A certain sum of money amounts to $$\frac{3}{2}$$ of itself in 2 years applying simple interest. Find the rate of simple interest per annum.

Let's assume the principal amount is 'P'.

A certain sum of money amounts to $$\frac{3}{2}$$ of itself in 2 years applying simple interest.

amount became after 2 years = $$\frac{3}{2}$$ of principal

= $$\frac{3}{2}$$ of P

= 1.5P

simple interest = amount became after 2 years - principal

= 1.5P - P

= 0.5P

$$simple \ interest = \frac{principal\times\ rate\times\ time}{100}$$

$$0.5P = \frac{P \times\ rate\times\ 2}{100}$$

$$0.5=\frac{\ rate}{50}$$

rate of interest = $$50\times0.5$$ = 25% per annum.