A certain sum is invested for 2 years in scheme A at 20% p.a. compound interest compounded annually. Same sum is also invested for the same period in scheme B at x%p.a. to a simple interest earned from scheme A is twice of that earned from scheme B. What is the value of x ?

Let sum invested in both schemes = $$Rs. P$$

Let interest earned in scheme A = $$Rs. 2x$$

In scheme A, time = 2 years and rate = 20% under compound interest.

=> $$C.I. = P [(1 + \frac{R}{100})^T - 1]$$

=> $$2x = P [(1 + \frac{20}{100})^2 - 1]$$

=> $$2x = P [(\frac{6}{5})^2 - 1]$$

=> $$2x = P (\frac{36}{25} - 1) = \frac{11 P}{25}$$

=> $$x = \frac{11 P}{50}$$ -----------(i)

Now, in scheme B,  interest earned = $$Rs. x$$

Time = 2 years and rate of interest = $$x \%$$ under simple interest

=> $$S.I. = \frac{P \times R \times T}{100}$$

=> $$x = \frac{P \times x \times 2}{100}$$

Using, equation(i), we get :

=> $$\frac{11 P}{50} = \frac{P \times x}{50}$$

=> $$x = 11 \%$$