A sum of Rs. 1600 gives a simple interest of Rs. 252 in 2 years and 3 months. The rate of interest per annum is = ?

$$\eqalign{ & {\text{Time = 2 years 3 months}} \cr & {\text{ = 2 + }}\frac{3}{{12}}{\text{ = }}\frac{9}{2}{\text{ years}} \cr & {\text{We know }}\boxed{{\text{SI = }}\frac{{{\text{P}} \times {\text{T}} \times {\text{R}}}}{{100}}} \cr & {\text{P = Rs 1600,}} \cr & {\text{T = }}\frac{9}{4}{\text{years,}} \cr & {\text{SI = Rs 252}} \cr & {\text{Put values in the formula ,}} \cr & \Rightarrow 252 = \frac{{1600 \times {\text{R}} \times 9}}{{100}} \cr & \Rightarrow 252 = 36{\text{R}} \cr & \Rightarrow {\text{R = }}\frac{{252}}{{36}} = 7\% \cr} $$