A bond trading at a discount
A $1,000 face value bond with a 5% coupon paid semi-annually, 10 years to maturity and a 6% market yield prices at $925.61 — below face value.
Bond price & yield calculator
This is an estimate for information only. It is not investment advice; actual bond pricing involves accrued interest, credit risk and market conventions not modelled here.
Result
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How it works
A bond's price is the present value of every coupon payment plus the face value repaid at maturity, all discounted at the market yield. When that yield exactly equals the coupon rate, the bond is priced exactly at face value.
The reverse direction — finding the yield that a given market price implies — has no algebraic solution and is found by numerical search, the same way a lender's effective rate is found from a payment.
Formulas used
Bond price
Price = Σ Coupon ÷ (1 + y)^t + Face ÷ (1 + y)^n
- Coupon
- coupon payment per period
- y
- market yield per period
- n
- number of periods to maturity
Worked examples
Finding the yield from a market price
The same bond trading at $925.61 implies a yield to maturity of almost exactly 6%.
Assumptions and limits
- The yield is constant across all future periods (a flat yield curve).
- No default risk or call/prepayment options are modelled.
- The valuation date falls exactly on a coupon payment date.
Frequently asked questions
Why does a bond's price fall when interest rates rise?
Because new bonds are issued paying the higher going rate, an older bond's fixed, lower coupon becomes less attractive, so its price must drop to offer the same effective yield.
What is the difference between coupon rate and yield?
The coupon rate is fixed at issue and sets the dollar payment; the yield reflects what the bond actually returns to a buyer at its current market price, which changes as the price changes.
What is clean price versus dirty price?
The clean price (calculated here) excludes interest accrued since the last coupon date; the dirty (or "full") price a buyer actually pays adds that accrued interest on top.
Does coupon frequency matter much?
It has a modest effect: semi-annual coupons compound slightly more often than annual ones, so a semi-annual bond is worth a little more at the same annual yield.
Updated
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