1. The difference between the compound interest compounding half yearly for 1 year and the simple interest for 1 year on a certain sum of money lent out at 8% per annum is Rs 64. What is the sum (in Rs)?
Write Comment
Comments
By: anil on 05 May 2019 01.48 am
Let the given sum = Rs. $$100x$$ Rate of interest = 8% and time period = 1 year Compound interest compounded half yearly = $$P [(1 + frac{R}{200})^{2T} - 1]$$ = $$100x [(1 + frac{8}{200})^2 - 1]$$ = $$100x [(frac{26}{25})^2 - 1] = 100x (frac{676 - 625}{625})$$ = $$100x imes frac{51}{625} = frac{204 x}{25}$$ Simple interest = $$frac{P imes R imes T}{100}$$ = $$frac{100x imes 8 imes 1}{100} = 8x$$ => Difference between simple and compound interests = $$frac{204 x}{25} - 8x = 64$$ => $$frac{204x - 200x}{25} = 64$$ => $$4x = 64 imes 25$$ => $$x = frac{64 imes 25}{4} = 16 imes 25 = 400$$ $$ herefore$$ Value of given sum = $$100 imes 400 = Rs. 40,000$$ => Ans - (A)
Terms And Service:We do not guarantee the accuracy of available data ..We Provide Information On Public Data.. Please consult an expert before using this data for commercial or personal use