Question
A certain sum of money yields Rs. 1261 as compound interest for three years at 5% per annum. The sum is ?
Answer: Option D
Let the principal be x Rs. Now,
$$\eqalign{
& C.I. = P\left[ {{{\left( {1 + \frac{R}{{100}}} \right)}^T} - 1} \right] \cr
& \Rightarrow 1261 = x\left[ {{{\left( {1 + \frac{5}{{100}}} \right)}^3} - 1} \right] \cr
& \Rightarrow 1261 = x\left( {\frac{{9261}}{{8000}} - 1} \right) \cr
& \Rightarrow 1261 = x\left( {\frac{{9261 - 8000}}{{8000}}} \right) \cr
& \Rightarrow 1261 = \frac{{1261x}}{{8000}} \cr
& \Rightarrow x = \frac{{1261 \times 8000}}{{1261}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,8000 \cr} $$
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Let the principal be x Rs. Now,
$$\eqalign{
& C.I. = P\left[ {{{\left( {1 + \frac{R}{{100}}} \right)}^T} - 1} \right] \cr
& \Rightarrow 1261 = x\left[ {{{\left( {1 + \frac{5}{{100}}} \right)}^3} - 1} \right] \cr
& \Rightarrow 1261 = x\left( {\frac{{9261}}{{8000}} - 1} \right) \cr
& \Rightarrow 1261 = x\left( {\frac{{9261 - 8000}}{{8000}}} \right) \cr
& \Rightarrow 1261 = \frac{{1261x}}{{8000}} \cr
& \Rightarrow x = \frac{{1261 \times 8000}}{{1261}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,8000 \cr} $$
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