What is the interest rate of each investment?

Question

The annual interest on an $11,000 investment exceeds the interest earned on a $9,000 Investment by $184. The $11,000 is invested at a 0.4% higher rate of interest than the $9,000.

Answer 1

Let x = % interest on $11,000

Let y = % interest on $ 9,000

 

The first equation would be:  11,000x - 9,000y = 184

The second equation would be:  x - 1.004y = 0

 

You can then put it into a matrix; followed by doing row operations.

 

This gives the following information:

 

Interest on 11,000 is about 0.0904

Interest on 9,000 is about 0.09

 

The test is:   994 - 184 = 810    [Check]

 

 

Answer 2

Let the lower interest rate be r

Simple interest is given by PRT

Then $11000X1X(r+0.4)/100=$9000X1Xr/100 +$184

          $110(r+0.4)=$90r+$184

          $110r +$44=$90r+$184

Subtracting $90r from both sides

          $20r +$44=$184

Subtracting $44 from both sides

           $20r=$140

                r=$140/$20=7%

Interest rate for the $9000 is 7%

Interest rate for the 11000 is 7.4%

 

Check:$11000X7.4%=$814

               $9000X7%=$630

               $814-$630=$184