A certain sum of money doubles in 4 years at a compound rate of interest per annum. The rate of interest is [Given; 21/2= 1.414, 21/4= 1.1892]

The correct option is ~18.9%.

Let us understand how to arrive at this result step-by-step.

Let the principal amount of money be $P$ and the annual compound interest rate be $r$ (expressed as a decimal fraction).
According to the formula for compound interest, the accumulated amount $A$ after $n$ years is given by:

$A=P{(1+r)}^n$

The problem states that the sum of money doubles in 4 years. This means when $n=4$, the amount $A$ becomes $2P$.
Substituting these values into our formula, we get:

$2P=P{(1+r)}^4$

Dividing both sides by $P$ gives:

$2={(1+r)}^4$

To solve for $r$, we take the fourth root of both sides of the equation:

$1+r=2^{1/4}$

Using the value given in the problem, $2^{1/4}=1.1892$, we can substitute this directly into our equation:

$1+r=1.1892$

Now, we solve for $r$ by subtracting 1 from both sides:

$r=1.1892-1$

$r=0.1892$

To convert the decimal rate of interest into a percentage, we multiply by 100:

$\text{Rate of Interest}=0.1892\times 100=18.92\%$

This is approximately equal to 18.9%, which matches the correct option.