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A trust fund worth $40500 is invested in two different portfolios. This year, one portfolio is expected to earn 4.3% interest and the other is expected to earn 7%. Plans are for the total interest on the fund to be $2,551.50 in one year. How much money should be invested at each rate?



Answer :

Okay, here e have this:

Considering the provided information we are going to calculate how much money should be invested at each rate. So we obtain the following:

Then we will assume the amount of money at 4.3 percent interest as x, and obtain the following expression:

[tex]0.043\mleft(x\mright)+0.07\mleft(40500-x\mright)=2551.5[/tex]

Let's solve for x:

[tex]\begin{gathered} 0.043x\cdot\: 1000+0.07\mleft(40500-x\mright)\cdot\: 1000=2551.5\cdot\: 1000 \\ 43x+70\mleft(40500-x\mright)=2551500 \\ -27x+2835000=2551500 \\ -27x+2835000-2835000=2551500-2835000 \\ -27x=-283500 \\ \frac{-27x}{-27}=\frac{-283500}{-27} \\ x=10500 \end{gathered}[/tex]

Finally we obtain that the amount of money at 4.3 percent interest should be 10500, and the amount of money at 7 percent interest should be (40500-10500)=30000.

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