SOLUTION: Betsy, a recent​ retiree, requires ​$6,000 per year in extra income. She has ​$50,000 to invest and can invest in​ B-rated bonds paying ​13% per year or in a certificate

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Betsy, a recent​ retiree, requires ​$6,000 per year in extra income. She has ​$50,000 to invest and can invest in​ B-rated bonds paying ​13% per year or in a certificate      Log On


   

Question 1168617: Betsy, a recent​ retiree, requires ​$6,000 per year in extra income. She has ​$50,000 to invest and can invest in​ B-rated bonds paying ​13% per year or in a certificate of deposit​ (CD) paying ​5% per year. How much money should be invested in each to realize exactly ​$6,000
in interest per​ year?
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
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Betsy, a recent​ retiree, requires ​$6,000 per year in extra income. She has ​$50,000 to invest and can invest
in​ B-rated bonds paying ​13% per year or in a certificate of deposit​ (CD) paying ​5% per year.
How much money should be invested in each to realize exactly ​$6,000
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She invests x dollars to 13% bonds and the rest 50000-x dollars to 5% CD.


To find the unknown x, we write the total interest equation

    0.13x + 0.05*(50000-x) = 6000  dollars.


Next, from this equation we express x and calculate

    x = %286000-0.05%2A50000%29%2F%280.13-0.05%29 = 43750  dollars.


ANSWER.  She invests $43750 to the 13% bonds and the rest 50000-43750 = 6250 dollars to CD.


CHECK.  0.13*43750 + 0.05*6250 = 6000  dollars.   ! Precisely 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.