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Jolene invests her savings in two bank accounts, one paying 4 percent and the other paying 12 percent simple interest per year. She puts twice as much in the lower-yielding account because it is less risky. Her annual interest is 8740 dollars. How much did she invest at each rate?Amount invested at 4 percent interest is $Amount invested at 12 percent interest is $

Respuesta :

We will have the following:

First, we recall that the simple interest formula is given by:

[tex]A=P(1+rt)[/tex]

Now, for the accounts that are described in the problem we will have that:

[tex]\begin{gathered} A_1+2P=2P(1+(0.04)(1))\Rightarrow A_1+2P=2P(1.04) \\ \\ A_2+P=P(1+(0.12)(1))\Rightarrow A_2+P=P(1.12) \end{gathered}[/tex]

Now, we have that:

[tex]A_1+A_2=8740[/tex]

Then:

[tex]\begin{gathered} A_1+A_2+2P+P=2P(1.04)+P(1.12) \\ \\ \Rightarrow8740+3P=3.2P\Rightarrow8740=0.2P \\ \\ \Rightarrow P=43710 \end{gathered}[/tex]

So, the amount invested at 4% interest is $87 420.

And, the amount invested at 12% interest is $43 710.

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