A sum of Rs. 10,500 amounts to Rs. 13,650 in 2 years a certain rate percent annum simple interest. The same sum will amount to what in 1 year at the same rate, if the interest in compounded half yearly (nearest to Rs. 1)

Solution (By Examveda Team)

\[P = 10500\xrightarrow{{\,\,\,\,\,2{\text{ year}}\,\,\,\,\,}}13650\]
$$\eqalign{ & 2{\text{ year}} \to 3150 \cr & 3150 = \frac{{10500 \times R \times 2}}{{100}} \cr & R = 15\% \cr & A = 10500{\left( {1 + \frac{{15}}{{200}}} \right)^2} \cr & = 10500 \times \frac{{215 \times 215}}{{200 \times 200}} \cr & = \frac{{105 \times 43 \times 43}}{{16}} \cr & = 12134 \cr} $$