A sum of money becomes Rs.11880 after 4 years and Rs.17820 after 6 years on compound interest, the interest is compounded annually. What is the half of the sum (in Rs.).

2640

 Sum          after 4 years              after 6 years 

                     11880            :          17820

Amount in ratio,    2            :        3       ( for 2 years)

So initial amount = 11880×\(\frac{2}{3}\)× \(\frac{2}{3}\)

Half of initial amount = 11880× \(\frac{2}{3}\)× \(\frac{2}{3}\)× \(\frac{1}{2}\) = 2640