1. The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 12% per annum is Rs 900. What is the value of given sum (in Rs)?
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By: anil on 05 May 2019 02.18 am
Let the given sum = Rs. $$100x$$ Rate of interest = 12% and time period = 2 years Compound interest = $$P [(1 + frac{R}{100})^T - 1]$$ = $$100x [(1 + frac{12}{100})^2 - 1]$$ = $$100x [(frac{28}{25})^2 - 1] = 100x (frac{784 - 625}{625})$$ = $$100x imes frac{159}{625} = frac{636 x}{25}$$ Simple interest = $$frac{P imes R imes T}{100}$$ = $$frac{100x imes 12 imes 2}{100} = 24x$$ => Difference between simple and compound interests = $$frac{636 x}{25} - 24x = 900$$ => $$frac{636x - 600x}{25} = 900$$ => $$36x = 900 imes 25$$ => $$x = frac{900 imes 25}{36} = 25 imes 25 = 625$$ $$ herefore$$ Value of given sum = $$100 imes 625 = Rs. 62,500$$
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