1. The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 18% per annum is Rs 81. 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 = 18% and time period = 2 years Compound interest = $$P [(1 + frac{R}{100})^T - 1]$$ = $$100x [(1 + frac{18}{100})^2 - 1]$$ = $$100x [(frac{118}{100})^2 - 1] = 100x (frac{13924 - 10000}{10000})$$ = $$frac{3924 x}{100}$$ Simple interest = $$frac{P imes R imes T}{100}$$ = $$frac{100x imes 18 imes 2}{100} = 36x$$ => Difference between simple and compound interests = $$frac{3924 x}{100} - 36x = 81$$ => $$frac{3924x - 3600x}{100} = 81$$ => $$324x = 81 imes 100$$ => $$x = frac{81 imes 100}{324} = frac{100}{4} = 25$$ $$ herefore$$ Value of given sum = $$100 imes 25 = Rs. 2500$$
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