Question

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 $

Answer 1

We will have the following:

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

`A=P(1+rt)`

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

`\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}`

Now, we have that:

`A_1+A_2=8740`

Then:

`\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}`

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

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