Question

Semi-annually.

Hint:

The effective annual rate (EAR) accounts for compounding and is given by \( r_{{eff}} = \left(1 + \frac{r}{n}\right)^n - 1 \). It is always greater than or equal to the nominal rate.

Answer 1

Step 1: For compounding semi-annually, the effective annual rate \( r_{{eff}} \) is calculated using the formula: \[ r_{{eff}} = \left(1 + \frac{r}{n}\right)^n - 1, \] where: - \( r \) is the nominal annual interest rate, - \( n \) is the number of compounding periods per year. 
Step 2: Substitute the given values \( r = 0.10 \) (10%) and \( n = 2 \): \[ r_{{eff}} = \left(1 + \frac{0.10}{2}\right)^2 - 1 = (1.05)^2 - 1. \] 
Step 3: Compute the value: \[ r_{{eff}} = 1.1025 - 1 = 0.1025 \quad {or} \quad 10.25\%. \]