The effective rate that is equivalent to a nominal rate of 10 % compounded semi-annually is :

10.25%

The correct answer is Option (2) → 10.25%

The effective rate of interest $(r_e)$ that is equivalent to a Nominal rate $(r_n)$ is,

$r_e=\left(1+\frac{r_n}{m}\right)^m-1$

$⇒r_e=\left(1+\frac{0.10}{2}\right)^2-1$

$=(1.05)^2-1$

$=0.1025$

$=10.25\%$