Question

Two certificates of deposit pay interest at rates that differ by 2%. Money invested for one year in the first CD earns $120 interest. The same principal invested in the other CD earns $160. Find the two rates of interest (in percent).smaller value: %larger value: %

Answer 1

The first thing we have to do is find the equations that describe the problem:

• Two certificates of deposit pay interest at rates that differ by ,2%,.

`\lvert i_2-i_1\rvert=2`

• Money invested ,for one year in the first CD ,earns, ,$120, interest.

`MI\cdot i_1=120`

• The same principal invested i,n the other CD earns , $160

`MI\cdot i_2=160`

We can see that we have the same money invested so we can match it to find another equation that helps us clear the interests:

`\begin{gathered} MI_{}=(120)/(i_1) \\ MI=(160)/(i_2) \\ (160)/(i_2)=(120)/(i_1) \\ 160\cdot i_1=120\cdot i_2 \\ i_1=(120)/(160)i_2 \\ i_1=(3)/(4)i_2 \end{gathered}`

With the equation cleared for interest 1, we plug into the first equation to find interest 2

`\begin{gathered} i_2-(3)/(4)i_2=2 \\ (1)/(4)i_2=2 \\ i_2=2\cdot4 \\ i_2=8 \end{gathered}`

Now we calculate the value of interest 1 using the first equation replacing the calculated value of interest 2

`\begin{gathered} 8-i_1=2 \\ i_1=8-2 \\ i_1=6 \end{gathered}`

So the 2 interest rates are

• smaller value:, ,6%

• larger value:, , 8%