1. If compound interest received on a certain amount in the 2nd year is Rs 1200, what will be the compound interest (in Rs) for the 4th year on the same amount at 10% rate of interest?
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By: anil on 05 May 2019 01.46 am
Let the sum = P = Rs. $$100x$$ Rate of interest = 10% Compound interest in the 2nd year = (Amount received at the end of 2 years) - (Amount received after 1st year) => $$P(1+frac{r}{100})^2-P(1+frac{r}{100})^1=1200$$ => $$[100x(1+frac{10}{100})^2]-[100x(1+frac{10}{100})]=1200$$ => $$[100x(frac{11}{10})^2]-[100x(frac{11}{10})]=1200$$ => $$121x-110x=1200$$ => $$x=frac{1200}{11}$$ $$ herefore$$ Compound interest for the 4th year = $$P(1+frac{r}{100})^4-P(1+frac{r}{100})^3$$ = $$[100x(1+frac{10}{100})^4]-[100x(1+frac{10}{100})^3]$$ = $$[100x(frac{11}{10})^4]-[100x(frac{11}{10})^3]$$ = $$(100x imes frac{11^3}{10^3})(frac{11}{10}-1)$$ = $$(100x imes frac{11^3}{10^3})(frac{1}{10})$$ = $$[(100 imes frac{1200}{11})(frac{11^3}{10000})]$$ = $$12 imes121=Rs.$$ $$1452$$ => Ans - (A)
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