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Question 1123023: Chris received $50,000 from his grandparents as a graduation gift. So, he has decided to invest the money to pay his living cost at a college, which is $3,000 a year. There are two options: a bond that pays 12% and a CD that pays 5%. How much should he invest in the bond?
Answer by ikleyn(52776)   (Show Source):
You can put this solution on YOUR website! .
Let x= "How much should he invest in the bond".
Then the rest, which is (50000-x) dollars, he invests in CD.
His yearly interest from the bond is 0.12x, according to the condition.
His interest from the CD is 0.05*(50000-x) dollars.
Your equation is
interest + interest = total interest, or
0.12x + 0.05*(50000-x) = 3000 dollars.
Simplify and solve for x:
0.12x + 0.05*50000 - 0.05x = 3000,
0.07x = 3000 - 0.05*50000
x =  = 7142.86.
Answer. He should invest $7142.86 at 12% and the rest $50000 - $7142.86 = $42857.14 at 5%.
Check. 0.12*7142.86 + 0.05*42857.14 = 3000.00 ! Correct !
Solved.
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It is a typical and standard problem on investment.
To see many other similar solved problems on investment, 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.
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