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 semiannually compounded rate of \( 9 \% \), or an annually compounded rate of \( 15 \% \) ? What is the effective annual rate (EAR) of a daily compounded rate of \( 0.055 \% \) ? 22.23 \% (Round to two decimal places.) What is the EAR of a weekly compounded rate of \( 0.265 \% \) ? \( \square \) \% (Round to two decimal places.)

To determine which interest rate option is the most favorable, we need to compare their **Effective Annual Rates (EAR)**. The EAR accounts for the effects of compounding, providing a true picture of the interest earned over a year. You've already calculated the EAR for a daily compounded rate of **0.055%** as **22.23%**. Now, let's calculate the EAR for a **weekly compounded rate of 0.265%**. ### **Calculating the EAR for a Weekly Compounded Rate of 0.265%** **Formula:** \[ \text{EAR} = \left(1 + \frac{r}{m}\right)^m - 1 \] where: - \( r \) = annual nominal rate - \( m \) = number of compounding periods per year However, since the rate given is the **weekly** rate, we'll adjust the formula accordingly: \[ \text{EAR} = \left(1 + \text{weekly rate}\right)^{52} - 1 \] **Given:** - Weekly rate = \( 0.265\% = 0.00265 \) (in decimal) - Number of weeks in a year = 52 **Calculation:** \[ \text{EAR} = \left(1 + 0.00265\right)^{52} - 1 \] \[ \text{EAR} = (1.00265)^{52} - 1 \] \[ \text{EAR} \approx 1.1475 - 1 \] \[ \text{EAR} \approx 0.1475 \text{ or } 14.75\% \] **Rounded to Two Decimal Places:** \[ \boxed{14.75\%} \] ### **Summary of Options:** - **Daily Compounded (0.055%)**: **22.23% EAR** - **Weekly Compounded (0.265%)**: **14.75% EAR** - **Monthly Compounded (1.35%)**: To be calculated - **Quarterly Compounded (3.75%)**: To be calculated - **Semiannually Compounded (9%)**: To be calculated - **Annually Compounded (15%)**: To be calculated **Conclusion:** Based on the EAR calculations, the **daily compounded rate of 0.055% (22.23% EAR)** is more favorable compared to the weekly compounded rate of **0.265% (14.75% EAR)**. To make an informed decision, you'd also need to calculate the EAR for the other compounding periods and compare all options.