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:

$\begin{gathered} MI_{}=\frac{120}{i_1} \\ MI=\frac{160}{i_2} \\ \frac{160}{i_2}=\frac{120}{i_1} \\ 160\cdot i_1=120\cdot i_2 \\ i_1=\frac{120}{160}i_2 \\ i_1=\frac{3}{4}i_2 \end{gathered}$

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

$\begin{gathered} i_2-\frac{3}{4}i_2=2 \\ \frac{1}{4}i_2=2 \\ i_2=2\cdot4 \\ i_2=8 \end{gathered}$

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%