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If the compound interest earned on a certain sum for 2 years is twice the amount of simple interest for 2 years, then the rate of interest per annum is _______ percent
Let, the principal be $$P$$, rate be $$r\%$$
So, C.I. earned in 2 years = $$P\left(1+\dfrac{r}{100}\right)^2-P$$
Also, S.I. earned in 2 years = $$\dfrac{P\times\ r\times\ 2}{100}$$
So, $$P\left(1+\dfrac{r}{100}\right)^2-P$$ = $$2\times\ $$ $$\dfrac{P\times\ r\times\ 2}{100}$$
or, $$\left(1+\dfrac{r}{100}\right)^2-1$$ = $$2\times\ $$ $$\dfrac{\ r\times\ 2}{100}$$
let, $$\dfrac{r}{100}=x$$
so, $$\left(1+x\right)^2-1=4x$$
or, $$1+2x+x^2-1=4x$$
or, $$x^2=2x$$
so, $$x=2$$
or, $$\dfrac{r}{100}=2$$
so, rate is $$200\%$$ per annum
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