Find the effective interest rate. Round to two decimal places when needed. Rate: \( 10 \% \) Compounded: Semiannually The effective rate is \%

To calculate the effective interest rate, you can use the formula: \[ (1 + \frac{r}{n})^{nt} - 1 \] Where: - \( r \) is the nominal interest rate (0.10 for 10%) - \( n \) is the number of compounding periods per year (2 for semiannual) - \( t \) is the number of years (1 for effective rate calculation) Plugging in the numbers: \[ (1 + \frac{0.10}{2})^{2 \cdot 1} - 1 = (1 + 0.05)^2 - 1 = 1.1025 - 1 = 0.1025 \] To express this as a percentage, multiply by 100: \[ 0.1025 \times 100 = 10.25\% \] So, the effective interest rate is **10.25%**. For anyone investing or borrowing in a semiannual compounding situation, understanding the effective interest rate is crucial. It gives a clearer view of the real cost or return on an investment, since compounding does indeed make the dollars work harder for you (or against you)! If you ever find yourself confused about compounding periods, remember: the more frequently interest is compounded, the more significant the impact on your total earnings or costs. Just a little time and understanding can help you make smarter financial decisions!