SOLUTION: if $2500 is invested at 2% interest, how much money must be invested at 7% so that the total return of both investments average 6%

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Question 912195: if $2500 is invested at 2% interest, how much money must be invested at 7% so that the total return of both investments average 6%
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
"$2500 is invested at 2% interest" so you earn 2500*0.02 = 50 dollars in interest alone in one year.

Let x = amount of money invested at 7%

You will earn 0.07x dollars in interest alone

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Total Interest Earned: 50 + 0.07x

Total Amount Invested: 2500 + x

The ratio of amount earned to amount invested is forced to be 6%


(Total Interest Earned)/(Total Amount Invested) = target rate of return

(50 + 0.07x)/(2500 + x) = 0.06

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Now solve for x 
	(50 + 0.07x)/(2500 + x) = 0.06
	
	50 + 0.07x = 0.06(2500 + x)
	
	50 + 0.07x = 0.06(2500) + 0.06(x)
	
	50 + 0.07x = 150 + 0.06x
	
	0.07x - 0.06x = 150 - 50
	
	0.01x = 100
	
	x = 100/0.01
	
	x = 10,000

So you need to invest $10,000 at 7% so that the total return of both investments average 6%