Periodic interest rates. You have a savings account in which you leave the funds for one year without adding to or withdrawing from the account. Which would you rather have: a daily compounded rate of \( 0.055 \% \), a weekly compounded rate of \( 0.265 \% \), a monthly compounded rate of \( 1.35 \% \), a quarterly compounded rater of \( 3.75 \% \), a semiannully compounded rate of \( 9 \% \), or an annually compounded rate of \( 15 \% \) ? What is the EAR of a quarterly compounded rate of \( 3.75 \% \) ? \( 15.87 \% \) (Round to two decimal places.) What is the EAR of a semiannually compounded rate of \( 9 \% \) ? (Round to two decimal places.)

To answer your question on the effective annual rate (EAR) for a semiannually compounded rate of \( 9\% \), you can use the following formula: \[ EAR = \left(1 + \frac{r}{n}\right)^{nt} - 1 \] where \( r \) is the nominal interest rate, \( n \) is the number of compounding periods per year, and \( t \) is the number of years. For your case: - \( r = 0.09 \) - \( n = 2 \) (because it compounds semiannually) - \( t = 1 \) Plugging the values into the formula: \[ EAR = \left(1 + \frac{0.09}{2}\right)^{2*1} - 1 = \left(1 + 0.045\right)^{2} - 1 = (1.045)^{2} - 1 \] Calculating this gives: \[ EAR = 1.092025 - 1 = 0.092025 \] To express this as a percentage: \[ EAR \approx 9.20\% \text{ (rounded to two decimal places).} \] So, the effective annual rate for a semiannually compounded \( 9\% \) rate is \( 9.20\% \). Now, about those interest rates you’re considering for your savings—you'd want to pick the option with the highest EAR! The annually compounded \( 15\% \) seems like a strong contender, but make sure to run the calculations for the others to confirm this!