1. The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 9% per annum is Rs 405. The sum is .
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By: anil on 05 May 2019 02.10 am
Let the given sum = Rs. $$100x$$ Rate of interest = 9% and time period = 2 years Compound interest = $$P [(1 + frac{R}{100})^T - 1]$$ = $$100x [(1 + frac{9}{100})^2 - 1]$$ = $$100x [(frac{109}{100})^2 - 1] = 100x (frac{11881 - 10000}{10000})$$ = $$frac{1881 x}{100}$$ Simple interest = $$frac{P imes R imes T}{100}$$ = $$frac{100x imes 9 imes 2}{100} = 18x$$ => Difference between simple and compound interests = $$frac{1881 x}{100} - 18x = 405$$ => $$frac{1881x - 1800x}{100} = 405$$ => $$81x = 405 imes 100$$ => $$x = frac{405 imes 100}{81} = 5 imes 100 = 500$$ $$ herefore$$ Value of given sum = $$100 imes 500 = Rs. 50,000$$
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