A certain sum becomes $\frac{36}{25}$ of itself after 2 years on compound interest. Find the rate of interest per annum.

20%

Let initial sum = 25

Then Sum after 2 years = 36

We know, with compound interest

Amount = Principal × ( 1 + \(\frac{R}{100}\) )²

36 = 25 × ( 1 + \(\frac{R}{100}\) )²

 \(\frac{36}{25}\) = ( 1 + \(\frac{R}{100}\) )²

 ( \(\frac{6}{5}\) )² = ( 1 + \(\frac{R}{100}\) )²

1 + \(\frac{R}{100}\) = \(\frac{6}{5}\)

\(\frac{R}{100}\) = \(\frac{1}{5}\)

R = 20%

Rate of interest = 20%