Price the coupons, then add discounted face
A fixed-rate coupon bond’s price immediately after a coupon payment is the present value of remaining coupons plus the present value of face. Coupons and yield are quoted annually and then divided by payments per year; US corporates and Treasuries usually pay twice a year. Present value discounts a lump or a level annuity without a redemption amount. Tax-equivalent yield compares tax treatment. This page applies one yield to every cash flow.
Periodic yield = yield to maturity ÷ payments per year
Periods = years × payments per year
Price = coupon annuity + face ÷ (1 + periodic yield)periods
At 0% yield, price = coupons × periods + face
Current yield = annual coupon ÷ price
Example
A $1,000 face bond with a 5% coupon, 10 years to maturity, and semiannual payments priced at a 6% yield is about $925.61, a $74.39 discount. Each coupon is $25. At a 5% yield the same bond is at par. A 6% coupon, 5 years, 5% yield is about $1,043.76, a premium.
What this price leaves out
Years and payments per year must be whole numbers. Accrued interest, settlement lag, call or put features, default risk, a term structure of spot rates, and day-count conventions stay outside this identity. The supported yield range is 0% to 100%; negative-yield bonds are outside it. Zero-coupon bonds use a 0% coupon rate.