A sum of ₹2400 becomes ₹3600 in 6 years at a certain rate of compound interest (compounded annually). What will be the amount after 12 years at the same rate of interest?

A sum of ₹2400 becomes ₹3600 in 6 years at a certain rate of compound interest (compounded annually).

A = $$P(1+\frac{R}{100})^N$$

Here P = principal amount, R = rate of interest, N = time and A = principal+interest.

3600 = $$2400(1+\frac{R}{100})^6$$

$$(1+\frac{R}{100})^6=\frac{3600}{2400}$$

$$(1+\frac{R}{100})^6=\frac{3}{2}$$

$$(1+\frac{R}{100})^6 = 1.5$$    Eq.(i)

After twelve years, A = $$2400(1+\frac{R}{100})^\text{12}$$

= $$2400\left[(1+\frac{R}{100})^6\right]^2$$

Put Eq.(i) in the above equation.

= $$2400\times[1.5]^2$$

= $$2400\times2.25$$

= ₹5400