simple interest and compound interest

Question

 a certain sum of money at simple interest ,amounts to $768 in 4 years and to $832 in 6 years what is rate percent.

Answer 1

I think that this might work.

 

A=P(1+rt) - where A is amount after t years at r% starting with P.

 

So,

    768 = x(1+4r)  -(1)

    862 = x(1+6r)  -(2)  

 

                                   Where r is the rate of interest (what we need to find) and x is the amount of money

                                   we started with (don't know, but that is okay)

 

    from (1) x = 768/(1+4r)

            (2) x = 862/(1+6r)

 

Now, set x=x

 

     768/(1+4r) = 862/(1+6r)

 

Cross multiply and we get

 

     768(1+6r) = 862(1+4r)

     768 + 4608r = 862 + 3448r

 

Then 

        4608r - 3448r = 862 - 768

or

       1160r = 94

   

Thus  

          r = 94/1160 = 0.081 or 8.1%

 

Hope this helps,

Bill.

 

I am available for online tutoring in math and science.

 

Answer 2

To set this up make y the capital and x the yearly interest. Y + 4x = 768, y +6x = 832. This gives 2x = 64 or x = 32. With this we know y =640.