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Bond Price Calculator
A bond’s price is the present value of all the cash it will pay: the regular coupons plus the face value at maturity, each discounted at the market yield. The coupons form an annuity, so the price is C × [1 − (1 + i)−n] ÷ i + F ÷ (1 + i)n, where C is the coupon per period, i the yield per period and n the number of periods left.
Formula
Where
- C
- coupon per period = F × annual coupon rate ÷ coupons per year
- F
- face (par) value repaid at maturity
- i
- yield per period = YTM ÷ coupons per year
- n
- number of coupon periods = years × coupons per year
Calculator
Result and step-by-step solution
The bond trades at a discount (coupon rate below the yield): 92.561% of face value.
- Per-period valuesC = 1,000.00 × 5% ÷ 2 = 25.00; i = 6% ÷ 2 = 0.03; n = 20
- Present value of the coupons25.00 × 1 − (1 + 0.03)−200.03 = 25.00 × 14.877475 = 371.94
- Present value of the face value1,000.00(1 + 0.03)20 = 553.68
- AddPrice = 371.94 + 553.68 = 925.61
How to use the formula
Most bonds pay coupons twice a year, so the calculator divides both the annual coupon rate and the yield by the number of payments per year and multiplies the years by it. It then shows the value of the coupon stream and of the face value separately and adds them. The result is the clean price on a coupon date; between coupon dates the price you pay also includes accrued interest.
A 10-year bond with a 1,000 face value and a 5% semi-annual coupon, priced to yield 6%, is worth 925.61: below par, because its coupon rate is below the market yield. When the coupon equals the yield the bond trades at par, and when it is higher it trades at a premium. That inverse link between price and yield is measured by duration. To go the other way, from price to yield, use the YTM calculator.
Frequently asked questions
- What is the bond price formula?
- Price = C × [1 − (1 + i)−n] ÷ i + F ÷ (1 + i)n, with C the coupon per period, i the yield per period, n the number of periods and F the face value.
- Why do bond prices fall when yields rise?
- The fixed cash flows are discounted at a higher rate, so their present value is lower.
- What is a discount or premium bond?
- A discount bond’s price is below face value (coupon rate below the yield); a premium bond’s price is above face value (coupon rate above the yield).
- Does this match Excel’s PRICE function?
- Yes on coupon dates. PRICE quotes per 100 of face value and handles settlement between coupon dates.
Last reviewed: September 26, 2026. Calculations run in your browser and were checked against numpy-financial, SciPy and published spreadsheet examples.