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The difference between the Compound Interest and Simple Interest on a certain sum of money at 4% per annum for 2 years is Rs. 1.40. Find the sum.
- ARs. 875
- BRs. 857
- CRs. 785
- DRs. 925
Answer not set
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CCommunity
Rate = 4%
Time = 2 years
Difference between C.I and S.I = Rs. 1.40
$({\rm{C}}.{\rm{I}} - {\rm{S}}.{\rm{I}} = \left[ {{\rm{P}}{{\left( {1 + \frac{{\rm{R}}}{{100}}} \right)}^{\rm{n}}} - {\rm{P}}} \right] - \frac{{{\rm{P}} \times {\rm{R}} \times {\rm{T}}}}{{100}})$
$(\Rightarrow 1.40 = \left[ {{\rm{P}}{{\left( {1 + \frac{4}{{100}}} \right)}^2} - {\rm{P}}} \right] - \frac{{{\rm{P}} \times 4 \times 2}}{{100}})$
$(\Rightarrow 1.40 = \left[ {{\rm{P}}{{\left( {1 + \frac{1}{{25}}} \right)}^2} - {\rm{P}}} \right] - \frac{{2{\rm{P}}}}{{25}})$
$(\Rightarrow 1.40 = \frac{{676{\rm{P}}}}{{625}} - {\rm{P}} - \frac{{2{\rm{P}}}}{{25}})$
$(\Rightarrow 1.40 = \frac{{676{\rm{P}} - 625{\rm{P}} - 50{\rm{P}}}}{{625}})$
$(\Rightarrow 1.40 = \frac{{676{\rm{P}} - 675{\rm{P}}}}{{625}} = \frac{{\rm{P}}}{{625}})$
∴ P = 1.40 × 625 = Rs. 875
Time = 2 years
Difference between C.I and S.I = Rs. 1.40
$({\rm{C}}.{\rm{I}} - {\rm{S}}.{\rm{I}} = \left[ {{\rm{P}}{{\left( {1 + \frac{{\rm{R}}}{{100}}} \right)}^{\rm{n}}} - {\rm{P}}} \right] - \frac{{{\rm{P}} \times {\rm{R}} \times {\rm{T}}}}{{100}})$
$(\Rightarrow 1.40 = \left[ {{\rm{P}}{{\left( {1 + \frac{4}{{100}}} \right)}^2} - {\rm{P}}} \right] - \frac{{{\rm{P}} \times 4 \times 2}}{{100}})$
$(\Rightarrow 1.40 = \left[ {{\rm{P}}{{\left( {1 + \frac{1}{{25}}} \right)}^2} - {\rm{P}}} \right] - \frac{{2{\rm{P}}}}{{25}})$
$(\Rightarrow 1.40 = \frac{{676{\rm{P}}}}{{625}} - {\rm{P}} - \frac{{2{\rm{P}}}}{{25}})$
$(\Rightarrow 1.40 = \frac{{676{\rm{P}} - 625{\rm{P}} - 50{\rm{P}}}}{{625}})$
$(\Rightarrow 1.40 = \frac{{676{\rm{P}} - 675{\rm{P}}}}{{625}} = \frac{{\rm{P}}}{{625}})$
∴ P = 1.40 × 625 = Rs. 875