A 6.55 percent coupon bond with 19 years left to maturity is offered for sale at $\$ 1,125.25$. What yield to maturity is the bond offering? (Assume interest payments are semiannual.) (Round your answer to $\mathbf{2}$ decimal places.)

Step 1 ：A 6.55 percent coupon bond with 19 years left to maturity is offered for sale at $1,125.25. The bond pays interest semiannually, so it pays 6.55%/2 = 3.275% of its face value every six months. The bond will make 19*2 = 38 payments.

Step 2 ：The yield to maturity (YTM) of a bond is the internal rate of return (IRR) if the bond is held until maturity. It can be defined as the discount rate at which the sum of all future cash flows (both interest and principal) is equal to the current price of the bond.

Step 3 ：We can set up the equation for the present value of the bond's cash flows and solve for the discount rate, which is the YTM. The equation is: \(1,125.25 = \sum_{i=1}^{38} \frac{C}{(1+YTM/2)^i} + \frac{F}{(1+YTM/2)^{38}}\), where C is the semiannual coupon payment, F is the face value of the bond, and YTM is the yield to maturity. We know that C = 3.275%*F, and F is typically $1,000 for bonds.

Step 4 ：This equation cannot be solved analytically, so we will need to use a numerical method such as the bisection method or Newton's method.

Step 5 ：Using these methods, we find that the yield to maturity (YTM) is approximately 0.0548, or 5.48%. However, because the bond pays interest semiannually, the annual YTM is 2*YTM = 10.96%. This is the annual interest rate that the bond is effectively offering.

Step 6 ：Final Answer: The yield to maturity that the bond is offering is approximately \(\boxed{10.96\%}\).