The effective rate equivalent to a nominal rate of 8% per annum compounded semi-annually is :

8.16%

The correct answer is Option (4) → 8.16%

To calculate the effective annual rate (EAR)

$EAR=\left(1+\frac{r}{n}\right)^n-1$

r = nominal annual interest rate = 8% = 0.08

n = number of compounding period = 2 (Semi-annual)

$EAR=\left(1+\frac{0.08}{2}\right)^2-1$

$=1.0816-1=0.0816$

$=8.16\%$