The compound interest on Rs. 30000 at 10 percent per annum for 2 years 73 days, is
Solution
Correct Answer: Option C
Time period = 2 years 73 days = 2 73/365 years = 2 1/5 years
When the interest is compounded annually, but the time is in fraction, then
\(\begin{array}{l} {\rm{A}} = {\rm{P}}{\left( {1 + {\rm{\;}}\frac{{\rm{R}}}{{100}}} \right)^2} \times \left( {1 + {\rm{\;R}} \times \frac{{\frac{1}{5}}}{{100}}} \right)\\ \Rightarrow {\rm{A}} = 30000{\left( {1 + {\rm{\;}}\frac{{10}}{{100}}} \right)^2} \times \left( {1 + 10 \times \frac{{\frac{1}{5}}}{{100}}} \right)\\ \Rightarrow {\rm{A}} = 30000{\left( {\frac{{11}}{{10}}} \right)^2} \times \left( {1 + {\rm{\;}}\frac{2}{{100}}} \right)\\ \Rightarrow {\rm{A}} = 30000{\left( {\frac{{11}}{{10}}} \right)^2} \times \left( {\frac{{102}}{{100}}} \right)\\ \Rightarrow {\rm{A}} = 30000{\rm{\;}} \times {\rm{\;}}\frac{{121}}{{100}}{\rm{\;}} \times {\rm{\;}}\left( {\frac{{102}}{{100}}} \right) \end{array}\)
⇒ A = 37026
∴ C.I. = A – P = Rs. (37026 – 30000) = Rs. 7026
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