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If the compound interest on a certain sum for 2 years in Rs. 105 and the simple interest Rs. 100; then the rate of interest per annum is
- A10%
- B5%
- C8%
- D2%
Answer not set
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CCommunity
Let the principal be ‘P’ and the rate of interest be ‘R%’ per annum.
? Simple Interest for 2 years = Rs.100
? (P × R × T)/100 = 100
?(P × R × 2)/100=100
? PR = 10000/2
? PR = 5000……(i)
? Compound Interest for 2 years = Rs.105
$(\begin{array}{l} \Rightarrow P{(1 + \frac{R}{{100}})^T} - P = 105\\ \Rightarrow P{(1 + \frac{R}{{100}})^2} - P = 105\\ \Rightarrow P\left[ {1 + \left( {{{\left( {\frac{R}{{100}}} \right)}^2} + \frac{R}{{50}}} \right]} \right) - P = 105\\ \Rightarrow \left[ {\frac{{P{R^2}}}{{10000}} + \frac{{PR}}{{50}}} \right] = 105 \end{array})$
From equation (i)
$(\Rightarrow \left[ {\frac{{5000R}}{{10000}} + \frac{{5000}}{{50}}} \right] = 105)$
? R = 10%
? Simple Interest for 2 years = Rs.100
? (P × R × T)/100 = 100
?(P × R × 2)/100=100
? PR = 10000/2
? PR = 5000……(i)
? Compound Interest for 2 years = Rs.105
$(\begin{array}{l} \Rightarrow P{(1 + \frac{R}{{100}})^T} - P = 105\\ \Rightarrow P{(1 + \frac{R}{{100}})^2} - P = 105\\ \Rightarrow P\left[ {1 + \left( {{{\left( {\frac{R}{{100}}} \right)}^2} + \frac{R}{{50}}} \right]} \right) - P = 105\\ \Rightarrow \left[ {\frac{{P{R^2}}}{{10000}} + \frac{{PR}}{{50}}} \right] = 105 \end{array})$
From equation (i)
$(\Rightarrow \left[ {\frac{{5000R}}{{10000}} + \frac{{5000}}{{50}}} \right] = 105)$
? R = 10%