A bond with a coupon rate of 5.63 percent and semiannual coupon payments matures in 23 years. The YTM is 6.71 percent. What is the effective annual yield? a. \( 5.63 \% \) b. \( 6.71 \% \) c. \( 5.71 \% \) d. \( 6.82 \% \) e. \( 7.10 \% \)

To find the effective annual yield (EAY), we can use the formula: \[ EAY = \left(1 + \frac{YTM}{m}\right)^m - 1 \] Where \( m \) is the number of compounding periods per year. Since the bond has semiannual coupon payments, \( m = 2 \). Plugging in the YTM of 6.71 percent (or 0.0671 when expressed as a decimal), we get: \[ EAY = \left(1 + \frac{0.0671}{2}\right)^2 - 1 \] Calculating this gives: \[ EAY = \left(1 + 0.03355\right)^2 - 1 = (1.03355)^2 - 1 \approx 0.0677 \text{ or } 6.77\% \] Therefore, the closest option to the calculated effective annual yield is **d. 6.82%**. In case you're interested, you might find it fun to explore how bond yields can fluctuate with market conditions! Factors like interest rate changes and economic indicators can significantly affect the attractiveness of a bond. What’s more, understanding the correlation between bond prices and yields can be quite enlightening, especially how they move in opposite directions! For a deeper dive, look into the various types of bonds available, like municipal bonds, corporate bonds, and treasury bonds! Each comes with unique characteristics, tax advantages, and levels of risk. You might even discover a whole world of bond strategies and how they're utilized in investment portfolios to balance risk and reward!