A bond's coupon rate is the actual amount of interest income earned on the bond each year based on its face value. A bond's yield to maturity (YTM) is the estimated rate of return based on the assumption that it will be held until its maturity date and not called.
Yield to maturity includes the coupon rate within its calculation, and in general, investors are more likely to make investing decisions based on an instrument's yield to maturity than on its coupon rate.
Calculating Coupon Rate
Suppose you purchase an IBM Corp. bond with a $1,000 face value, and it is issued with semiannual payments of $10. To calculate the bond's coupon rate, divide the total annual interest payments by the face value. In this case, the total annual interest payment equals $10 x 2 = $20. The annual coupon rate for IBM bond is therefore equal to $20 ÷ $1000 = 2%.
These coupons are fixed; no matter what price the bond trades for, the interest payments always equal $20 per year. So if interest rates went up, driving down the price of IBM's bond to $980, the 2% coupon on the bond will remain unchanged.
A Bond's Yield
The coupon rate is often different from the yield. A bond's yield is more accurately thought of as the effective rate of return based on the actual market value of the bond. At face value, the coupon rate and yield equal each other.
If you sell your IBM Corp. bond at a $100 premium, the bond's yield is now equal to $20 / $1,100 = 1.82%. Assuming interest rates increased and the price of your bond fell to $980, your yield from selling the bond at a discount will be $20 / $980 = 2.04%. In this way, yield and price are inversely related.
Yield to Maturity Calculation
Because coupon payments are not the only source of bond profits, the yield to maturity calculation incorporates the potential gains or losses generated by variations in market price. If an investor purchases a bond at its par value, the yield to maturity is equal to the coupon rate. If the investor purchases the bond at a discount, its yield to maturity is always higher than its coupon rate.
Conversely, a bond purchased at a premium always has a yield to maturity that is lower than its coupon rate.
Yield to maturity approximates the average return of the bond over its remaining term. A single discount rate is applied to all future interest payments to create a present value roughly equivalent to the price of the bond. The entire calculation takes into account the coupon rate, the current price of the bond, the difference between price and face value, and time until maturity.
Along with the spot rate, yield to maturity is one of the most important figures in bond valuation.

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Short Coupon
A short coupon is a payment made on a bond within a shorter time ... 
Bond Yield
Bond yield is the amount of return an investor will realize on ... 
Discount Bond
A discount bond is a bond that is issued for less than its par ... 
Premium Bond
A premium bond is a bond that is trading above its par value. ... 
Gross Yield
The gross yield is the yield on an investment before the deduction ... 
Realized Yield
Realized yield is the actual amount of return earned on a security ...