Define Simple Interest variables

Let the principal be $P$. If the money doubles, the final amount $A = 2P$. The interest earned $SI$ is $A - P = 2P - P = P$.

$SI = P$

Apply the rate formula

The formula for simple interest is $SI = \frac{P \times R \times T}{100}$. Substituting $SI = P$ and $T = 8$ years, we get $P = \frac{P \times R \times 8}{100}$.

$P = \frac{P \times R \times 8}{100}$

Solve for R

Cancel $P$ from both sides and solve for $R$: $1 = \frac{R \times 8}{100} \implies R = \frac{100}{8} = 12.5\%$.

$R = 12.5\%$