Question 1161616: A stock broker is required to keep $100,000 in low-risk funds. He splits the money between a fund that has an interest rate of 9.2% and one that pays 8.6%. In the first year, the money earns $8960 in interest. How much of the $100,000 was invested in the fund with 9.2% interest?
Found 2 solutions by Boreal, greenestamps:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! x in low risk making .092 interest or .092x $ a year
100000-x making .086 a or $8600-0.086x a year
0.092x+8600-0.086x=8960. The interest of each of the above added together is $8960.
Collect terms
0.092x-0.086x=8960-8600
so 0.006x=360
x=$60000 making 9.2% or $5520 a year
100000-x=$40000 making 8.6% or $3440 a year
Answer by greenestamps(13219)  (Show Source):
You can put this solution on YOUR website!
Without formal algebra....
(1) All $100,000 at 8.6% would yield $8600 interest; all at 9.2% would yield $9200 interest.
(2) The actual interest of $8960 is 3/5 of the way from $8600 to $9200. ($8600 to $9200 is a difference of $600; $8600 to $8960 is a difference of $360; 360/600 = 3/5.)
(3) That means 3/5 of the total was invested at the higher rate.
ANSWER: 3/5 of $100,000, or $60,000, at 9.2%; the other $40,000 at 8.6%.
CHECK:
.086(40,000)+.092(60,000) = 3440+5520 = 8960
|
|
|
