has been given a total of $900,000 by a corporate client to invest in
certain types of stocks over the next year. Stuck must be restricted to a certain class of low-risk
stocks and another class of medium risk stocks. The pension fund manager assumes from
historical data that the low-risk stocks should return 6 % annually and the medium risk stocks
12% annually. If the client demands an annual return of 8%, what should the pension fund
manager do?
~~~~~~~~~~~~~~~~~ 

Let x be the amount invested at 12%, in dollars.

Then the amount invested at 6% is the rest  (900000-x)  dollars.


Write the total interest equation

    0.12x + 0.06(900000-x) = 0.08*900000.


Here right side represents 8% return of the total investment.


Simplify equation and find x

    0.12x + 0.06*900000 - 0.06x= 0.08*900000

    0.12x - 0.06x = 0.08*900000 - 0.06*900000

         0.06x    =          18000

            x     =          18000/0.06 = 300,000  dollars.


ANSWER.  $300,000 to invest at 12%,  and the rest $900,000 - $300,000 = $600,000 to invest at 6%.


CHECK.   0.12*300000 + 0.06*600000 = 72000 dollars, same as 0.08*900000 = 72000, total annual interest.   ! correct !

Solved.

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

It is a standard and typical problem on investments.

If you need more details,  or if you want to see other similar problems solved by different methods,  look into the lesson
    - Using systems of equations to solve problems on investment
in this site.

You will find there different approaches  (using one equation or a system of two equations in two unknowns),  as well as
different methods of solution to the equations  (Substitution,  Elimination).

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic  "Systems of two linear equations in two unknowns".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.



Answer by greenestamps(13215)   (Show Source): You can put this solution on YOUR website!


Here is a quick and easy non-algebraic approach to solving any 2-part "mixture" problem like this.

(1) The desired percent return, 8%, is 1/3 of the way from 6% to 12%. (Picture the three percentages on a number line, if it helps.)

(2) That means 1/3 of the total should be invested at the higher rate.

ANSWER: 1/3 of $900,000, or $300,000 at 12%; the other $600,000 at 6%.

CHECK:
.12(300,000)+.06(600,000) = 36000+36000 = 72000
.08(900000) = 72000
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