On a certain sum of money, the Compound Interest for 2 years is Rs.309 and the Simple Interest is Rs.300. Find the rate of interest per annum.

SI for 2 years = 300

SI for 1 year = $$ \frac{300}{2} = 150 $$

CI for 1 year = 150

CI for 2 years = 309

CI for 2 years = CI for 1st year + CI for 2nd year

CI for 2nd year = 309 - 150 = 159

CI for 2nd year - CI for 1st year = 159 - 150 =9

after 1 year

amount = Rs 159

Principal = 150

$$ A = P( 1 + \frac{r}{100})^2 $$

$$ \frac{159}{150} = ( 1 + \frac{r}{100}) $$

$$ \frac{53}{50} = 1 + \frac{r}{100} $$

solving,  r = 6%