1. The simple and compound interest that can be earned in two years at the same rate is Rs 1,000 and Rs 1,040 respectively. What is the rate (percent per annum) of interest?
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By: anil on 05 May 2019 01.44 am
Let the sum = Rs. $$100x$$ and rate of interest = $$r\%$$ Time period = 2 years Simple interest = $$frac{P imes r imes t}{100}$$ => $$frac{100x imes r imes2}{100}=1000$$ => $$2rx=1000$$ => $$x=frac{1000}{2r}=frac{500}{r}$$ Compound interest = $$P[(1+frac{r}{100})^t-1]$$ => $$100x[(1+frac{r}{100})^2-1]=1040$$ => $$frac{100 imes500}{r}[1+frac{r^2}{10000}+frac{2r}{100}-1]=1040$$ => $$frac{50000}{r} imes (frac{r^2}{10000}+frac{2r}{100})=1040$$ => $$5r+1000=1040$$ => $$5r=1040-1000=40$$ => $$r=frac{40}{5}=8\%$$ => Ans - (C)
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