A) ` 1
B) ` 1.25
C) ` 1.5
D) ` 2
Correct Answer: B
Solution :
Sol. [b] Rate of interest (R) = 10% per annum Principal (P) = ` 500 Time = 1 yr Now, SI =\[=\,\frac{P\times R\times T}{100}\,=\,\frac{500\times 10\times 1}{100}\,=\,500\] Compound interest rate half-yearly. So, T = 1 yr = 2 half-yearly. And \[r\,=\,\frac{10}{2}\]%= 5% \[CI\,=\,p\left[ {{\left( 1+\frac{R}{100} \right)}^{T}}-1 \right]\] \[CI\,=\,500\left[ {{\left( 1+\frac{5}{100} \right)}^{2}}-1 \right]\] \[[\therefore \,T\,=\,2\,half\,year,\,R=\,5%\,half\,yearly]\] \[CI\,=\,500\left[ {{\left( \frac{21}{20} \right)}^{2}}-1 \right]\] \[CI\,=\,500\left[ \frac{441-400}{400} \right]\] \[CI\,=\,500\left[ \frac{41}{400} \right]\] CI =` 51.25
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