A sum invested at a certain rate of interest per annum, compounded annually, amounts to ₹3,600 in 2 years and to ₹6,480 in 4 years. What is the sum invested?

Amount after 2 years = $$principal\left[\left(1+\frac{rate}{100}\right)^{time}\right]$$

$$3600 = principal\left[\left(1+\frac{rate}{100}\right)^{2}\right]$$    Eq.(i)

Amount after 4 years = $$principal\left[\left(1+\frac{rate}{100}\right)^{time}\right]$$

$$6480 = principal\left[\left(1+\frac{rate}{100}\right)^{4}\right]$$

$$6480=principal\left(1+\frac{rate}{100}\right)^2\ \left(1+\frac{rate}{100}\right)^2$$

Put Eq.(i) in the above equation.

$$6480=3600\times\ \ \left(1+\frac{rate}{100}\right)^2$$

Put Eq.(ii) in Eq.(i).

$$3600 = principal \times \frac{6480}{3600}$$

principal = $$\frac{3600\times3600}{6480}$$

= $$\frac{12960000}{6480}$$

= ₹2,000

So the sum invested is ₹2,000.