SOLUTION: Brandon invested $20 000. He invested part of the money in a term deposit paying 4% annual interest, three times as much in a government bond paying 5% annual interest, and the res

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Question 1203293: Brandon invested $20 000. He invested part of the money in a term deposit paying 4% annual interest, three times as much in a government bond paying 5% annual interest, and the rest in a second mortgage paying 7% annual interest. If he earned a total of $1130 interest in one year, how much did he invest at each rate?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
Brandon invested $20 000. He invested part of the money in a term deposit paying 4% annual interest,
three times as much in a government bond paying 5% annual interest, and the rest in a second mortgage
paying 7% annual interest. If he earned a total of $1130 interest in one year, how much did he invest at each rate?
~~~~~~~~~~~~~~~~~~ 

Invested  x         at  4%
         3x         at  5%
and      (20000-4x) at  7%.


Write the total interest equation

    0.04x + 0.05*(3x) + 0.07*(20000-4x) = 1130  dollars.


Simplify and find x

    0.04x + 0.15x + 1400 - 0.28x = 1300

    -0.09x = 1130-1400

     0.09x = 270

     x = 270/0.09 = 27000/9 = 3000.


ANSWER.  $3000 invested at 4%;  3*3000 = 9000 dollars invested at 5%;
         and the rest (20000-3000 - 9000) = 8000 dollars invested at 7%.

Solved.



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


Here is a very non-standard solution without algebra. With practice, many similar problems can be solved using the ideas demonstrated in this solution.

The interest of $1130 on a $20,000 investment represents and average rate of return of 1130/20000, which is 5.65%.

Since he invested 3 times as much at 5% as at 4%, 3/4 of the total invested at those two rates was at the higher rate. That means the average rate of return for those two investments was 3/4 of the way from 4% to 5%; that is 4.75%.

So we can view the investment as one amount at 4.75% and the other amount at 7%.

Now look at the three rates of 4.75%, 5.65%, and 7.00% (on a number line, if it helps), and observe/calculate that 5.65% is 0.90/2.25 = 2/5 of the way from 4.75% to 7%. That means 2/5 of the total of $20,000 was invested at the higher rate of 7%. 2/5 of $20,000 is $8000, so $8000 was invested at 7%.

That leaves $12,000 invested at 4% or 5%; with 3 times as much invested at 5% as at 4%, simple mental calculations show that $3000 was invested at 4% and $9000 at 5%.

ANSWERS: $3000 at 4%, $9000 at 5%, and $8000 at 7%

CHECK: .04(3000) + .05(9000) + .07(8000) = 120 + 450 + 560 = 1130
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