Question 1198822: $24000 is invested in three different accounts, each paying 1%, 2%, and 3% interest, respectively. After 1 year, the simple interest earned from all three accounts amounts to $440. If the account paying 1% interest contains three times the amount in the account paying 2% interest, how much was invested ni the three accounts?
Answer by greenestamps(13203)   (Show Source):
You can put this solution on YOUR website!
ANSWER: $24000 was invested in the three accounts.
But that is not the question you meant to ask. What you really meant to ask is to find the amounts invested in EACH OF the three accounts.
Since three times as much is invested at 1% as at 2%,
let x = amount invested at 2%
then 3x = amount invested at 1%
and so 24000-4x is the amount invested at 3%
The total interest is $440:
.02(x)+.01(3x)+.03(24000-4x) = 440
.02x+.03x+720-.12x = 440
-.07x+720 = 440
280 = .07x
x = 280/.07 = 4000
ANSWERS:
x = $4000 invested at 2%
3x = $12000 invested at 1%
$24000-$16000 = $8000 invested at 3%
CHECK:
.02(4000)+.01(12000)+.03(8000) = 80+120+240 = 440
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Here is a very different method for solving problems like this. It "works" for me because of the way my brain works. It might or might not "work" for you; give it a try.
First determine the average rate of return on the 1% and 2% investments, knowing that there is 3 times as much at 1% as at 2%.
let x = amount invested at 2%
then 3x = amount invested at 1%
So 1/4 of the amount invested at 1% or 2% is invested at 2% and 3/4 of it is invested at 1%. You can find the average rate of return on those two investments using formal algebra:
(.02(x)+.01(3x))/(4x) = .05x/(4x) = .0125 (or 1.25%)
However, to use this alternative method, we can just look at the 1% and 2% on a number line and observe/calculate that 1.25% is 1/4 of the way from 1% to 2%.
Now use a similar method using the two percentage rates of 3% and 1.25% to find the amounts invested at those two rates that yield the total interest of $440.
$24000 all invested at 1.25% would yield $300 interest; all invested at 3% would yield $720 interest; the actual total interest was $440.
Use those three interest amounts (on a number line again, if it helps) to calculate that $440 is one-third of the way from $300 to $720. (720-300 = 420; 440-300 = 140; 140/420 = 1/3).
That means one-third of the total was invested at the higher rate of 3%; the other two thirds were split between the investments at 1% and 2%.
1/3 of $24000 is $8000, so $8000 was invested at 3%.
The other $24000-$8000 = $16000 was split between the 1% and 2% investments, with 3 times a much at 1% as at 2%. That means $12000 at 1% and $4000 at 2%.
And again we have the same result that we got using formal algebra:
$12000 invested at 1%; $4000 at 2%; and $8000 at 3%.
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