Bond Price Calculator
Find what a bond is worth today by discounting its coupons and face value at the market yield. See whether it trades at a premium or a discount, how sensitive the price is to rate changes, and the full cash flow schedule.
Use 0 for a zero-coupon bond.
Annual yield, quoted on the same basis as the coupon frequency.
Optional: total cost of several bonds.
How to use the Bond Price Calculator
- Enter the face value (par value repaid at maturity), for example 1,000.
- Enter the annual coupon rate and choose how often coupons are paid. Use 0% for a zero-coupon bond.
- Enter the market yield (yield to maturity) that comparable bonds offer, and the years left to maturity.
- Read the price: the result shows the price, the premium or discount, and the price per 100 of face value.
- Check the risk with duration, the price at other yields and the price-yield chart, then download the cash flow table.
Bond price formula
A bond is a stream of fixed coupons plus the face value at the end, so its price is the present value of those payments at the market yield:
Price = C × [1 − (1 + r)−n] ÷ r + F ÷ (1 + r)n
- C = coupon per period = face value × annual coupon rate ÷ payments per year
- r = market yield per period = annual yield ÷ payments per year
- n = number of periods left = years × payments per year
- F = face (par) value repaid at maturity
Example: $1,000 face, 5% coupon paid semi-annually, 6% market yield, 10 years. C = $25, r = 3%, n = 20. PV of coupons = 25 × (1 − 1.03−20) ÷ 0.03 = $371.94; PV of face = 1,000 ÷ 1.0320 = $553.68. Price = $925.61, a discount of $74.39 because the 5% coupon is below the 6% the market demands.
Coupon rate vs yield: premium, par or discount
| 10-year bond, 5% semi-annual coupon | Market yield | Price | Trades at |
|---|---|---|---|
| Yield below coupon | 3% | $1,171.69 | Premium |
| Yield below coupon | 4% | $1,081.76 | Premium |
| Yield equals coupon | 5% | $1,000.00 | Par |
| Yield above coupon | 6% | $925.61 | Discount |
| Yield above coupon | 7% | $857.88 | Discount |
Notice the price rises more when yields fall 1 point ($81.76) than it drops when they rise 1 point ($74.39). That curvature is convexity. As a bond approaches maturity, a premium or discount shrinks toward zero and the price is "pulled to par".
Frequently asked questions
How do you calculate the price of a bond?
Discount every remaining payment at the market yield and add them up: Price = C × (1 − (1 + r)^−n) ÷ r + F ÷ (1 + r)^n, where C is the coupon per period, r the yield per period, n the number of periods and F the face value. A $1,000 bond with a 5% semi-annual coupon, 6% yield and 10 years left is worth about $925.61.
Why does a bond sell at a premium or a discount?
If the bond's coupon rate is higher than the market yield, investors pay more than face value (a premium) because the coupons are above market rates. If the coupon is lower than the yield, the price drops below face value (a discount) so the buyer's total return still matches the market. When coupon rate equals yield, the price equals par.
Why do bond prices fall when interest rates rise?
A bond's coupons are fixed. When new bonds pay higher rates, older bonds are only attractive at a lower price, so their price falls until their yield matches the market. The longer the maturity and the lower the coupon, the bigger the price change, which is what duration measures.
What are duration and convexity?
Macaulay duration is the weighted average time, in years, until you receive the bond's cash flows. Modified duration (Macaulay ÷ (1 + periodic yield)) estimates the percent price change for a 1 percentage point change in yield. Convexity measures the curvature of the price-yield relationship and improves that estimate for larger moves.
How do I price a zero-coupon bond?
Set the coupon rate to 0%. The price is then just F ÷ (1 + r)^n. For example, a $1,000 zero-coupon bond with 5 years left at a 4% annual yield is worth 1,000 ÷ 1.04^5 = $821.93.
What is the difference between clean and dirty price?
The clean price excludes interest that has built up since the last coupon; the dirty (full) price includes it. This calculator assumes you are on a coupon date, so there is no accrued interest and clean equals dirty. Between coupon dates, add accrued interest = coupon × days since last coupon ÷ days in the period.
What does a price of 98.5 mean?
Bond prices are usually quoted per 100 of face value. A quote of 98.5 means 98.5% of par, so a $1,000 bond costs $985 and a $10,000 bond costs $9,850. The calculator shows this quote alongside the money price.