A certain sum of money amounts to 3 times of itself in 13 years when interest is compounded annually at a certain rate of interest per annum. In how many years will the initial sum amount to 9 times of itself at the same rate of interest per annum, also compounded annually?

A certain sum of money amounts to 3 times of itself in 13 years when interest is compounded annually at a certain rate of interest per annum.

$$P\left(1+\frac{R}{100}\right)^{13}\ =3P$$

$$(1+\frac{R}{100})^{13} = 3$$    Eq.(i)

Let's assume that in 't' years will the initial sum amount to 9 times of itself at the same rate of interest per annum, also compounded annually.

$$P\left(1+\frac{R}{100}\right)^t\ = 9P$$

$$(1+\frac{R}{100})^t = 9$$

$$(1+\frac{R}{100})^t = 3^2$$    Eq.(ii)

So by comparing Eq.(i) and Eq.(ii), we can say that t = $$13\times2$$

= 26 years