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