A sum invested at a certain rate of interest per annum, compounded annually, amounts to ₹14,400 in 2 years and to ₹25,920 in 4 years. What is the sum invested?

In both of the cases, principal amount and rate of interest are the same which are assumed as 'P' and 'R' respectively.

$$14400\ =\ P\left(1+\frac{R}{100}\right)^2$$    Eq.(i)

$$25920\ =\ P\left(1+\frac{R}{100}\right)^4$$    Eq.(ii)

Eq.(i) divided by  Eq.(ii).

$$\frac{14400}{25920}\ =\frac{P\left(1+\frac{R}{100}\right)^2}{P\left(1+\frac{R}{100}\right)^4}$$

$$\frac{5}{9}\ =\frac{\left(1+\frac{R}{100}\right)^2}{\left(1+\frac{R}{100}\right)^4}$$

$$\frac{5}{9}\ =\frac{1}{\left(1+\frac{R}{100}\right)^2}$$

$$\left(1+\frac{R}{100}\right)^2=\frac{9}{5}$$ Eq.(iii)

Put Eq.(iii) in Eq.(i).