How this instrument works
A bond's price is the present value of two separate promises rolled into one security: the coupon payments due every year until maturity, and the single lump-sum repayment of face value on the maturity date itself. Both promises are discounted at the same rate — the yield to maturity, y — because a buyer pricing the bond today demands one consistent required return across every dollar it will ever pay out, whether that dollar arrives next year or in year ten.
Because both legs share the same discount rate, price and yield always move in opposite directions: raise y and every discount factor shrinks, pulling both the coupon leg and the principal leg down together. A wealth manager pricing a client's secondary-market corporate bond, or a retail investor comparing a newly issued Treasury note against one already trading, uses exactly this arithmetic to check whether an asking price is consistent with the yield the market is currently demanding for bonds of similar maturity and risk.
The model prices a bond exactly at a coupon date, assumes coupons arrive once a year, and takes yield to maturity as a single given number rather than deriving it from a market price. Real bonds quoted between coupon dates carry accrued interest on top of this clean price, many pay semiannually rather than annually, and the yield itself reflects the issuer's credit risk, call provisions, and liquidity — none of which this formula prices in on its own.
- Enter the dollar coupon the bond pays each year into Annual coupon payment, $ — for a 5% coupon on $1,000 face value, that is $50.
- Set Face value, $ to the amount the issuer repays at maturity, almost always $1,000 for a standard bond.
- Enter the market's current required return in Yield to maturity, % — the rate buyers demand today, not the coupon rate printed on the bond.
- Set Years to maturity to how many annual coupon periods remain before the bond matures.
- Read Fair price today: above face value means the bond trades at a premium, below means a discount, and equal means it prices at par.
Worked example — a 10-year, $50 coupon bond at 6% yield
Set Annual coupon payment, $ to 50, Face value, $ to 1,000, Yield to maturity, % to 6, and Years to maturity to 10 — a bond paying $50 a year with $1,000 due in ten years, priced at a 6% required return. Fair price today reads $926.40, below the $1,000 face value, because the market wants a 6% return but the bond itself only pays a 5% coupon rate ($50 divided by $1,000).
Hold the coupon and term fixed and drop Yield to maturity, % to exactly 5% — matching the coupon rate — and the price rises to exactly $1,000.00, par value, the defining case where a bond's price and face value coincide. Strip Annual coupon payment, $ to 0 instead at the original 6% yield and the price falls to $558.39: with no coupon leg left at all, the entire price is just the discounted face value ten years out.
Questions
Why does bond price fall when yield to maturity rises?
Both legs of the price share the same discount rate, so a higher y shrinks every discount factor (1+y)⁻ⁿ at once — the coupon leg and the principal leg both lose value together. This inverse relationship is the source of what bond investors call interest rate risk: a bond bought at one yield is worth less the moment the market's required yield rises, before a single coupon has changed.
What is the difference between coupon rate and yield to maturity?
Coupon rate is fixed at issuance and sets the dollar coupon — a $50 coupon on $1,000 face value is a 5% coupon rate for the life of the bond. Yield to maturity is the market's current required return, and it moves daily with the bond's trading price. The two are equal only when the bond happens to price at exactly par; the worked example above prices at a 6% yield against a 5% coupon rate, which is why it trades below face value.
Why would a bond trade above or below its face value?
Below face value — a discount — when yield to maturity exceeds the coupon rate, because the market demands more return than the fixed coupon supplies, so price must fall to make up the difference. Above face value — a premium — when yield to maturity sits below the coupon rate. Exactly at face value, or par, only when the two rates match.
Does this price include interest accrued since the last coupon?
No. This is a clean price, calculated as though pricing happens exactly on a coupon date. A bond bought between coupon dates also owes the seller accrued interest for the days since the last payment, added on top as a separate dirty price; brokerage confirmations usually show both figures separately, and only the clean price is what this formula computes.
Why does this model assume one coupon a year when many bonds pay twice?
For clarity in the formula — many real bonds, especially U.S. Treasury and corporate issues, pay semiannually. To approximate a semiannual bond, halve Annual coupon payment, $, halve Yield to maturity, %, and double Years to maturity before entering them, since each of those inputs then represents one coupon period rather than one calendar year.
Why does price move toward face value as maturity approaches?
Every discount factor in the formula is raised to the power n, the number of years remaining, and any number raised to the power zero equals one. As Years to maturity falls toward zero the discount factors for both legs approach 1, so price is pulled toward face value regardless of the yield — a pattern bond traders call pulling to par.
References
- SEC Investor.gov — Bonds or fixed income products
- Federal Reserve — Selected interest rates, H.15 release
Read this first: This instrument shows arithmetic, not advice. Real offers add fees, taxes and terms that vary by lender and place — verify the figures against your actual paperwork before deciding anything.