SOLUTION: A bank loaned out $27,000, part of it at the rate of 7% annual interest, and the rest at 13% annual interest. The total interest earned for both loans was $2,820.00. How much was l

Question 1161440: A bank loaned out $27,000, part of it at the rate of 7% annual interest, and the rest at 13% annual interest. The total interest earned for both loans was $2,820.00. How much was loaned at each rate?

Answer by ikleyn(52800) (Show Source): You can put this solution on YOUR website!
.


Let x be the amount at 13%;

then the amount at 7% is the rest (27000-x) dollars.


The equation for the total interest is

    0.13x + 0.07*(27000-x) = 2820  dollars.


From this equation,

    x =  = 15500  dollars.


ANSWER.  $15500 at 13% and the rest, (27000-15500) = 11500 dollars at 7%.


CHECK.   0.13*15500 + 0.07*11500 = 2820 dollars.    ! Correct !

Solved.

------------------

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
a bank loaned out 11,500, part of its interest rate of 7% annual interest, and the rest... (answered by ikleyn)

A bank loaned out $20,500, part of it at the rate of 13% annual interest, and the rest at (answered by ikleyn)

A bank loaned out $13,500, part of it at the rate of 9% annual interest, and the rest at... (answered by Amily_2190,MathTherapy,greenestamps)

A bank loaned out P 23,000, part of it at the rate of 5% annual interest, and the rest at (answered by ikleyn)

A bank loaned out $29,000, part of it at the rate of 4% annual interest, and the rest at... (answered by checkley77)

A bank loaned out $19,500, part of it at the rate of 2% annual interest, and the rest at... (answered by richwmiller)

A bank loaned out $29,000, part of it at the rate of 8% annual interest, and the rest at... (answered by Boreal)

A bank loaned out $7,000, part of it at the rate of 12% annual interest, and the rest at... (answered by ikleyn)

A bank loaned out $15,000, part of it at the rate of 4% annual interest, and the rest at... (answered by josmiceli,greenestamps)