Question
The compound interest on Rs. 30000 at 7% per annum for a certain time is Rs. 4347. The times is = ?
Answer: Option C
$$\eqalign{
& {\text{Principal = Rs}}{\text{. 30000}} \cr
& {\text{CI = Rs 4347}} \cr
& {\text{Rate = 7}}\% \cr
& {\text{By using formula, }} \cr
& \Rightarrow \left( {30000 + 4347} \right) = 30000{\left( {1 + \frac{7}{{100}}} \right)^{\text{t}}} \cr
& \Rightarrow 34347 = 30000{\left( {1 + \frac{7}{{100}}} \right)^{\text{t}}} \cr
& \Rightarrow \frac{{34347}}{{30000}} = {\left( {\frac{{107}}{{100}}} \right)^{\text{t}}} \cr
& \Rightarrow \left( {\frac{{11449}}{{10000}}} \right) = {\left( {\frac{{107}}{{100}}} \right)^{\text{t}}} \cr
& \Rightarrow {\left( {\frac{{107}}{{100}}} \right)^2} = {\left( {\frac{{107}}{{100}}} \right)^{\text{t}}} \cr
& \Rightarrow {\text{t}} = 2\,{\text{years}} \cr} $$
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$$\eqalign{
& {\text{Principal = Rs}}{\text{. 30000}} \cr
& {\text{CI = Rs 4347}} \cr
& {\text{Rate = 7}}\% \cr
& {\text{By using formula, }} \cr
& \Rightarrow \left( {30000 + 4347} \right) = 30000{\left( {1 + \frac{7}{{100}}} \right)^{\text{t}}} \cr
& \Rightarrow 34347 = 30000{\left( {1 + \frac{7}{{100}}} \right)^{\text{t}}} \cr
& \Rightarrow \frac{{34347}}{{30000}} = {\left( {\frac{{107}}{{100}}} \right)^{\text{t}}} \cr
& \Rightarrow \left( {\frac{{11449}}{{10000}}} \right) = {\left( {\frac{{107}}{{100}}} \right)^{\text{t}}} \cr
& \Rightarrow {\left( {\frac{{107}}{{100}}} \right)^2} = {\left( {\frac{{107}}{{100}}} \right)^{\text{t}}} \cr
& \Rightarrow {\text{t}} = 2\,{\text{years}} \cr} $$
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