Let the principal amount be \(x\) taka, which becomes \(2x\) in \(n\) years under compound interest. \[ ∴\ 2x = x(1 + \frac{r}{100})^n \] Or, \[ 2 = (1 + \frac{r}{100})^n \] So, \[ (1 + \frac{r}{100}) = 2^{\frac{1}{n}} \quad \text{— (i)} \] Now, let the principal \(x\) taka become \(4x\) in \(y\) years. \[ ∴\ 4x = x(1 + \frac{r}{100})^y \] Using equation (i): \[ 2^2 = (2^{\frac{1}{n}})^y \] \[ 2^2 = 2^{\frac{y}{n}} \] \[ \frac{y}{n} = 2 \] \[ y = 2n \] ∴ At a fixed compound interest rate, if a sum doubles in \(n\) years, it will become four times in \(2n\) years.