SOLUTION: Last year, Michael had $20,000 to invest. He invested some of it in an account that paid 6% simple interest per year, and he invested the rest in an account that paid 9% simple int

Algebra ->  Finance -> SOLUTION: Last year, Michael had $20,000 to invest. He invested some of it in an account that paid 6% simple interest per year, and he invested the rest in an account that paid 9% simple int      Log On


   

Question 1189688: Last year, Michael had $20,000 to invest. He invested some of it in an account that paid 6% simple interest per year, and he invested the rest in an account that paid 9% simple interest per year. After one year, he received a total of $1710 in interest. How much did he invest in each account?
Answer by ikleyn(52781) About Me  (Show Source):
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Last year, Michael had $20,000 to invest. He invested some of it in an account that paid 6% simple interest
per year, and he invested the rest in an account that paid 9% simple interest per year.
After one year, he received a total of $1710 in interest. How much did he invest in each account?
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Let x be amount invested at 9%, in dollars;

then amount invested at 6% is the rest (20000-x) dollars.


Write an equation for the total annual interest

    0.09x + 0.06*(20000-x) = 1710  dollars.


From the equation,

    x = %281710+-+0.06%2A20000%29%2F%280.09-0.06%29 =  17000.


ANSWER.  $17000 invested at 9% and the rest  20000-17000 = 3000 dollars invested at 6%.


CHECK.   0.09*17000 + 0.06*3000 = 1710, total annual interest.   ! 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.