Question 1123687: Ken just retired, and has $650,000 to invest. A very safe Certificate of Deposit (CD) account pays 1%, while a riskier bond fund pays 5% in interest. Ken figures he needs $23,000 a year in interest to live on. How much should he invest in each account to make enough interest while minimizing his risk?
Answer by ikleyn(52802)   (Show Source):
You can put this solution on YOUR website! .
0.05*x + 0.01*(650000-x) = 23000
0.05*x + 65000 - 0.01x = 23000
0.04x = 23000-6500 = 16500
x =  = 412500.
Answer. Invest $412500 to the 5% bond and the rest, $650000 - $412500 = $237500 to the 1% CD.
Check. 0.05*412500 + 0.01*237500 = 23000 dollars. ! Correct !
Solved.
Notice that the given data admits only one solution and does not leave the room to minimize the risk.
--------------------
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.
|
|
|
