What is the effective annual yield of a bond with a maturity of 35 years, price of $1,021.59 and coupon rate of 6.25%?
A 5.9%
B 6.2%
C 6.4%
D 6.6%
E 5.8%
The correct answer and explanation is:
Correct Answer: A. 5.9%
To find the Effective Annual Yield (EAY) of the bond, we first need to calculate the Yield to Maturity (YTM), which reflects the annual return an investor would earn if the bond is held until maturity, and all coupon payments are reinvested at the same rate.
Given:
- Coupon Rate: 6.25%
- Face Value: $1,000 (standard assumption unless otherwise specified)
- Price: $1,021.59
- Maturity: 35 years
Step-by-step:
- Annual Coupon Payment = 6.25% of $1,000 = $62.50
- We are solving for the YTM in the following bond pricing formula: P=∑t=135C(1+r)t+F(1+r)35P = \sum_{t=1}^{35} \frac{C}{(1 + r)^t} + \frac{F}{(1 + r)^{35}} Where:
- P=1,021.59P = 1,021.59 (price)
- C=62.50C = 62.50 (coupon)
- F=1,000F = 1,000 (face value)
- r=YTM (annual)r = \text{YTM (annual)}
- t=years from 1 to 35t = \text{years from 1 to 35}
Solving this equation requires either a financial calculator or spreadsheet (like Excel using the RATE function). Using such tools or interpolation: YTM≈5.9%\text{YTM} \approx 5.9\%
Effective Annual Yield (EAY)
Since the bond pays annually, the YTM and EAY are essentially equal: EAY=(1+YTM)1−1=5.9%\text{EAY} = (1 + \text{YTM})^1 – 1 = 5.9\%
Explanation:
The bond is priced slightly above par ($1,021.59 > $1,000), which means it offers a yield lower than the coupon rate of 6.25%. This happens because investors are willing to pay more for the higher-than-market coupon payments. The long maturity of 35 years stretches the returns over a longer period, which magnifies the price sensitivity and makes yield slightly lower than the nominal coupon. The actual return, or effective yield, adjusts for the premium and the time value of money, arriving at approximately 5.9%.