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

10.25%

The correct answer is Option (3) → 10.25%

$\text{Nominal rate} = 10\%,\;\; \text{compounded semi-annually}$

$\text{Rate per half-year} = \frac{10}{2} = 5\%$

$\text{Effective rate} = (1 + 0.05)^2 - 1$

$= 1.1025 - 1 = 0.1025$

$= 10.25\%$

The effective rate is $10.25\%$.