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?

₹5400

The Formula that we used here is -

Amount = P$(1 \;+\; \frac{R}{100})^t$

3600 = 2400 [ 1 + \(\frac{R}{100}\)]⁶

\(\frac{3}{2}\) = [ 1 + \(\frac{R}{100}\)]⁶

Now,

For 12 years ,

A = 2400 [ 1 + \(\frac{R}{100}\)]¹²

= 2400 [( 1 + \(\frac{R}{100}\) )⁶ ]²

= 2400 [ \(\frac{3}{2}\) ]²

= 2400 × \(\frac{3}{2}\) × \(\frac{3}{2}\)

= Rs. 5400