Time Value of Money

Concept:The effective annual rate accounts for compounding within a year, calculated from the nominal rate.Explanation:Let the nominal rate be $r = 8\% = 0.08$. Compounding semi-annually gives $n = 2$ periods per year. The effective rate formula is: $\text{Effective rate} = \left(1 + \frac{r}{n}\right)^n - 1$. Substitute: $\left(1 + \frac{0.08}{2}\right)^2 - 1 = (1 + 0.04)^2 - 1$. Calculate: $(1.04)^2 = 1.0816$, then subtract $1$ to get $0.0816$. Convert to percentage: $0.0816 \times 100\% = 8.16\%$.Answer:The effective rate is $8.16\%$, which corresponds to option C.