1. **State the problem:** Calculate the effective annual interest rate for a loan with a nominal interest rate of 6.00% compounded semi-annually. 2. **Formula:** The effective annual rate (EAR) is given by: $$EAR = \left(1 + \frac{r}{n}\right)^n - 1$$ where $r$ is the nominal annual interest rate (as a decimal), and $n$ is the number of compounding periods per year. 3. **Identify values:** Here, $r = 0.06$ and $n = 2$ (since interest is compounded semi-annually). 4. **Calculate EAR:** $$EAR = \left(1 + \frac{0.06}{2}\right)^2 - 1 = \left(1 + 0.03\right)^2 - 1 = 1.03^2 - 1$$ 5. **Evaluate:** $$1.03^2 = 1.0609$$ 6. **Subtract 1:** $$EAR = 1.0609 - 1 = 0.0609$$ 7. **Convert to percentage:** $$EAR = 0.0609 \times 100 = 6.09\%$$ **Final answer:** The effective annual interest rate is **6.09%**.