SOLUTION: You have already invested $500 in a stock with an annual return of 11%. How much of an additional $1,600 should be invested at 12% and how much at 6% so that the total return on th

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Question 798234: You have already invested $500 in a stock with an annual return of 11%. How much of an additional $1,600 should be invested at 12% and how much at 6% so that the total return on the entire $2,100 is 9%?
Answer by mananth(16946) About Me  (Show Source):
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You have already invested $500 in a stock with an annual return of 11%. How much of an additional $1,600 should be invested at 12% and how much at 6% so that the total return on the entire $2,100 is 9%?
total return 2100 @9%= $189
500 @11% = $55
Difference = 189-55= 135
Invest $ x at 12%
and 1600-x @ 6 %
Total return = $ 135
Part I 12.00% per annum ------------- Amount invested =x
Part II 6.00% per annum ------------ Amount invested = y
1600
Interest----- 135.00

Part I 12.00% per annum ---x
Part II 6.00% per annum ---y
Total investment
x + 1 y= 1600 -------------1
Interest on both investments
12.00% x + 6.00% y= 135
Multiply by 100
12 x + 6 y= 13500.00 --------2
Multiply (1) by -12
we get
-12 x -12 y= -19200.00
Add this to (2)
0 x -6 y= -5700
divide by -6
y = 950 - x)
Part I 12.00% $ 650
Part II 6.00% $ 950