SOLUTION: You have $50,000 to invest, you invest some at 5% and the rest at 4%, you earn $2100 in annual interest, how much did you invest at each rate?

Question 86954: You have $50,000 to invest, you invest some at 5% and the rest at 4%, you earn $2100 in annual interest, how much did you invest at each rate?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Interest(I)=Principal(P) times Rate(R) times Time(T) (note: in this problem, T=1 year)
Let P=amount invested at 5%
Interest at 5%=P(0.05)(1)=0.05P
Then 50,000-P=amount invested at 4%
Interest at 4%=(50,000-P)(0.04)(1)=(0.04)(50,000-P)
Now we are told that the interest earned at 5%((0.05)(P)) plus the interest earned at 4%((0.04)(50,000-P)) equals $2100. So, our equation to solve is:
0.05(P)+0.04(50,000-P)=2100 get rid of parens
0.05P+2000-0.04P=2100 subtract 2000 from each side
0.05P+2000-2000-0.04P=2100-2000 collect like terms
0.01P=100 divide both sides by 0.01
P=$10,000-----------------------------------amount invested at 5%
50,000-P=50,000-10,000=$40,000--------------amount invested at 4%
CK
0.05*10,000+0.04*40,000=2100
500+1600=2100
2100=2100

Hope this helps---ptaylor

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