An investment of $1000 was made in a certain account and earned interest that was compounded annually. The annual interest rate was fixed for the duration of the investment, and after 12 years the $1000 increased to $4000 by earning interest. In how many years after the initial investment was made the $1000 have increased to $8000 by earning interest at that rate?
A. 16
B. 18
C. 20
D. 24
E. 30
The correct answer here is (B). The approach used was that since it takes 12 years for the amount to quadruple , it would take 6 years for it to double so the total years = 12+6 =18 years.
I took a similar approach but I considered that going from 1000$ to 8000$ is 8 times. It took 12 years for it to be 4 times, so it will take 24 years for it to be 8 times. Why is this approach wrong?