A. 10% B. 11.5% C. 5% D. 20% Answer: Option A $$\eqalign{ & {\text{According to the question,}} \cr & {\text{compounded half yearly}} \cr &
{\text{Rate = }}\frac{{\text{R}}}{2} \cr & {\text{Time = }}\frac{{{\text{2T}}}}{3} \cr & {\text{Amount = P}}{\left( {1 + \frac{{\text{R}}}{{2 \times 100}}} \right)^3} \cr & \Rightarrow 2315.25 = 2000{\left( {1 + \frac{{\text{R}}}{{2 \times 100}}} \right)^3} \cr & \Rightarrow \frac{{2315.25}}{{2000}} = {\left( {1 + \frac{{\text{R}}}{{2 \times 100}}} \right)^3} \cr & \Rightarrow \frac{{231525}}{{200000}} = {\left( {1 + \frac{{\text{R}}}{{2 \times 100}}} \right)^3} \cr &
\Rightarrow \frac{{9261}}{{8000}} = {\left( {1 + \frac{{\text{R}}}{{2 \times 100}}} \right)^3} \cr & \Rightarrow {\left( {\frac{{21}}{{20}}} \right)^3} = {\left( {1 + \frac{{\text{R}}}{{2 \times 100}}} \right)^3} \cr & \Rightarrow 1 + \frac{{\text{R}}}{{200}} = \frac{{21}}{{20}} \cr & \Rightarrow {\text{R = 10}}\% \cr} $$ Find the rate percent per annum if Rs. 2000 amounts to Rs. 2315.25 in one and half years interest being compounded half yearly.
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According to the questioncompounded half yearly Rate = R2Time = 2T3Amount = P(1+R2×100) 3⇒2315.25=2000(1+R2×100)3⇒2315.252000=( 1+R2×100)3⇒231525200000=(1+R2×100)3 ⇒92618000=(1+R2×100)3⇒(2120) 3=(1+R2×100)3⇒1+R200=2120⇒R = 10%
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According to the question, compounded half yearly
Rate = \( \Large \frac{R}{2} \)
Time =\( \Large \frac{2T}{3} \)
Amount=\( \Large P \left(1+\frac{R}{2 \times 100}\right)^{3}\)
2315.25=\( \Large 2000 \left(1+\frac{R}{200}\right)^{3}\)
\( \Large \frac{2315.25}{2000}= \left(1+\frac{R}{200}\right)^{3}\)
\( \Large \frac{231525}{200000}= \left(1+\frac{R}{200}\right)^{3}\)
\( \Large \frac{9261}{8000}= \left(1+\frac{R}{200}\right)^{3}\)
\( \Large\left(\frac{21}{20}\right)^{3} = \left(1+\frac{R}{200}\right)^{3}\)
\( \Large 1+\frac{R}{200}=\frac{21}{20}=R = 10\% \)
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Updated On: 27-06-2022
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`11.5%``10%``5%``20% `
Answer : B
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यदि मूलधन = Rs 1,00,000 और वार्षिक ब्याज की दर = 10% अर्ध वार्षिक संयोजित है, तो ज्ञात कीजिए- <br> एक वर्ष बाद मिश्रधन
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