SOLUTION: 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

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(52803) (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.

RELATED QUESTIONS
Dustin just retired, and has $530,000 to invest. A very safe Certificate of Deposit (CD)... (answered by Boreal)

Luis just retired, and has $900,000 to invest. A very safe Certificate of Deposit (CD)... (answered by ikleyn,greenestamps)

Miguel just retired, and has $590,000 to invest. A very safe Certificate of Deposit (CD)... (answered by Boreal)

A retired woman has $80,000 to invest but needs to make $6,000 a year from the interest... (answered by Theo)

A retired couple has $192,000 to invest. A safe investment yields 9.5% per year, but a... (answered by ikleyn)

A recently retired couple have $150,000 to invest in two different accounts: a bank... (answered by ikleyn)

A retired couple has $380,000 to invest. They chose one relatively safe investment fund (answered by ikleyn)

Sue has $80,000 to invest in a savings account, which pays 7% and a certificate of... (answered by Fombitz)

A mother wants to invest $11,000 for her son's future education. She invests a portion of (answered by scott8148)