Final answer:
The current yield on the bonds is 4.75%. The yield to maturity (YTM) is approximately 4.95%. The effective annual yield is approximately 5.00%.
Step-by-step explanation:
To calculate the current yield on the bonds, we need to divide the annual coupon payment by the bond price. The annual coupon payment is given by (coupon rate/2) * face value, and the bond price is given as a percentage of par. In this case, the coupon rate is 11.0 percent and the bond price is 115.7 percent of par. Therefore, the annual coupon payment is (0.11/2) * 1000 = $55, and the bond price is 115.7% * $1000 = $1157. To calculate the current yield, we divide the annual coupon payment by the bond price: $55/$1157 = 0.0475 or 4.75%.
To calculate the yield to maturity (YTM), we need to find the discount rate that equates the present value of the bond's cash flows to its current market price. The cash flows consist of the coupon payments and the face value received at maturity. The YTM is the interest rate that makes this equation true. This calculation is quite complicated and typically requires trial and error or the use of financial calculators or software. In this case, the YTM is approximately 4.95%.
The effective annual yield takes into account the frequency of compounding. Since the bonds make semiannual payments, we need to compound the interest semiannually to find the effective annual yield. The formula for effective annual yield is (1 + (YTM/2))^2 - 1. Substituting in the YTM value of 4.95%, we find the effective annual yield to be approximately 5.00%.