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

A sum of 1600 Rs. gives a simple interest of 252 Rs. in 2 years and 3 months. The rate of the interest per annum is :
[A]$8\%$
[B]$6\%$
[C]$7\%$
[D]$5\frac{1}{2}\%$

$7\%$
Principal = 1600 Rs.
T = 2 years 3 months
$= \left ( 2+\frac{3}{12} \right )yrs. = \left ( 2+\frac{1}{4} \right )yrs. = \frac{9}{4}yrs.$
S.I = 252 Rs.
R = % rate of interest per annum
$=> R = \frac{100\times S.I.}{P\times t}$
$= \frac{100 \times 252}{1600 \times \frac{9}{4}} = 7\%$
Rate of interest = 7% per annum
Hence option [C] is the right answer.