At a certain rate of interest per annum, compounded annually, a certain sum of money amounts to two times of itself in 11 years. In how many years will the sum of money amount to four times of itself at the previous rate of interest per annum, also compounded annually?

22 years

Sum amounts to three times of itself in 13 years,

ATQ,

Amount = P$(1 \;+\; \frac{R}{100})^t$

2P = P[ 1 + \(\frac{R}{100}\) ]¹¹

2 = [ 1 + \(\frac{R}{100}\) ]¹¹

On squaring both side ,

2² = { [ 1 + \(\frac{R}{100}\) ]¹¹ }² 

4 = [ 1 + \(\frac{R}{100}\) ]²²

So, sum become 9 times of itself in 22 years.