Question 1137064: An executive invests $25,000, some at 6% and the rest at 5% annual interest. If he receives an annual return of $1,440, how much is invested at each rate?
Found 2 solutions by VFBundy, greenestamps:
Answer by VFBundy(438)   (Show Source):
You can put this solution on YOUR website! 6% investment:
Principal = p
Rate = 0.06
Interest = 0.06p
5% investment:
Principal = 25000 - p
Rate = 0.05
Interest = 0.05(25000 - p) = 1250 - 0.05p
(0.06p) + (1250 - 0.05p) = 1440
0.01p + 1250 = 1440
0.01p = 190
p = 19000
6% investment:
Principal = p = $19,000
5% investment:
Principal = 25000 - p = $6000
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
Here is a COMPLETELY different method for solving a problem like this. It is essentially a mixture problem -- you are mixing investments at two different rates and getting a yield that is somewhere between those two rates.
The key to this method of solving mixture problems is that the ratio in which the two parts are mixed exactly determines where the overall percentage lies.
Here are all the simple steps required to solve the problem by this method:
(1) Find what the returns would be if all the money were invested at each rate:
$25,000 at 5% yields $1250; $25,000 at 6% yields $1500.
(2) Find where the actual yield lies between those two extremes:
1500-1250 = 250; 1440-1250 = 190; 190/250 = 19/25
The actual yield is 19/25 of the way from $1250 to $1500.
(3) That means 19/25 of the total is invested at the higher rate:
ANSWER: (19/25)*$25,000 = $19,000 at 6%; the rest, $6,000, at 5%.
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