On a certain sum, the interest is compounded annually. If the compound interest for the second year is ₹400 and the compound interest for the fourth year is 576, then what is the rate of interest per annum?

20%

A particular sum of money with a particular rate of interest in 2 years = Rs.400

A particular sum of money with a particular rate of interest in 4 years = Rs.576

Ratio of Amount after 2 years and 4 years ,

400 :  576

{ as there is gap of 2 years in both the amount , so on square root both side }

\(\sqrt {400 }\) :   \(\sqrt { 576}\)

20  :  24

Rate of Interest = \(\frac{24 - 20 }{20}\) × 100%

= \(\frac{1 }{5}\) × 100% 

= 20%