SOLUTION: A bank loaned out $7,500, part of it at the rate of 14% annual interest, and the rest at 9% annual interest. The total interest earned for both loans was $825.00. How much was loan

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Question 1164802: A bank loaned out $7,500, part of it at the rate of 14% annual interest, and the rest at 9% annual interest. The total interest earned for both loans was $825.00. How much was loaned at each rate?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52800)   (Show Source): You can put this solution on YOUR website!
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A bank loaned out $7,500, part of it at the rate of 14% annual interest, and the rest at 9% annual interest.
The total interest earned for both loans was $825.00. How much was loaned at each rate?
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Let x be the amount loaned at 14% annual interest.

Then the amount loaned at 9% interest is  (7500-x) dollars.


The total interest equation is


    0.14x + 0.09*(7500-x) = 825  dollars.


From the equation,


    x =  = 3000.


ANSWER.  $3000 was loaned at 14%  and  the rest, 7500-3000 = 4500 dollars was loaned at 9%.


CHECK.  0.14*3000 + 0.09*4500 = 825  dollars.   ! Correct !

Solved.



Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


Here is a quick and easy path to the solution, if a solution using formal algebra is not required.

$825 interest on $7500 is an interest rate of 825/7500 = 0.11 = 11%.

11% is 2/5 of the way from 9% to 14%.

Therefore, 2/5 of the money was loaned at the higher rate.

ANSWER: 2/5 of $7500, or $3000, at 14%; the other $4500 at 9%.

CHECK: .14(3000)+.09(4500) = 420+405 = 825
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