Find the rate percent per annum if Rs. 2000 amounts to Rs. 2315.25 in one and half years interest being compounded half yearly.
A. 10%
B. 11.5%
C. 5%
D. 20%
Answer: Option A
Solution(By Examveda Team)
$$\eqalign{ & {\text{According to the question,}} \cr & {\text{compounded half yearly}} \cr & {\text{Rate = }}\frac{{\text{R}}}{2} \cr & {\text{Time = }}\frac{{{\text{2T}}}}{3} \cr & {\text{Amount = P}}{\left( {1 + \frac{{\text{R}}}{{2 \times 100}}} \right)^3} \cr & \Rightarrow 2315.25 = 2000{\left( {1 + \frac{{\text{R}}}{{2 \times 100}}} \right)^3} \cr & \Rightarrow \frac{{2315.25}}{{2000}} = {\left( {1 + \frac{{\text{R}}}{{2 \times 100}}} \right)^3} \cr & \Rightarrow \frac{{231525}}{{200000}} = {\left( {1 + \frac{{\text{R}}}{{2 \times 100}}} \right)^3} \cr & \Rightarrow \frac{{9261}}{{8000}} = {\left( {1 + \frac{{\text{R}}}{{2 \times 100}}} \right)^3} \cr & \Rightarrow {\left( {\frac{{21}}{{20}}} \right)^3} = {\left( {1 + \frac{{\text{R}}}{{2 \times 100}}} \right)^3} \cr & \Rightarrow 1 + \frac{{\text{R}}}{{200}} = \frac{{21}}{{20}} \cr & \Rightarrow {\text{R = 10}}\% \cr} $$Related Questions on Compound Interest
A. Rs. 120
B. Rs. 121
C. Rs. 122
D. Rs. 123
E. None of these
A. 625
B. 630
C. 640
D. 650
E. None of these
A. Rs. 2160
B. Rs. 3120
C. Rs. 3972
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