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?

At a certain rate of interest per annum, compounded annually, a certain sum of money amounts to two times of itself in 11 years.

Let's assume prinicipal and rate of interest are 'P' and 'R' respectively.

 $$P+interest\ =\ P\left(1+\frac{R}{100}\right)^{time}$$

Let's assume in 't' years will the sum of money amount to four times of itself at the previous rate of interest per annum, also compounded annually.

$$4P\ =\ P\left(1+\frac{R}{100}\right)^t$$
$$4\ =\ \left(1+\frac{R}{100}\right)^t$$

$$2^2\ =\ \left(1+\frac{R}{100}\right)^t$$    Eq.(ii)

By comparing Eq.(i) and Eq.(ii), we can say that t = $$11\times2$$ = 22 years
So in 22 years will the sum of money amount to four times of itself.