Question 1141789: Luis just retired, and has $900,000 to invest. A very safe Certificate of Deposit (CD) account pays 2%, while a riskier bond fund pays 4.5% in interest. Luis figures he needs $36,000 a year in interest to live on. How much should he invest in each account to make enough interest while minimizing his risk?
How much $ at 2%?
How much $ at 4.5%
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52790)   (Show Source):
You can put this solution on YOUR website! .
Let x dollars be the amount (now unknown) to invest at 4.5%.
Then the amount at 2% is the rest (900000-x) dollars.
The total interest equation is
0.02*(900000-x) + 0.045*x = 36000.
From the equation, express x and calculate
x =  = 720000.
ANSWER. $720000 must be invested at 4.5% and the rest (900000-720000) = 180000 dollars must be invested at 2%.
CHECK. 0.045*720000 + 0.02*180000 = 36000 dollars. ! Correct !
Solved.
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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(13200)  (Show Source):
You can put this solution on YOUR website!
Here is an alternative to the standard algebraic solution method shown by the other tutor. If you understand this method, it will get you to the solution to any mixture problem like this much faster and with far less effort than the algebraic method.
The method is based on the fact that the ratio in which the money must be split between the two investments is exactly determined by where the average interest rate lies between the two individual interest rates.
$36,000 on an investment of $900,000 is an interest rate of 4%.
Picture the three rates on a number line -- 2%, 4%, and 4.5%. Simple arithmetic shows that the 4% is 4/5 of the way from 2% to 4.5%. (4.5-2 = 2.5; 4-2 = 2; 2/2.5 = 4/5)
That means 4/5 of the total investment must be at the higher rate.
ANSWER: 4/5 of $900,000 = $720,000 at 4.5%, the rest, $180,000, at 2%.
CHECK: 
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