If after two years a sum becomes ₹4000 and after four years it becomes ₹6000 at the same rate of compound interest (compounded annually), then what is the sum?

If after two years a sum becomes ₹4000 and after four years it becomes ₹6000.

As per the formula of compound interest two equations will be formed from the given information.

Here P = principal amount and R = rate of interest.

$$P(1+\frac{R}{100})^{2} = 4000$$    Eq.(i)

$$P(1+\frac{R}{100})^{4} = 6000$$    Eq.(ii)

So Eq.(i) divided by Eq.(ii).

$$\frac{Eq.(i)}{Eq.(ii)} = \frac{P(1+\frac{R}{100})^{2}}{P(1+\frac{R}{100})^{4}} = \frac{4000}{6000}$$

$$\frac1{(1+\frac{R}{100})^{2}} = \frac{2}{3}$$

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

Put Eq.(iii) in Eq.(i).

$$\frac{3}{2}P=4000$$

$$P=\frac{8000}{3}$$

= ₹2666.66