theory of interest

Question

Hello. I am trying to solve this problem: "Suppose that the annual effective rate of interest is 6%, and an investment of $X is made at time 0. The investment has a return of $2000 after 4 years and $1000 after 8 years. Find X." The way I thought about it was the following:

 

x(1.06)^4-x=2000

x(1.06)^8-x=1000

 

x=x(1.06)^4-2000 and x=x(1.06)^8-1000

x(1.06)^4-2000=x(1.06)^8-1000

 which leads to a negative answer. I can't figure out why this doesn't work and what is the right way to approach this problem.

 

Any help would be appreciated.

 

Answer 1

Hi Nade, my name is Elizabeth.

Did you accidentally type this problem in wrong? It's odd that in double the time the return would be less.