Bond interests, bond yields, and the yield curve

A municipal bond issued by a government is an agreement that the government will pay back certain amount of long-term debt to investors on a specific (maturity) date.

Interests of bonds are reflected either explicitly by coupons when bonds are sold by their par values, or implicitly by the difference between par values and their discounted selling prices. Bond interests constitute the major cost of borrowing for a bond issue, but there are additional costs for the issuer (government) including the payments for professional services by bond counsels, financial advisers, or underwriters.

The yield of a municipal bond is the rate of return an investor will receive by holding the bond to maturity. It is determined based on the actual market value of a bond rather than its par value. For instance, the "current yield" of a bond calculates the percentage return that the annual coupon payment provides the investor based on the the price the investor pays for the bond (See the following equation from Investopedia).

Although a bond may carry a fixed coupon interest rate over its term, its actual bond yield fluctuates with that of all other bonds currently offered in the market and have similar credit quality and maturity.

The yield curve is the relation between the bond yield and the time to maturity of the bond. The yield on the Y axis is often, but not always, an increasing function of t on the X axis. (See the figure above from wiki.)