SOLUTION: Terry placed $15,000 in an account paying 6%. How much additional money should she deposit at 4% so that the average return on the two investments is 5.5%?

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Question 98721: Terry placed $15,000 in an account paying 6%. How much additional money should she deposit at 4% so that the average return on the two investments is 5.5%?
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Interest(I)=Principal(P) times Rate(R) times(T) or I=PRT
Let P=additional amount of principal needed to be deposited at 4%

0.06(15,000)=return for 1 year on the 15,000
0.04P=return for 1 year on the amount deposited at 4%
0.055(15000+x)=return for 1 year on the combined deposit
Now we know that the return on the two separate deposits must equal the return on the combined deposit. So our equation to solve is:
0.06(15000)+0.04P=0.055(15000+P) get rid of parens
900+0.04P=825+0.055P subtract 825 and also 0.04P from both sides
900-825+0.04P-0.04P=825-825+0.055P-0.04P collect like terms
75=0.015P divide both sides by 0.015
P=$5000-----------additional amount of principal needed to be deposited at 4%
CK
0.06*15000+0.04*5000=0.055*20000
900+200=1100
1100=1100
Hope this helps----ptaylor