What is the present value of Rs. 10,000 received in 2 years, if the interest rate is 12% per year discounted semi-annually?

Solution(By Examveda Team)

$$\eqalign{ & {\text{Amount received in 2 years}} = {\text{Rs}}{\text{. }}10,000 \cr & {\text{Interest rate}} = 12\% {\text{ per year}} \cr & {\text{Time}} = 2{\text{ years}} \cr & {\bf{Formula \,used:}} \cr & {\text{Amount}} = {\text{Principal}}{\left[ {1 + \left( {\frac{R}{{100}}} \right)} \right]^n} \cr & {\bf{Calculation:}} \cr & A = 10000 \cr & R = 6\% {\text{ }}\left( {{\text{semi - annually}}} \right) \cr & n = 4\% {\text{ }}\left( {{\text{semi - annually}}} \right) \cr & {\text{Thus,}} \cr & \Rightarrow 10000 = P{\left[ {1 + \left( {\frac{6}{{100}}} \right)} \right]^4} \cr & \Rightarrow 10000 = P{\left[ {\frac{{106}}{{100}}} \right]^4} \cr & \Rightarrow 10000 = P \times {\left( {1.06} \right)^4} \cr & \Rightarrow P = \frac{{10000}}{{{{1.06}^4}}} \cr & \Rightarrow P = 7920.9426 \cr & \Rightarrow P = {\text{Rs}}{\text{. }}7920.94 \cr & {\text{Hence, the correct answer is Rs}}{\text{. 7,920}}{\text{.94}} \cr} $$